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The track circuits are very important equipments used in the railway transportation system. Today these are used to send vital information, to the running train, in the same time with the integrity checking of the rail. The actual track circuits have a small problem due to the use of the same transmission medium by the signals containing vital information and the return traction current, the running track rails. But this small problem can produce big disturbances in the train circulation, especially in the rush hours. To improve the data transmission to the train on-board equipment, the implementation of new track circuits using new communication technology were studied. This technology is used by the mobile and satellite communications and applies the principle of diversity encoding both time and space through the use of multiple transmission points of the track circuit signal for telegram which is sent to the train. Since this implementation does not satisfy the intended purpose, other modern communication principles such as 8PSK signals modulation and encoding using Trellis Coded Modulation were developed. This new track circuit aims to solve the problems which appeared in the current operation of track circuits and theoretically manages to transmit vital information to the train on board equipment without being affected by disturbances in electric traction transport systems.

International audience; We present a method for joint decode-and-forward physical layer network coding in two-way relay networks. The two source nodes send their packets simultaneously over time-varying channels to a relay node, then the relay broadcasts the received superimposed packets to the source nodes using network coding. The nodes use trellis coding for the sake of error correction and multi-antenna equipments to combat multipath fading. A challenging multiple access problem occurs at the relay node, which performs joint channel estimation and decoding for the individual source packets. We design message passing algorithms based on factor-graphs to solve this problem. The relay has two separate modules that perform channel estimation and decoding for the packets received from each source node. The interference generated by the other source node is taken into account by exchanging messages between the two modules.

Spatial modulation (SM), in which multiple antennas are used to convey information besides the conventional M-ary signal constellations, is a new multiple-input multiple-output (MIMO) transmission technique, which has recently been proposed as an alternative to V-BLAST (vertical Bell Labs layered space-time). In this paper, a novel MIMO transmission scheme, called spatial modulation with trellis coding (SM-TC), is proposed. Similar to the conventional trellis coded modulation (TCM), in this scheme, a trellis encoder and an SM mapper are jointly designed to take advantage of the benefits of both. A soft decision Viterbi decoder, which is fed with the soft information supplied by the optimal SM decoder, is used at the receiver. A pairwise error probability (PEP) upper bound is derived for the SM-TC scheme in uncorrelated quasi-static Rayleigh fading channels. From the PEP upper bound, code design criteria are given and then used to obtain new 4-, 8- and 16-state SM-TC schemes using quadrature phase-shift keying (QPSK) and 8-ary phase-shift keying (8-PSK) modulations for 2,3 and 4 bits/s/Hz spectral efficiencies. It is shown via computer simulations and also supported by a theoretical error performance analysis that the proposed SM-TC schemes achieve significantly better error performance than the classical space-time trellis codes and coded V-BLAST systems at the same spectral efficiency, yet with reduced decoding complexity.

Bu tez çalışmasında yeni birleşik iletişim sistemleri önerilmektedir. Önerilen sistemler konvolusyonel çarpım kodları, uzay zaman kodları ve kafes kodlamalı modülasyon içermektedirler. İlk önerilen birleşik sistemin oluşturulmasında konvolusyonel çarpım kodları ile uzay zaman kodları kullanılmıştır. İkinci önerilen sistem ise konvolusyonel çarpım kodları ile kafes kodlamalı modülasyon kullanılarak meydana getirilmiştir. Önerilen sistemler yinelemeli çözüm algoritmaları kullanılarak çözülebilmektedir. Konvolusyonel çarpım kodlarının yapılarından ötürü önerilen sistemler paralel olarak çalışan işlemciler tarafından çözümlenebilmektedir. Bu da çözümleme esnasında meydana gelen gecikme miktarının klasik birleşik sistemlere göre çok daha az olmasına sebep olmaktadır. Ayrıca çoklu anten kullanımı da spektral verimliliğin üst düzeyde olmasını sağlamaktadır. In this thesis we propose new concatenated joint communication structures involving convolutional product codes, space time codes and trellis coded modulation. The first structure consists of convolutional product codes and space time codes. The second one includes convolutional product codes and trellis coded modulation. The proposed structures are all parallel decodable due to the structure of convolutional product codes and have low decoding latencies, which are the main advantages of these proposed structures considering their classical counterparts constructed using serially concatenated convolutional codes, space time codes and trellis coded modulation. The use of multi-antennas at the proposed structures increases the spectral efficiency. 68

Kablosuz iletişim sistemlerinde denkleştirici tasarımı çoklu yol iletişiminin sebep olduğu etkileri yok etmek için gerekli olan önemli bir konsepttir. Turbo denkleştirici bir kaç on yıl önce tasarlanan en etkili denkleştiricilerden birisidir. Denkleştiricilerin etkili performans sergileyebilmeleri için kanal katsayılarının düzgün olarak tahmin edilmesi zaruridir. Kanal katsayıları genel olarak iki yöntemle hesaplanırlar, bunlar, bilgisiz olarak kanal katsayılarını tahmin etme ve bilgili olarak kanal katsayılarını hesaplama yöntemleridir. Bilgisiz olarak kanal katsayılarını hesaplamak için kazanan patika yöntemi ile en az ortalama kare yöntemleri birlikte kullanılmıştır. Bilgili olarak kanal katsayılarını hesaplamak için eğitim dizileri kullanılmıştır. Bilgisiz olarak kanal katsayılarını hesaplamak için iyileştirilmiş bilgisiz kanal hesaplama yöntemi önerilmiştir ve bilgisayar benzetim sonuçlarından görüleceği üzere önerilen yöntemle hesaplanana kanal katsayıları diğer yöntemle hesaplananlara göre turbo denkleştiricide daha iyi performans göstermiştir. Equalizer design is an important concept for the wireless communication systems suffering from multipath effects such as ISI. Turbo equalizers are one of the most powerful equalizers introduced several decades ago. For the equalizers to be efficient in removing ISI reliable channel estimation is essential. In this thesis the performance of turbo equalizers for blind and non-blind channel estimators is inspected. For blind channel estimation per-survivor processing with least mean square method is employed. For non-blind channel estimation training sequences are used for channel estimation. An improved channel estimation approach for non-blind technique was suggested and via simulation results, it was seen that the proposed method shows better performance in turbo equalizer than the classical blind and non-blind channel estimation methods do. 57

ÖZET `Kısmi Yanıtlı Sönümlemeli Kanallarda Uzay-Zaman Kodlamalı Sistemlerin Hata Başarımı` isimli bu tezde, Uzay-Zaman Kafes Kodlamalı modülasyonlu sistemler tasarlanmış ve hata başarımları sönümlemeli kanallarda incelenmiştir. Kafes Kodlamalı Modülasyon (Trellis Coded Modulation, TCM), kodlama ve modülasyonun bir arada düşünüldüğü ve iletişim sisteminin güvenilirliğini artırmak için band genişliğini yada iletilen gücü artırmayı gerektirmeyen bir modülasyon yöntemidir. Uzay Zaman Kodlama, birden fazla anten kullanılarak iletişimi mümkün kılmaktadır. Uzay-zaman kodlaması güç ve bant verimli bir kodlama yöntemi olmasının yanında iletişim sistemin kapasitesini de artırır. Bu çalışmada, bu iki kodlama yöntemi birleştirilerek bir sistem tasarlanmıştır. Tasarlanan sistem TCM yönteminin güç ve band verimliliğine ek olarak Uzay-Zaman sisteminin kanal kapasitesini iyileştirme özelliklerini barındırmaktadır. Alıcı kısımda ise alman iki farklı işaretleri basitleştirmek ve özelliklerini korumak için kestirimci-birleştirici yapılan kullanılmıştır. Böylece alıcı kısımdaki kod çözme karmaşıklığı azaltılmıştır. İncelenen sistem için iki adet örnek sistem tasarlanmış, bu sistemlerin kısmi yanıtlı sönümlemeli kanallardaki başarımları bilgisayar benzetimleri yardımlarıyla elde edilmiş ve tasarlanan sistemin başarım üstünlükleri kanıtlanmıştır. vn SUMMARY In this study which is named `Error Performance of Space-Time Coded Systems in Partial Response Fading Channel`, Space-Time Trellis Coded systems are designed and their error performance is studied in fading channels. Trellis-Coded Modulation is a kind of modulation technique which integrates coding and modulation together. Without the need of increasing bandwidth or transmitted power, TCM systems enhance the reliability of communication system. Space-Time Coding provides the communication by using multiple antennas in transmitter and/or receiver. Space-Time Coding systems are not only power and bandwidth efficiency systems but also they increase the capacity of communication system. In this study, a system is designed by integrating these two methods. The designed system enables improving the channel capacity in addition to power and bandwidth efficiency. At the receiver part, estimator-combiner combination is utilized to simplify two different signals that received from two transmitters and preserves their properties. Therefore, decoding complexity is decreased at the receiver. For the investigated systems performance analysis, two example systems are designed and error performances are examined in the partial-response fading channels and its error performance superiority is proved by using computer simulations. vm 70

Recently multiple antenna systems have received significant attention from researchers as a means to improve the energy and spectral efficiency of wireless systems. Among many classes of schemes, Space-Time Block codes (STBC) and Space-Time Trellis codes (STTC) have been the subject of many investigations. Both techniques provide a means for combatting the effects of multipath fading without adding much complexity to the receiver. This is especially useful in the downlink of wireless systems. In this thesis we investigate the impact of channel estimation error on the performance of both STBC and STTC. Channel estimation is especially important to consider in multiple antenna systems since (A) for coherent systems there are more channels to estimate due to multiple antennas and (B) the decoupling of data streams relies on correct channel estimation. The latter effect is due to the intentional cross-talk introduced into STBC. Master of Science

SAYISAL HABERLEŞME SİSTEMLERİNDE KAFES KODLAMA BASARIMININ MİKRODALGA KANALLARINDA BENZETİMİ ÖZET Sayısal haberleşme sistemlerinde gönderilen bilginin güvenli ve hızlı bir şekilde iletilmesi çok önemlidir. Kafes kodlamalı kipleme (TCM), haberleşme sistemlerinde bilgi iletiminde büyük oranda güvenilirlik ve hız sağlar. Kafes kodlamalı kipleme bant genişliğini artırmadan hata performansının iyileştirilmesini sağlamaktadır. Kafes kodlamalı kipleme ilk olarak toplanır beyaz Gauss gürültülü (AWGN) kanalında incelenmiştir, fakat daha sonraları bayılma kanallarındaki kafes kodlama yöntemi üzerinde birçok araştırma yapılmıştır. Bu tezde kafes kodlamalı kipleme yönteminin tabakalı mikrodalga bayılma kanalındaki başarımı değişen haberleşme sistemi parametrelerine göre benzetimi yapılarak hesaplanmıştır. Tezin birinci bölümünde, konunun önemi belirtilerek, yapılan kabuller açıklanmış ve gerçekleştirilen çalışmalar ile ulaşılan sonuçlar belirltilmiştir. Konu ile ilgili daha önce yapılmış olan çalışmalar anlatılmıştır, ikinci bölümde, çoklu faz kaydırmalı modülasyon (kipleme) tekniği ve kafes kodlama yöntemi anlatılmıştır. Üçüncü bölümde bayılma kanalının istatiksel özellikleri açıklanmış ve tabakalı mikrodalga kanalına denklemler verilmiştir. Dördüncü bölümde kafes kodlama yönteminin toplanır beyaz Gauss gürültüsü (AWGN) ve tabakalı mikrodalga bayılma kanalındaki hata başarımı zaman domeninde yapılan bilgisayar benzetimi ile hesaplanarak grafikler halinde gösterilmiştir. Sonuç bölümünde, tezde elde edilen veriler değerlendirilerek, ileride yapılacak çalışmalar için öneriler yapılmıştır. Bu tez çalışmasında kafes kodlama yönteminin tabakalı mikrodalga bayılma kanallarındaki başarımı zaman domeninde yapılan bilgisayar benzetimi üzerinde incelenmiş ve sonuçlan gösterilmiştir. viii PERFORMANCE EVALUATION OF TRELLIS CODING IN MICROWAVE FADING CHANNEL SUMMARY During the past decade there has been a rapidly growing research in the area of bandwidth-efficient coded-modulation techiques. The primary advantage of these schemes over modulation schemes employing traditional error correcting codes is their ability to improve the performance of the communication system without bandwidth expansion. A typical example of such channels is wireless communication channel, where it is desired to accommodate a large number of users in a given bandwidth. During the latter 1980s, trellis coding, especially trellis-coded modulation (TCM), became a hot research topic. In the past, coding and modulation were treated as separate operations with regard to overall system design. In TCM, coding and modulation are considered as an entity. TCM is a channel coding technique that achieves remarkable coding gains, without sacrificing the data rate or expanding the bandwidth of the transmitted signal. In this thesis, performance of the TCM schemes over layered microwave fading channel is analysed according to the changing communication parameters. In the first chapter, the thesis subject is explained and previous research are given. In the second chapter, Multiple Phase Shifting Keying (MPSK) technique and Trellis coding technique are explained by using their analytical expression. In the third chapter, statitical properties of the fading channel which Trellis coding technique is used is introduced. In the fourth chapter, by using computer simulation, error probabilities of the Trellis coded modulation schemes over layered microwave fading channel are obtained. Results and conclusion of the thesis are given last chapter. ^sssr-2* IX 61

ÖZET Bu tezin amacı simetrik kafes kodlamalı modülasyon (TCM), asimetrik kafes kodlamalı modülasyon (ATCM), çoklu kafes kodlamalı modülasyon (MTCM), delinmiş kafes kodlamalı modülasyon (PTCM) ve oran uyumlu delinmiş TCM (RCPTCM) gibi değişik kafes kodlamalı modülasyonların karma ARQ protokollarının başanmları üzerindeki etkisini göstermektir. Veri haberleşmesinde amaç kanal gürültüsünün sebep olduğu iletim hatalarının kontrol edilmesidir. Veri haberleşmesinde iki temel hata kontrol şeması vardır. İleri hata düzeltme (FEC) ve otomatik tekrar isteği (ARQ) şemaları. Karma ARQ (HARQ) temel ARQ protokollarının başarımlarını geliştiren, FEC sisteminin güvenirliliğini arttıran başka bir paket iletim semasıdır. Karma ARQ, FEC sisteminden daha yüksek güvenirlilik ARQ sisteminden daha yüksek başarım sağlar. Başarım verimini arttırmak için kod birleştirme teknikleri karma ARQ şemalarına uygulanmıştır. Bu tür şemalarda alınan hatalı veri paketleri iptal edilmeyip birbirleriyle uygun şekilde birleştirilir ve bu birleşmeden elde edilen veri paketleri çözülür. Kafes kodlamalı modülasyon (TCM) sayısal iletimin güvenirliliğini arttıran birleşik bir kodlama ve modülasyon şeklidir. Güç ve band genişliği verimi sağlar. Birinci bölümde temel ARQ ve karma ARQ protokollan basitçe özetlenmiştir. İkinci bölümde, kafes kodlamalı modülasyon türleri detaylıca açıklanmış ve transfer fonksiyonları verilmiştir. Bu transfer fonksiyonlarından toplanabilir beyaz Gauss gürültülü (AWGN) ve sönümlü kanallar için spektral katsayılar bulunmuştur. Üçüncü bölümde, TCM, ATCM, MTCM, RCPTCM kullanan karma ARQ protokollarının başanmları verilmiştir. Son bölümde sonuçlar tartışılmış ve öneriler sunulmuştur. VI ABSTRACT The aim of this thesis is to show the effect of various types of trellis coded modulations such as symmetric trellis coded modulation (TCM), asymmetric trellis coded modulation (ATCM), ' multiple trellis coded modulation (MTCM), punctured trellis coded modulation (PTCM) and rate compatible punctured TCM (RCPTCM) on the throughputs of hybrid ARQ protocols for AWGN and fading channel. Major concern in data communication is how to control transmission error caused by the channel noise. There are two basic error control schemes for data communications: Forward error correction (FEC) and automatic repeat request (ARQ) schemes. Hybrid automatic repeat request (HARQ) scheme is another packet transmission technique for improving the throughputs of basic ARQ protocols and for improving the reliability of FEC protocol. Hybrid ARQ provides higher reliability than FEC system alone and higher throughput than ARQ system alone. In order to increase throughput efficiency, code combining technique is applied to hybrid ARQ schemes. In these kinds of schemes, received erroneous packets are not discarded, but combined with their repeated copies in an optimum manner and then the decoder decodes this combined packet. Trellis coded modulation (TCM) is a combined coding and modulation scheme for improving the reliability of a digital transmission. It achieves both power and bandwidth efficiency. In the first chapter, basic ARQ and hybrid ARQ protocols have been summarized briefly. In the second chapter, types of trellis coded modulations have been explained in detail and their transfer functions have been given. From transfer functions, their spectral coefficients for additive white Gaussian noise (AWGN) and fading channels are evaluated. In the third chapter, the throughputs of hybrid ARQ protocols using TCM, ATCM, MTCM and RCPTCM have been given. In the last chapter, results have been discussed and succession have been introduced. 87

IV ÖZET Bu çalışmada, kafes kodlamalı kiplenimin (trellis-coded modulation, TCM), toplanır beyaz Gauss gürültülü (additive white Gaussian noise, AWGN), kanalın yamsıra Rayleigh, Rice ve Nakagami dağılımlı sönümlemeli kanallardaki, başanmı incelenmiştir. Kafes kodlamalı kiplenimin genel kavramı ve temel ilkeleri özetlenmiştir. Ayrıca kullanılan kümelere ayırma (set partitioning) yöntemi anlatılmıştır. TCM' in Nakagami dağılımlı sönümlemeli kanaldaki başanmı farklı sönümleme parametre değerleri için incelenmiştir. Çalışmalar sırasında kanalın ideal bit dağıtım özelliğine sahip olduğu vede evre uyumlu olduğu varsayılmıştır. Nakagami sönümleme parametresinin artan değerlerinde başarımın arttığı sonucuna ulaşılmıştır. Son olarak çoklu TCM' in Nakagami tipi sönümlemeli kanaldaki başanmı incelenmiş ve klasik TCM ile karşılaştırmalar yapılmıştır. Analiz sonuçlan çoklu TCM' in klasik TCM' e göre daha başanlı olduğunu göstermiştir. Anahtar kelimeler: Kafes kodlamalı kiplenim, Nakagami dağılımlı sönümleme, hata olasılığı, çoklu kafes kodlamalı kiplenim. ABSTRACT In this study, trellis-coded modulation, which is a bandwidth-efficient coded modulation scheme is analyzed in various types of channels, namely, additive white Gaussian noise channel (AWGN), Rayleigh, Rician and Nakagami fading channels. The concept and fundamentals of trellis coded modulation (TCM) and the set partitioning technique as a tool for designing TCM schemes are studied. Performance of TCM over Rician and Nakagami fading channels are comparitively studied. It is observed that the increase in the Nakagami fading parameter improves the performance of TCM over Nakagami fading channel. Bit error probabilities of conventional and multiple TCM in Nakagami fading channel are derived. Multiple TCM systems are analyzed. The results show that multiple TCM has superior bit error rate performance over conventional TCM systems. Keywords: Trellis coded modulation, Nakagami fading, error probability, multiple trellis coded modulation. 109

KANAL KODLAMASl VE ŞİFRELİ HABERLEŞME (Yüksek Lisans Tezi) Hamza GERÇEKÇİOĞLU GAZİ ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ Ocak 2000 ÖZET Kanal kodlaması, konvolüsyonel kodlama kullanılarak bilgisayarda gerçekleştirilmiş ve işleme tabi tutulan bu kodlama modelinden şifreli haberleşmeye bir geçiş sağlanması üzerinde durulmuştur. Konvolüsyonel kodlama ve kod çözücü algoritmaları yazılım olarak Pascal ve Assembly programlama dillerinde ifade edilmiştir. Programlamalar için gereken sayısal bilgiler, analog / sayısal çeviricilerle (ADC) elde edilmiş; bilgi biüerinin analog sinyallere dönüştürülmesinde de sayısal / analog çeviriciler (DAC) kullanılmıştır. Bilgi iletimi, radyo dalgalan (RF) ile, deney amaçlı frekans modülasyonu (FM) ortamında alıcı ve vericilerle sağlanmıştır, iki farklı kod oranı için, konvolüsyonel kodlama, hem bilgi kaybım önleme, hem de şifreleme amaçlı kullanılmıştır. Bu örnekler için hala olasılığı hesaplamaları yapılmış ve bunun geçerliliği deneysel olarak gözlenmiştir. Haberleşme alanında yapılan bu çalışma, haberleşme teknolojisinde var olan bazı iletişim tekniklerini ele alıp, bunların bir araya getirilmesi amacıyla yapılmıştır. Bilim Kodu : 609.01.00 Anahtar Kelimeler : Konvolüsyonel kodlama, Vilerbi algoritması, kodlayıcı, kod çözücü, ADC, DAC. Sayfa Adedi : 186 Tez Yöneticisi : Prof. Dr. Müzeyyen SAR1TAŞ CHANNEL CODING AND CODED COMMUNICATION (M.Sc. Thesis) Hamza GERÇEKÇİO?LU GAZİ UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY January 2000 ABSTRACT Channel coding has been performed using convohrtional coding in computer and this coding model has been studied to provide a transition into coded communication. Convolutions! coding and decoding algorithms have been written in Pascal and Assembly languages as software. The necessary digital data for the programmes are obtained by the analog / digital converters (ADC), and the digital / analog converters (DAC) have been used to convert the data bits to analog signals. The data transmission has been achieved through the RF signals by the receivers and the transmitters in FM for experimental purposes. For two different coding ratios, the convolutional coding has been used in order to prevent loss of data bits and for coding. For these cases, error probability calculations have been carried out and its validity has been checked experimentally. This study which is performed in the field of communication, has been made in order to take into account and combine some of the known communication techniques. Science Code : 609.01.00 Key Words : Convolution coding, Viterbi algorithm, encoder, decoder, ADC, DAC. Page number :186 Adviser : Prof. Dr. Müzeyyen SARITAŞ 186

Öz GELENEKSEL, ASİMETRİK VE ÇOKLU KAFES KODLU MODÜLE EDİLMİŞ SİSTEMLERİN ÇEŞİTLİ KANALLARDAKİ ANALİZİ VE BENZETİMİ Çetingül, Serdar Yüksek Lisans, Elektrik ve Elektronik Mühendisliği Bölümü Tez Yöneticisi : Doç. Dr. Melek D. Yücel Mart 1998, 125 sayfa Bu çalışmada, band verimli kodlamalı modülasyon sistemlerinin Gaussian, Rayleigh ve Rician kanallarındaki analizi ve benzetimi Viterbi kodçözücü dizgesi ile gerçekleştirilmiştir. Kafes kodlamalı modülasyon (TCM) sisteminin genel kavram ve esasları ve TCM sistemlerinin tasarlanmasında kullanılan set bölünme tekniği üzerinde çalışılmıştır. Asimetrik işaret seti tasarlanıp, optimize edilmiş kafes koduyla birleştirildiğinde ortalama gücü veya en yüksek gücü veya band sınırlamasını değiştirmeden kodlamalı sistemlerin başarımnı daha da geliştirmenin mümkün olduğu analiz ve benzetimlerle gösterilmiştir. Bunun yanısıra, yeni bir kod tasarlanmış ve literatürdeki bir kodla aynı başarımı sağladığı gösterilmiştir. Ek olarak, geleneksel, asimetrik ve çoklu TCM MPSK sistemlerinin sönümlü kanallardaki ikil hata olasılıkları çıkartılmıştır. En kısa hata yolu ve en kısahata yolu üzerindeki dal uzunlukları çarpımı gibi başarımı etkileyen değişkenler tartışılmıştır. Çoklu TCM sistemlerinin de analizi ve benzetimi yapılmıştır. Analiz ve benzetim sonuçlan, çoklu kafes kodlu modülasyon yönteminin geleneksel ve asimetrik kafes kodlu modülasyon yöntemlerine göre daha iyi ikil hata oram başarımı sağladığım göstermektedir. Anahtar Kelimeler: Kafes kodlu modülasyon, Viterbi kodçözücü dizgesi, en kısa hata yolu boyu, dal uzunlukları çarpımı, asimetrik işaret seti, çoklu TCM. vi ABSTRACT ANALYSIS AND SIMULATION OF CONVENTIONAL, ASYMMETRIC AND MULTIPLE TRELLIS CODED MODULATION IN VARIOUS TYPES OF CHANNELS Çetingül, Serdar M.S., Department of Electrical and Electronics Engineering Supervisor : Assoc. Prof. Dr. Melek D. Yücel March 1998, 125 pages In this study, bandwidth-efficient coded modulation schemes are analyzed and simulated in various types of channels, namely, additive white Gaussian channel (AWGN), Rayleigh and Rician channels using Viterbi decoder algorithm. The concept and fundamentals of trellis coded modulation (TCM) and the set partitioning technique as a tool for designing TCM schemes are studied. It is analyzed and simulated that by designing asymmetric signal constellations and combining them with optimized trellis coding, one can further improve the performance of coded systems without increasing average or peak power or changing the bandwidth constraints imposed on the system. A new code is designed which shows similar performance to the one given in the literature. Bit error probabilities of conventional, asymmetric and multiple TCM MPSK systems in fading channels are derived. Parameters which affect the iiiperformance, i.e., maximization of branch distance product and length of the shortest error event path are discussed. Multiple TCM systems are also analyzed and simulated. The analysis and simulation results show that in all of the analyzed channels, multiple TCM has superior bit error rate performance over the conventional and asymmetric TCM systems. Keywords : Trellis coded modulation, Viterbi decoding algorithm, length of the shortest error event path, product of the branch distance, asymmetric signal sets, multiple TCM. IV 125

öz ÇİT KODLAMALI MODÜLASYON İÇİN UZAKLIK GÖRÜNGESİNİN FARKLI YÖNTEMLERLE HESAPLANMASI Yavuz, Emre Altuğ Yüksek Lisans, Elektrik Elektronik Mühendisliği Bölümü Tez Yöneticisi : Doç. Dr. Melek D. Yücel Haziran 1998, 118 sayfa Bu tezde, çit kodlu modülasyonlann başaranlarının hesaplanmasında kullanılan yöntemler anlatılmış, bu yöntemler hesaplama karmaşası açısından karşılaştınlmış, başarım ölçütleri ve çit kodlu modülasyon şemalarının sınıflandırılması sunulmuştur. Başarım ölçütleri bir kodun aktarma fonksiyonu ya da bir kod sınıfi için yaratılan algoritma ile hesaplanabilir. Değişik yöntemler kullanılarak bir kodun sayıl ( skalar ) ya da matris olarak aktarma fonksiyonunun oluşturulması ele alınmış ve bu aktarma fonksiyonunu kullanarak başarım ölçütlerinin nasıl hesaplanabileceği örneklerle gösterilmiştir. Değişik sınıflara ait olan kodların uzaklık görüngelerini hesaplamak için önerilen algoritmalar sunulmuş ve Rouanne ve Costello tarafindan ortaya konulan algoritma ayrıntılı olarak anlatılmıştır. 2 ve 4 durumlu, 2/3 hızlı, 8 PSK kodlanılın ve 4 durumlu, 2/3 hızlı, 8 AMPM kodunun uzaklık görüngeleri, aktarma fonksiyonlarının seri açılımı ve Rouanne Costello algoritması temel alınarak yazılan bilgisayar programı kullanılarak hesaplanmıştır. Bulunan değerler Trofimov ve Kudryashov'un önerdiği aktarma fonksiyonunun seri açılımından bulunanlarla karşılaştınlmıştır.Anahtar Sözcükler : Çit Kodlamalı Modülasyon, Aktarma Fonksiyonu, Hesaplama Karmaşıklığı, Başarım Değerlendirmesi, Uzaklık Görüngesi vı ABSTRACT DIFFERENT COMPUTATIONAL METHODS FOR DISTANCE SPECTRA OF TRELLIS CODED MODULATION ( TCM ) Yavuz, Emre Altuğ M.S., Department of Electrical and Electronics Engineering Supervisor : Assoc. Prof. Dr. Melek D. Yücel June 1998, 118 pages In this thesis, the methods which are used for the evaluation of the performance of a TCM code, are introduced and a comparison is made between them in terms of the computational complexity. The performance measures and the classification of TCM schemes are presented. The performance criteria, like dfe., Nfee or the distance spectrum can be evaluated by the help of the transfer function of the code or an algorithm constructed for the class of the code. The construction of the transfer function in scalar or matrix forms for a code using different methods is considered and how the performance criteria can be found using the transfer function is given with the examples. The description of the algorithms for the various classes of codes are presented and the Rouanne and Costello algorithm for the quasi-regular codes is discussed in detail. Distance spectra of 2 state and 4 state, rate 2/3, 8 PSK codes and a 4 state, rate 2/3, 8 AMPM code are computed using the series expansion of their transfer functions and the computer program based on the Rouanne and Costello algorithm. These results and the ones computed by the series expansion proposed by Trofimov and Kudryashov are compared. mKeywords : Trellis Coded Modulation ( TCM ), Transfer Function, Computational Complexity, Performance Evaluation, Distance Spectrum IV 118

oz ÇOK BOYUTLU TRELLİS-KODLAMALI MODÜLASYON Kocatepe, Unsal Yüksek Lisans, Elektrik-Elektronik Mühendisliği Bölümü Tez Yöneticisi : Doç. Dr. Melek D. Yücel Haziran 1998, 148 sayfa Bu çalışma, çok boyutlu M-li faz değişim anahtarlamalı trellis-kodlamalı modülasyon kodlan oluşturmak için önerilen bir yöntemi açıklamaktadır. Bu yöntem, trellis kodların dış kısımda kullanıldığı ve blok M-li faz değişim anahtarlamalı modülasyon kodlarının işaret uzayım oluşturduğu çok katlı ekleme metoduna dayanmaktadır. Ayrıca bu şekilde oluşturulan kodlar için önerilmiş olan çok aşamalı kod çözme metodu da incelenmiştir. Bu kod oluşturma ve çözme yöntemleri bir örnek üzerinde açıklanmış ve beyaz gürültü eklenen iletişim kanalları için literatürde yer alan çok boyutlu trellis-kodlamalı modülasyon kodlarının simülasyonlarında kullanılmıştır. Yapılan simülasyon sonuçlarına göre bu kodlar iyi performans göstermekte ve kodlanmamış referans sistemlere göre oldukça iyi kazançlar sağlamakta, ayrıca kod çözme karmaşıklığı açısından literatürde yer alan kodlar karşısında daha avantajlı da olabilmektedir. Anahtar Kelimeler : Ekleme, trellis-kodlamalı modülasyon, çok aşamalı kod çözme iv ABSTRACT MULTIDIMENSIONAL TRELLIS-CODED MODULATION Kocatepe, Unsal M.Sc, Department of Electrical and Electronics Engineering Supervisor : Assoc. Prof. Dr. Melek D. Yücel June 1998, 148 pages This work explains a technique for constructing multidimensional M-ary phase shift keying ( MPSK ) trellis-coded modulation ( TCM ) codes. The construction is based on a multilevel concatenation approach, in which binary convolutional codes with good free branch distances are used as the outer codes and block MPSK modulation codes are used as the inner codes or signal spaces. The multistage decoding scheme proposed for these codes is also examined. The construction and decoding techniques are explained by an example and then used in simulations of multidimensional trellis-coded modulation codes for the additive white Gaussian noise channels available in literature. The simulation results show that these codes perform very well and achieve significant coding gains over uncoded reference modulation systems and can also have a decoding complexity advantage over the codes listed in literature. Keywords : Concatenation, trellis-coded modulation, multistage decoding m 148

ÖZET FAZ SEYIRMELI VE RICIAN SÖNÜMLEMELİ KANALLAR İÇİN KAFES KODLAMALI SİSTEM TASARIMI VE BAŞARIM ANALİZİ Sayısal iletişim sistemlerinin tasarımında temel amaç, veri dizilerinin bozucu etkenlerden en az düzeyde etkilenecek şekilde iletilmesinin sağlanmasıdır. Hata sezme ve düzeltme özelliği, iletilecek işarete kanal kodlaması uygulanarak kazandırılır. Bu nedenle, veri dizileri doğrudan iletilmek yerine kanal kodlaması işleminden geçirildikten sonra genlik kaydırmalı anahtarlama, faz kaydırmak anahtarlama veya dik genlik modülasyonu gibi çeşitli sayısal modülasyon yöntemlerinden birisi ile modüle edilerek kanala uygulanır. Klasik kanal kodlayıcıları, n bitlik ikili veri dizilerini m-n tane kontrol biti ekleyerek m (m>n) uzunluklu ikili veri dizilerine dönüştürürler. Fazladan kontrol biti ekleme işlemi, sisteme hata sezme ve düzeltme özelliğini kazandırmakla beraber, iletilecek ikili dizilerin uzunluğunu arttırdığından veri iletim hızında kayıba neden olur. Bu kayıp, modülasyon hızı ve dolayısıyla band genişliği arttırılarak engellenebilir. Bandı sınırlı kanallarda ise, kanal işaretleri kümesi genişletilerek aynı amaca ulaşılabilir, ancak genişletilmiş işaret kümesi yardımıyla tasarım, kodlama ve modülasyon işlemleri birbirinden ayrı düşünüldüğünde başarılı olamamaktadır. Bunun temel nedeni, kodlama sırasında Hamming uzaklığına dayanarak yapılan tasarımın modülasyonlu işaret dizilerinin işaret uzayında optimum olarak birbirlerinden uzaklaşmasını sağlamamasıdır. Kodlama ve modülasyonun tasarım sırasında birlikte düşünüldüğü kafes kodlamalı modülasyon (trellis coded modulation-TCM) tekniği ilk defa Ungerboeck tarafından 1982 yılında önerilmiştir. Bu teknik, band sınırlaması altında, kullanılacak modülasyonlu işaret kümesini gereğinden geniş tutarak bir kodlama fazlalığı sağlanması ve bu fazlalığın kodlanmış işaret dizileri arasındaki minimum Öklid uzaklığının artması amacıyla kullanılması ilkesine dayanmaktadır. Böylece aynı iletim hızı ve işaret gücünde sabit band genişliği için, kafes kodlamasız durumda elde edilemeyen hata başarımlarına kafes kodlamalı modülasyon kullanılması durumunda ulaşılabilmektedir. Şekil 1' de kafes kodlamalı modülasyon tekniğinin kullanıldığı kodlayıcı/modülatör yapısı görülmektedir. Bu yapıda, her iletim aralığında m bitlik ikili veri dizisi sistemin girişine uygulanmaktadır, n < m tanesi n/(n+l) oranlı bir katlamak kodlayıcı tarafından n+1 bitlik kodlanmış ikili diziye dönüştürülürken, veri bitlerinin m-n tanesine kodlama işlemi uygulanmaz. Katlamak kodlayıcının çıkışındaki n+1 bitlik dizi gereğinden fazla işaret içeren 2m+1 elemanlı işaret kümesinin 2n+1 alt kümesinden birini seçmek için kullanılır. Geriye kalan m-n kodlanmamış bit, seçilen alt kümede 2m`n işaretten hangisinin iletileceğini belirler. Eşleyici girişindeki m+1 bitlik dizinin 2m+1 kanal işaretleri ile eşlenmesi, Ungerboeck tarafından önerilen küme ayrıştırarak eşleme (mapping by set partitioning) xm SUMMARY In this study, the performance of trellis coded M-PSK systems is investigated over Rician fading channels in the presence of imperfect phase reference. Thus the results reflect not only the degradation due to the effect of fading on the amplitude of the received signal, but also the impairment caused by the noisy carrier reference, which is usually neglected with the assumption of perfect phase tracking is employed. Analytical upper bounds on pairwise error probability for Rayleigh and Rician fading channels are derived using Chernoff bounding technique in both cases of channel state information is available or not. The bit error probability performances are evaluated based on the transfer function approach. The numerical examples clearly demonstrate the error performance degradation due to both amplitude fading and phase noise process. Besides the performance analysis of trellis coded systems, a code search has been carried out in the case of Rayleigh fading and channel state information is not available in order to find schemes more robust against phase noise over the fading channel. It is based on a performance criterion which is valid especially at high signal-to-noise ratios and involves the effective signal-to-noise ratio in the carrier tracking loop besides the well known TCM design parameters, namely the effective code length and the minimum product distance. The codes of optimum performance are found after an exhaustive computer search and their bit error performances are evaluated based both on the transfer function upper bounding techniques and computer simulations. Xll 95

Doğrusal olmayan kanal etkilerine karşı duyarlılığı azaltan, sabit zarf ve band verimliliğini artıran faz sürekliliği özellikleriyle gezgin iletişim sistemleri için oldukça çekici bir modülasyon türü olan sürekli faz modülasyonunun (CPM) özel bir biçimi olan çok modülasyon indisli faz kodlamalı modülasyon (MHPM) tekniğini kullanan sistemlerin gürültülü ve sönümlemeli kanallarda hata başarmamı artıran çoklu kafes kod tasarımı, bu tezin konusunu oluşturmaktadır. Kafes yapılarının her işaretleşme aralığında çevrimsel olarak yinelenmesinden yani zamanla değişme sinden dolayı MHPM sistemler, CPM sistemler gibi tek bir işaretleşme aralığında zamanla değişmeyen bir doğrusal faz kodlayıcısı ile onu izleyen bir. belleksiz modülatöre ayrıştırılamazlar. Bu nedenle, MHPM vericisi, k farklı modülasyon indis sayısı kadar işaretleşme aralığını yapısında toplayan, zamanla değişmeyen bir sürekli faz kodlayıcısına (fc-CPE) ve onun çıkışını k ardışıl kanal işaretine eşleyen, yine zamanla değişmeyen bir çoklu belleksiz modülatöre ayrıştırılarak modellenmiştir. Bu model, çoklu MHPM yapılarının kodlanarak gerek Gauss gürültülü gerekse sönümlemeli kanallardaki başarımlarının artırılmasında yararlı olmaktadır. &-CPE ile bir katlamalı önkodlayıcının birleşiminden oluşan eşdeğer kodlayıcının aynı durumdan ayrılan işaretlerinin arasındaki Oklid uzaklıklarını maksimum yapmak için çoklu MHPM kafeslerine küme bölmeleme yöntemi uygulanmıştır. Tasarlanan 4 ve 8 durumlu kodlanmış MHPM sistemler, kodlanmamış MHPM yapılarına ve seçilen modülasyon indis kümelerinin ortalama değerini kullanan CPM'e göre önemli kod- lama kazançları sağlamaktadır. Ayrıca bu yeni MHPM kafes kodların Gauss gürül tülü kanallardaki hata başarımları, gerek analitik yöntemlerle gerekse geliştirilen bir bilgisayar benzetim programı yardımıyla değerlendirilmiştir. Gauss gürültülü kanallardan farklı özellikler gösteren, buna bağlı olarak kafes kod tasarımında etkin kod uzunluğu, çarpımsal uzaklık gibi farklı tasarım ölçütlerinin kullanımını gerektiren sönümlemeli kanal modelleri için çoklu MHPM kafes kodların tasarımları gerçekleş tirilmiş, 4 durumlu kodlanmış çoklu MHPM sistemlerin hata başarımları, kuramsal olarak ve bilgisayar benzetim yöntemleriyle incelenerek ilişkin kodlanmamış sistemlere olan üstünlükleri ortaya konmuştur. Continuous phase modulation (CPM) is a very attractive digital modulation technique for the transmission of digital information over band and/or power limited channels. The phase continuity provides to CPM signals good spectral properties and some error correction possibilities. Multi-/i phase coded modulation technique (MHPM) has received a great deal of attention for application in satellite modems due to its power and bandwidth efficiency which are even better than that of CPM. MHPM is a special case of CPM where the modulation index (h) is periodically changed for successive signalling intervals. In this thesis, multiple trellis codes are designed for the systems which use MHPM technique, in order to increase their error performances over gaussian and fading channels. »Since their trellis structures are time-variant, MHPM schemes can not be decomposed as CPM schemes into a ti me-invariant continuous phase encoder (CPE) followed by a memoryless modulator (MM), over one symbol interval. A new representation for M-ary MHPM is intro duced to overcome this problem, namely to obtain a time invariant CPE followed by a time invariant MM. We simply consider k consecutive symbol intervals together during the constitution of the CPE where k is the number of different modulation indexes. The outputs of this fc-CPE are then mapped to multiple signal set consti tuted by k consecutive MHPM signals. This kind of decomposition makes easier the optimal combination of an external encoder with MHPM. Since the CPE is linear over a finite field, the cascade of an external convolutional encoder with the CPE can be reduced to an equivalent single convolutional encoder. The set partitioning method is applied to the multiple MHPM trellis structures to maximize the Euclide an distances between all signal pairs originating from and merging to the same state. The proposed multiple coded MHPM systems for the gaussian channels which use 4 and 8 state decoding trellis provide significant asymptotic coding gains with respect to the corresponding uncoded MHPM and related CPM systems. The design of mul tiple trellis codes for MHPM is also realized for the fading channels which request different design criteria such as the effective code length and the product distance. It is shown by analytical methods and by means of computer simulation that these new coded MHPM systems significantly outperform their uncoded counterparts in this type of channels. 153

In Code Division Multiple Access (CDMA) systems forward error correction (FEC) is an important factor in improving system performance. Because of the multiple access interference observed in asynchronous CDMA, FEC is required to improve system capacity. Several alternative coding techniques are available, including "trellis codes" specifically designed for CDMA, very low rate convolutional codes and conventional convolutional codes. An analytic approach is developed to compare the performance of different coding techniques for CDMA on the same basis by extending several improved analysis techniques which were developed for uncoded CDMA. Analytic results are presented for additive white Gaussian noise (AWGN) channels and frequency non-selective Rician Fading (FNRF) channels. The performance of coded CDMA systems in frequency selective Rayleigh fading channels is also analyzed using simulation techniques. Both analytic and simulation results show that by using trellis codes or very low rate convolutional codes significant performance improvement is achieved over conventional convolutional codes. Trellis codes outperform very low rate convolutional codes in AWGN and FNRF channels while both codes show similar performance in frequency selective Rayleigh fading channels. Master of Science

Conventional convolutional codes are normally optimized in terms of their free Hamming distance[11], [12]. These codes can also be combined with continuous phase modulation (CPM) or specifically CPFSK. A larger class of schemes is obtained by combining convolutional coding with CPM[13]. In [13], Lindell and Sundberg is optimized the Euclidean distance for combination of the channel coding and CPFSK modulation. In a code trellis minimum merge length is increased by prior encoding of the data symbols, generally, the longer the merge length, the larger the minimum normalized squared Euclidean distance and hence the better the error performance. This is the one of the reasons that coding is used in conjunction with CPM. Error performance analysis of an arbitrary trellis code is different from that of binary convolutional code due to the nonlinearity induced by the memoryless mapper. For a nonlinear code the Euclidean distance between any incorrect path and the correct path is dependent upon the correct path. Biglieri[14], has proposed a method based on generalized generating function which involves an error state diagram where the number of states is equal to the square of the number of trellis states. But this method is impractical for codes with more than 2 or 4 states. For example a code with 8 trellis states requires 64 states in its error state diagram to compute the generalized generating function. Zehavi and Wolf[15] showed that the modified generating function can be calculated from error state diagram with number of states equal to that of the encoder trellis if the code satisfy some symmetry properties. Most of the Ungerboeck' s type codes satisfy these properties. Bounds on the bit-error or error-event probabilities can be then derived. In this thesis, an extended version of minimum shift keying known as multi-amplitude minimum shift keying is considered and its inherent trellis structure with four states is explored. After that, optimum combination of convolutional codes and multi-amplitude minimum shift keying modulation is suggested. In the second chapter of the thesis, minimum shift keying modulation is explained in detail and inherent error control properties of this modulation scheme is examined. Than, trellis coded-modulation technique and free Euclidean distance calculation algorithm are presented. In the third chapter, the extended version of minimum shift keying which have multi-amplitudes signals known as multi-amplitude minimum shift keying modulation (MAMSK), is considered. A trellis code structure for multi- amplitude minimum shift keying is obtained with prescribed initial phases IX and amplitudes. The MAMSK is then presented in coded-modulation scheme. After that, error performance of uncoded MAMSK signal is investigated. in chapter four, in order to improve the error performance of multi- amplitude minimum shift keying, the optimum combinations of convolutional codes and multi-amplitude minimum shift keying modulation are explored. VVith R=1/2, K=1 coded MAMSK modulation, an asymptotic coding gain of 6.5 dB över uncoded MAMSK modulation is obtained. R=1/2, K=2 coded MAMSK modulation offers an asymptotic coding gain of 7 dB över uncoded modulation.Conventional convolutional codes are normally optimized in terms of their free Hamming distance[11], [12]. These codes can also be combined with continuous phase modulation (CPM) or specifically CPFSK. A larger class of schemes is obtained by combining convolutional coding with CPM[13]. In [13], Lindell and Sundberg is optimized the Euclidean distance for combination of the channel coding and CPFSK modulation. In a code trellis minimum merge length is increased by prior encoding of the data symbols, generally, the longer the merge length, the larger the minimum normalized squared Euclidean distance and hence the better the error performance. This is the one of the reasons that coding is used in conjunction with CPM. Error performance analysis of an arbitrary trellis code is different from that of binary convolutional code due to the nonlinearity induced by the memoryless mapper. For a nonlinear code the Euclidean distance between any incorrect path and the correct path is dependent upon the correct path. Biglieri[14], has proposed a method based on generalized generating function which involves an error state diagram where the number of states is equal to the square of the number of trellis states. But this method is impractical for codes with more than 2 or 4 states. For example a code with 8 trellis states requires 64 states in its error state diagram to compute the generalized generating function. Zehavi and Wolf[15] showed that the modified generating function can be calculated from error state diagram with number of states equal to that of the encoder trellis if the code satisfy some symmetry properties. Most of the Ungerboeck' s type codes satisfy these properties. Bounds on the bit-error or error-event probabilities can be then derived. In this thesis, an extended version of minimum shift keying known as multi-amplitude minimum shift keying is considered and its inherent trellis structure with four states is explored. After that, optimum combination of convolutional codes and multi-amplitude minimum shift keying modulation is suggested. In the second chapter of the thesis, minimum shift keying modulation is explained in detail and inherent error control properties of this modulation scheme is examined. Than, trellis coded-modulation technique and free Euclidean distance calculation algorithm are presented. In the third chapter, the extended version of minimum shift keying which have multi-amplitudes signals known as multi-amplitude minimum shift keying modulation (MAMSK), is considered. A trellis code structure for multi- amplitude minimum shift keying is obtained with prescribed initial phases IXand amplitudes. The MAMSK is then presented in coded-modulation scheme. After that, error performance of uncoded MAMSK signal is investigated. in chapter four, in order to improve the error performance of multi- amplitude minimum shift keying, the optimum combinations of convolutional codes and multi-amplitude minimum shift keying modulation are explored. VVith R=1/2, K=1 coded MAMSK modulation, an asymptotic coding gain of 6.5 dB över uncoded MAMSK modulation is obtained. R=1/2, K=2 coded MAMSK modulation offers an asymptotic coding gain of 7 dB över uncoded modulation.Conventional convolutional codes are normally optimized in terms of their free Hamming distance[11], [12]. These codes can also be combined with continuous phase modulation (CPM) or specifically CPFSK. A larger class of schemes is obtained by combining convolutional coding with CPM[13]. In [13], Lindell and Sundberg is optimized the Euclidean distance for combination of the channel coding and CPFSK modulation. In a code trellis minimum merge length is increased by prior encoding of the data symbols, generally, the longer the merge length, the larger the minimum normalized squared Euclidean distance and hence the better the error performance. This is the one of the reasons that coding is used in conjunction with CPM. Error performance analysis of an arbitrary trellis code is different from that of binary convolutional code due to the nonlinearity induced by the memoryless mapper. For a nonlinear code the Euclidean distance between any incorrect path and the correct path is dependent upon the correct path. Biglieri[14], has proposed a method based on generalized generating function which involves an error state diagram where the number of states is equal to the square of the number of trellis states. But this method is impractical for codes with more than 2 or 4 states. For example a code with 8 trellis states requires 64 states in its error state diagram to compute the generalized generating function. Zehavi and Wolf[15] showed that the modified generating function can be calculated from error state diagram with number of states equal to that of the encoder trellis if the code satisfy some symmetry properties. Most of the Ungerboeck' s type codes satisfy these properties. Bounds on the bit-error or error-event probabilities can be then derived. In this thesis, an extended version of minimum shift keying known as multi-amplitude minimum shift keying is considered and its inherent trellis structure with four states is explored. After that, optimum combination of convolutional codes and multi-amplitude minimum shift keying modulation is suggested. In the second chapter of the thesis, minimum shift keying modulation is explained in detail and inherent error control properties of this modulation scheme is examined. Than, trellis coded-modulation technique and free Euclidean distance calculation algorithm are presented. In the third chapter, the extended version of minimum shift keying which have multi-amplitudes signals known as multi-amplitude minimum shift keying modulation (MAMSK), is considered. A trellis code structure for multi- amplitude minimum shift keying is obtained with prescribed initial phases IXand amplitudes. The MAMSK is then presented in coded-modulation scheme. After that, error performance of uncoded MAMSK signal is investigated. in chapter four, in order to improve the error performance of multi- amplitude minimum shift keying, the optimum combinations of convolutional codes and multi-amplitude minimum shift keying modulation are explored. VVith R=1/2, K=1 coded MAMSK modulation, an asymptotic coding gain of 6.5 dB över uncoded MAMSK modulation is obtained. R=1/2, K=2 coded MAMSK modulation offers an asymptotic coding gain of 7 dB över uncoded modulation. 76

Bu tez çalışmasında, kodlama ve modülasyon işlemlerinin bir bütün olarak ele alındığı kafes kodlamalı Hızlı Frekans Kaydırmalı Anahtar lama (Fast Frequency Shift Keying, FFSK> modülasyonu, iletişim sistemlerinde hata kontrolü için kullanılan bir yöntem olan Otomatik Yineleme istemeli f. Automatic Repeat Request, ARQ> tekniğine uygulanmıştır. Tene! yapı oluşturulduktan sonra, alıcı tarafta bellek kullanılması ve kod sözcüğünün ilk iletiminde hata serildiğin de verici tarafından aynı sözcüğün `m` kez ard arda iletilmesi gibi iyileştirmeler sisteme ilave edilerek, başarımın arttırılması yoluna gidilmiştir. Oluşturulan sistemlerin Gauss gürültülü ve Rayleigh genlik sünümlemeli kanallardaki iş çıkarma yetenekleri ve bit hata olasılık üst sınırları analitik yöntemlerle incelendiği gibi oluşturulan bir benzetim modeli yardımıyla da değerlendirilmiştir. SUMMARY THE APPLICATION OF TRELLIS CODED FAST FREQUENCY SHIFT KEYING MODULATION TO THE AUTOMATIC REPEAT REQUEST SYSTEMS In this thesis, trellis coded fast frequency shift keying (FFSK) technique is introduced for modula tion operation in automatic-repeat-request (ARQ) schemes in order to improve their throughput performances. The performance of the proposed system is investigated in noisy and fading environment by both analytical and simulation approaches. On the other hand, some modifica tions like the m>l times retransmission of the codeword detected in error or the use of a memory in the receiver are also considered. There are two basic types of error-control schemes in data transmission systems: the forward-error control . Each block of 3 information symbols coming out of the source is encoded in a codeword g of a code C(6,3). g is G symbols long. Code C is able to correct 2 = 26_3=8 errors and to detect 2n-2k=26 -23=56 errors. C

ÖZET Bu tezde, çok-düzeyli kafes kodlama ve çok-aşamalı kodçözme tekniğine dayanarak, 8-PSK, 32-CROSS ve 2FSK/4PSK modülasyon türleri için kodlama kazancı yüksek, kodçözme karmaşıklığı düşük sayısal veri iletim sistemleri tasarlanmıştır. Kodlama kazancını artırmak amacıyla her düzey için uygun kodlama oranları belirlenmiş ve bu kodlama oranları için her düzeyin bölmelediği işaret kümesine ilişkin en küçük Oklid uzaklığını maksimum yapan konvolüsyonel kodlar kullanılmıştır. Kod çözme karmaşıklığını azaltmak amacıyla ise, belli bir kodlayıcı serbest Hamming uzaklığı için sınırlı uzunluğu (bellek elemanı sayısı) en küçük olan konvolüsyonel kodlar, kimi düzeylerde de boşluktu konvolüsyonel kodlar kullanılmıştır. Böylece, ele alınan modülasyon türleri için literatürde bulunan klasik Ungerboeck tipi sistemlere göre aynı kodlama hızında ve aynı bandgenişliğinde daha yüksek kodlama kazançlı ve daha düşük kodçözme karmaşıklıktı yeni sistemler elde edilmiştir. -V- SUMMARY MULTILEVEL CODING/MULTISTAGE DECODING AND ITS APPLICATION TO FREQUENCY/PHASE SHIFT KEYING MODULATION The main purpose in digital communication systems is to transmit most possible data with the minimum number of error from the source to the user in a given time interval. Error probability of the receiver, for a given data rate is considered as a performance criterion. In classical digital communication systems the functions of modulation and coding are considered separetely. Modulators and demodulators convert an analog waveform channel into a discrete channel, whereas encoders and decoders correct errors that occur on the discrete channel. Conventional encoders and decoders for error correction operate code symbols transmitted over the channel. If encoder has the code of rate k/n, n-k redundant check symbols are added to every k information symbols, where k s n. Although, certain number of errors can be corrected by using error-correcting codes, this method causes to rate loss. There are two methods to compansate the rate loss: One of them to increase the modulation rate if the channel permits bandwidth expansion, the other is to enlarge the signal set of the modulation system. But, these methods are not suitable for some band-limited channels such as telephone channels, so that good results couldn't be obtained. In the last of 1970's, Ungerboeck [1],(2],[3] proposed a channel coding technique that achieves remarkable coding gains, without sacrificing the data rate or expanding the bandwidth of the transmitted signal. The basic idea consists of encoding k information bits, by means of a rate R«k/k+1 convolutional encoder, into (k+1) bits which select points from one of the 2k+1 signal constellations according to mapping by set partitioning. That is, coding and modulation are considered as an entity. This technique is known as Trellis-Coded Modulation (TCM) where coding gain is a function of the constraint length of the code and the signal constellation. Maximum likelihood soft decoding of the unquantized demodulator outputs is assumed, thus avoiding loss of information prior to final decoding. This implies that codes can be -VI-designed to achieve minimum free Euclidean distance rather than Hamming distance. Based on this distance measure more powerful codes can be designed. After introducing the TCM, research s increased on this subject. The first method for error and bit error probability upper bounds were given by Biglieri [41 for TCM. Later, Zehavi and Wolf {5J improved a better and easily applicable method for only trellis codes that have a certain symmetry property. In the Zehavi's and Wolf's method, generating function techniques for analyzing error-event and bit-error probabilities for trellis codes are considered. The conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states can not be applied directly to arbitrary trellis codes, and instead, a state diagram where the number of states is equal to the square of the number of trellis states must be used. It is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states is equal to the number of trellis states. Furthermore, the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convoiutional code with the same number of trellis states. TCM was rapidly adopted for implementation in high speed telephone-line modems in the mid-1 980's. The most advanced modulation and equalization techniques have often been developed and first implemented in telephone-line modems, because of the applicability of a linear Gaussian model, the commercial importance of the modem industry, the significance of higher data rates or improved signal-to-noise ratio (SNR) margin to the costumer and the relatively low symbol rates (2400 symbols per second) of modems. Many kinds of modems were designed till today. But, neither of these modems was standardized. By the time CCITT began to consider a standart for 9600 bps dial modems in 1983, Ungerboeck's paper had appeared and it was recognized that the 3 or more dB of coding gain that TCM could provide would be essential for reliable 9600 bps operation over the dial network. A variant of Ungerboeck's 8-state 2-dimensional code, due to Wei {6], (7] who introduced nonlinear elements into the convoiutional encoders to prevent phase rotation, was adopted in CCITT Recommendation V.32. with a coding gain of 4 dB [8], [9] and also subsequently in the V.33 standart for 14400 bps private-line modems. The binary partitions of Ungerboeck have been generalized by Calderbank and Sloane via the concept of cosets.This permits -Vil-multidimensional signal sets to be conveniently partitioned. Forney employs the coset code notation to include block codes such as lattice codes in this common framework. While the coset notation encompasses many classes of codes, including binary and Ungerboeck codes, in many cases the algebraic structure implied in the notation has no simple geometric interpretation. Thus it is convenient to apply it to a number of codes related to Ungerboeck's codes, such as those of Padovani and Wolf for phase-shift-keyed (PSK)/ frequency-shift-keyed (FSK) modulations [10] and some codes on irregular signal sets. Another bandwidth efficient coding technique is continuous- phase frequency modulation (CPFSK). The progenitor of CPFSK is the now well-known minimum shift keying (MSK) modulation scheme. Other CPFSK techniques such as multi-h, M-ary CPFSK exploit two advantages of phase continuity. First, these schemes yield transmitted signals whose spectrum falls off more sharply than noncontinuous phase schemes. Second, the requirement of the phase continuity prohibits certain sequences of signals from occuring. This prohibition results in signal sequences with greater minimum Euclidean distance as compared to uncoded modulation. Padovani and Wolf [10] designed the codes which have better coding gains than Ungerboeck's codes by using frequency/phase shift keying (FSK/PSK) modulation. As a result of all these researches, the performance attainable with practical trellis codes is now approaching to the Shannon [11] limit. For example, Ungerboeck's 256-state codes obtain effective coding gains of about 5.5 dB. But, these codes have too high decoding complexity. So, the researches focused on the codes having high coding gains and low decoding cornplexities[12],[13],[14]. The optimal decoding operation for convolutional codes requires a memory that stores a function of the entire past history of the received bit stream. The performance (as measured by error rate) of a convolutional coding system improves as the complexity allowed for the decoder is increased. Several methods of decoding convolutional codes have been developed. The optimal (maximum likelihood ) scheme is generally known as the Viterbi Algorithm. Viterbi decoding for reasonably short lengths (number of memory elements) is feasible to implement and high decoding speeds are achievable. For extremely low error probabilities, a large constraint length is required. This method finds in terms of a defined measure the symbol sequence which is closest to the received symbol sequence. This recursive procedure requires that the shortest path, called the survivor, entering at each state of the trellis be retained at time d. To proceed to time (d+1), all-time-d -VIII-survivors are extended by computing the metrics {lengths) of the extended path segments based on the calculated branch metrics, which depend on the branch symbols in the trellis and the value of the received sample. The metric of the extended path into each state are compared, and the shortest of these is isolated. This shortest length path into each state, which represents the time- (d+1) survivor, is retained. The procedure is repeated for iime- (d+2), and so on. Error control techniques using convolutional codes have been dominated by low rate R=»1/n codes. Optimal low rate codes providing large coding gains are available in the literature and practical implementations of powerful decoders such as Viterbi exist for data rates in the range of 10-40 M bits/sec. However, as the trend for ever increasing data transmission and high error performance continues while conserving bandwith, the needs arise for good high-rate R=k/n convolutional codes as well as practical encoding and decoding techniques for these codes. Unfortunately a straightforward application of Viterbi and sequential decoding to high rate codes becomes very rapidly impractical as the coding rate increases. Furthermore, a conspicuous lack of good nonsystematic long memory convolutional codes with rates R larger than 2/3 prevails in the literature. A significant breakthough occured recently with the advent of high rate `punctured` convolutional codes where the inherent difficulties of coding and decoding of high rate codes can be almost entirely circumvented. Viterbi or sequential decoding of rate k/n punctured convolutional codes is hardly more complex than for rate 1/n codes and furthermore, either technique may be easily applicable to adaptive and variable-rate decoding. A punctured code is a high rate code obtained by periodically del eti ng( i.e. puncturing) certain symbols from the output stream of a low rate encoder. The resulting high rate code depends on both the original low rate code and perforation pattern, that is, the number and positions of the punctured symbols. Cain et ai. have defined a class of punctured rate (n-1)/n convolutional codes and clarified the Viterbi decoding procedure for the punctured code. Yasuda et al. have described an optimum soft decision Viterbi decoding scheme and the configuration of a variable-rate Viterbi decoder where the various rates were obtained by deleting bits from a low-rate code in different ways. Hardware experiments and theoretical calculation showed that punctured convolutional coding and soft Viterbi decoding enable reliable communication over band-limited satellite channels. ?IX-Imai and Hirakawa [15] proposed a coded modulation scheme based on a multilevel code which admits a multistage decoder. In this method, the channel signal set is binary partitioned, using the set partitioning rule, where the binary labels of the edges from one level of the partition chain to the next are encoded by independent either block or convolutional codes. In the earliest time of their work due to the use of the block codes and hard-decision decoders, significantly coding gain could not obtained. In a multilevel coded modulation system, there is a tight connection between the Euclidean and Hamming distances. By using this propertly, Yamaguchi and Imai [16] designed systems which contain convolutional codes and soft-decision decoders and showed that these systems have high coding gains and reduced decoding complexity compored to the Ungerboeck's approach. Pottie and Taylor f17] are generalized the multilevel coding technique and showed that most of the trellis codes, in fact, are subclasses of multilevel codes, including Ungerboeck codes. From the coding point of view there are differences between the codes proposed by Pottie-Taylor and the codes proposed by Imai- Hirakawa, although ail the codes are multilevel. Pottie-Taylor and also Calderbank [16] tried to increase the coding gain by using different kinds of encoders in several levels. Error performance of multilevel codes was firstly analysized by Kofman.Zehavi and Shamai {19], [20]. As mentioned before, for the Gaussian channel, Ungerboeck's like codes achieve a remarkable coding gain when compared to uncoded modulation system with the same spectral efficiency and data rate. However, this codes often poor performance when operating over fading channels. The reason is that codes for the Gaussian channel designed to achieve mainly a large minimum Euclidean distance, where as for fading channels, such as Rician and Rayieigh fading channels or channels distributed by jamming and impuls noise, a good error probability performance demands both large Euclidean distances and Hamming distances between channel signal sequences. By using this criterion Zhang, Vucetic [21] and also Kofman et. al. [22] investigated error probability of multilevel systems for fading channels. On the other hand, Kasami et. al. [23] investigated the multilevel technique for combining block coding and modulation. At this investigation, first, a general formulation was presented for multilevel modulation codes in terms of component codes with -X-appropriate distance measures. Then a specific method for constructing multiievet block modulation codes with interdependency among component codes was proposed, in addition a technique was presented for analyzing the error performance of block modulation codes for Gaussian channels based on soft decision maximum likelihood decoding. In this thesis, by using multilevel coding and multistage decoding techniques explained above (Pottie-Taylor coding and Imai-Hirakawa coding) new systems are constructed for 8-PSK, 32- CROSS and 2FSK/4PSK modulations. For the 8-PSK modulation, by using convolutional codes and punctured convolutional codes in the several levels, multilevel systems with rate 2/3 are designed and comparisons are done for the coding gains, decoding complexitiys and error performances with respect to the Ungerboeck's technique. By using a computer simulation model, error probabilities of the Ungerboeck and multilevel systems are compared. On the other hand, the code structure of the V.32 modem using 32-CROSS modulation at rate 9600 bit/s were designed by the multilevel Imai- Hirakawa coding technique and comparisions are given. The FSK/PSK modulation which use several carrier frequencies and phases is very suitable for multilevel coding technique due to the large minimum Euclidean distance at the first partitioning step. So, multilevel coding technique is applied to 2FSK/4PSK modulation and new systems are compared to the Padovani-Wolf systems. It is shown that the new systems have better error performances and reduced decoding complexities. In the second chapter of the thesis, Trellis Coded Modulation technique is explained, error performance and decoding complexity concepts are defined. Chapter 3 is destinated to the presentation of the multilevel coding and multistage decoding. The multilevel Pottie-Taylor coding and Imai-Hirakawa coding approaches are explained and the decoding complexity related to these schemes are defined. Also, the error performance of the Imai-Hirakawa coding technique is analysed. In the fourth chapter, 2FSK/4PSK modulation that uses two different carrier frequencies and four phases is presented. Multilevel systems with rate 2/3 based on several convolutional codes are designed. The analytical error performance calculations are also done and the upper bound curves of several related system are compared..XI- 174

ÖZET Bu tezde, sayısal İletişim sistemlerinin verici ve alıcıları arasında çeşitli bozucu etkenlerin sonucu olarak ortaya çıkan faz kaymasının kafes kodlamalı sistemlere etkisi ele alınmış, bu sistemlerin sözedilen etkilere olan duyarlılıkları azaltma amaçlı çalışmalar incelenmiştir. Karma modülasyon kullanılarak tasarım yöntemi 4/2-PSK ve 16/8-PSK sistemlerine uygulanarak literatürde 4/ 8-PSK. sis temi için verilen sonuçlar genelleştirilmiş, serbest Öklid uzaklığını maksimum yapan karma kafes yapılar tasarlanmış tır. Sabit faz kayması varsayımı altında ve istatistiksel bir modele dayanarak faz seyirmesi altında karma sistemlerin bata başarından incelenerek, klasik kafes kodlamalı ve kodlamasız sistemler ile karşılaştırmalar yapılmıştır. Oluşturulan bir bilgisayar benzetim modelinin yardımı ile klasik ve karma sistemlerin alıcılarına ilişkin faz izleme başarımını yansıtan S-eğrileri elde edilerek faz kaymasına ilişkin başarım araştırmaları bu doğrultuda yapılmıştır. SUMMARY mSPECTIOH OF TOE phase aübiguhes nr trellis coded SYSTEMS AND SEDUCING ITS EFFECTS BY HEANS OF HYHBID TRELLIS STKÜCTÖHES In digital communication system design the main purpose is to increase the error performance in transmitting binary data sequences and the function of modulation and error correction coding are separated Conventional encoders and decoders for error correction operate on binary code symbols transmitted over a discrete channel. With a code of rate k/n. n-k redundant check symbols are appended to every k information symbols. Since the decoder receives only discrete code symbols. Hamming distance is the appropriate measure of distance for decoding, the rate loss is occured by sending redundant check symbols. Generally, there exist two posibilities to compensate for the rate loss; increasing the modulation rate if the channel permits bandwidth expansion, or enlarging the signal set of the modulation system if the channel is band limited. However, when modulation and error-correction coding are performed in the clasical independent manner, dissappointing results are obtained. Trellis coded modulation (TCM) is involved by Ungerboeck [1],[2] as combined coding and modulation technique for digital transmission over band limited channels its main attraction is the achievement of significant coding gains over conventional uncoded multilevel modulation without compromising bandwidth efficiency. The Viterbi algorithm (YA) was proposed in 196? as a method of decoding convolutional codes. Since that time, it has been recognized as an attractive solution to a variety of digital estimation problems, somewhat as the Kalman filter has been adapted to a variety of analog estimation problems. Like the Kalman filter, the VA tracks the state of a stochastic process with a recursive method that is optimum in a certain sense, and that lends itself readily to implementation and analysis. However, the underlying process is assumad to be fi nite state Markov rather than Gaussian, which leads ; to marked differences in structure. Decoding is assumed to be by the VA, a maximum like lihood sequence estimation pro cedure for any trellis code. The complexity of such a de coder is roughly proportional to the number of encoder VIÖZET Bu tezde, sayısal İletişim sistemlerinin verici ve alıcıları arasında çeşitli bozucu etkenlerin sonucu olarak ortaya çıkan faz kaymasının kafes kodlamalı sistemlere etkisi ele alınmış, bu sistemlerin sözedilen etkilere olan duyarlılıkları azaltma amaçlı çalışmalar incelenmiştir. Karma modülasyon kullanılarak tasarım yöntemi 4/2-PSK ve 16/8-PSK sistemlerine uygulanarak literatürde 4/ 8-PSK. sis temi için verilen sonuçlar genelleştirilmiş, serbest Öklid uzaklığını maksimum yapan karma kafes yapılar tasarlanmış tır. Sabit faz kayması varsayımı altında ve istatistiksel bir modele dayanarak faz seyirmesi altında karma sistemlerin bata başarından incelenerek, klasik kafes kodlamalı ve kodlamasız sistemler ile karşılaştırmalar yapılmıştır. Oluşturulan bir bilgisayar benzetim modelinin yardımı ile klasik ve karma sistemlerin alıcılarına ilişkin faz izleme başarımını yansıtan S-eğrileri elde edilerek faz kaymasına ilişkin başarım araştırmaları bu doğrultuda yapılmıştır.SUMMARY mSPECTIOH OF TOE phase aübiguhes nr trellis coded SYSTEMS AND SEDUCING ITS EFFECTS BY HEANS OF HYHBID TRELLIS STKÜCTÖHES In digital communication system design the main purpose is to increase the error performance in transmitting binary data sequences and the function of modulation and error correction coding are separated Conventional encoders and decoders for error correction operate on binary code symbols transmitted over a discrete channel. With a code of rate k/n. n-k redundant check symbols are appended to every k information symbols. Since the decoder receives only discrete code symbols. Hamming distance is the appropriate measure of distance for decoding, the rate loss is occured by sending redundant check symbols. Generally, there exist two posibilities to compensate for the rate loss; increasing the modulation rate if the channel permits bandwidth expansion, or enlarging the signal set of the modulation system if the channel is band limited. However, when modulation and error-correction coding are performed in the clasical independent manner, dissappointing results are obtained. Trellis coded modulation (TCM) is involved by Ungerboeck [1],[2] as combined coding and modulation technique for digital transmission over band limited channels its main attraction is the achievement of significant coding gains over conventional uncoded multilevel modulation without compromising bandwidth efficiency. The Viterbi algorithm (YA) was proposed in 196? as a method of decoding convolutional codes. Since that time, it has been recognized as an attractive solution to a variety of digital estimation problems, somewhat as the Kalman filter has been adapted to a variety of analog estimation problems. Like the Kalman filter, the VA tracks the state of a stochastic process with a recursive method that is optimum in a certain sense, and that lends itself readily to implementation and analysis. However, the underlying process is assumad to be fi nite state Markov rather than Gaussian, which leads ; to marked differences in structure. Decoding is assumed to be by the VA, a maximum like lihood sequence estimation pro cedure for any trellis code. The complexity of such a de coder is roughly proportional to the number of encoder VIÖZET Bu tezde, sayısal İletişim sistemlerinin verici ve alıcıları arasında çeşitli bozucu etkenlerin sonucu olarak ortaya çıkan faz kaymasının kafes kodlamalı sistemlere etkisi ele alınmış, bu sistemlerin sözedilen etkilere olan duyarlılıkları azaltma amaçlı çalışmalar incelenmiştir. Karma modülasyon kullanılarak tasarım yöntemi 4/2-PSK ve 16/8-PSK sistemlerine uygulanarak literatürde 4/ 8-PSK. sis temi için verilen sonuçlar genelleştirilmiş, serbest Öklid uzaklığını maksimum yapan karma kafes yapılar tasarlanmış tır. Sabit faz kayması varsayımı altında ve istatistiksel bir modele dayanarak faz seyirmesi altında karma sistemlerin bata başarından incelenerek, klasik kafes kodlamalı ve kodlamasız sistemler ile karşılaştırmalar yapılmıştır. Oluşturulan bir bilgisayar benzetim modelinin yardımı ile klasik ve karma sistemlerin alıcılarına ilişkin faz izleme başarımını yansıtan S-eğrileri elde edilerek faz kaymasına ilişkin başarım araştırmaları bu doğrultuda yapılmıştır.SUMMARY mSPECTIOH OF TOE phase aübiguhes nr trellis coded SYSTEMS AND SEDUCING ITS EFFECTS BY HEANS OF HYHBID TRELLIS STKÜCTÖHES In digital communication system design the main purpose is to increase the error performance in transmitting binary data sequences and the function of modulation and error correction coding are separated Conventional encoders and decoders for error correction operate on binary code symbols transmitted over a discrete channel. With a code of rate k/n. n-k redundant check symbols are appended to every k information symbols. Since the decoder receives only discrete code symbols. Hamming distance is the appropriate measure of distance for decoding, the rate loss is occured by sending redundant check symbols. Generally, there exist two posibilities to compensate for the rate loss; increasing the modulation rate if the channel permits bandwidth expansion, or enlarging the signal set of the modulation system if the channel is band limited. However, when modulation and error-correction coding are performed in the clasical independent manner, dissappointing results are obtained. Trellis coded modulation (TCM) is involved by Ungerboeck [1],[2] as combined coding and modulation technique for digital transmission over band limited channels its main attraction is the achievement of significant coding gains over conventional uncoded multilevel modulation without compromising bandwidth efficiency. The Viterbi algorithm (YA) was proposed in 196? as a method of decoding convolutional codes. Since that time, it has been recognized as an attractive solution to a variety of digital estimation problems, somewhat as the Kalman filter has been adapted to a variety of analog estimation problems. Like the Kalman filter, the VA tracks the state of a stochastic process with a recursive method that is optimum in a certain sense, and that lends itself readily to implementation and analysis. However, the underlying process is assumad to be fi nite state Markov rather than Gaussian, which leads ; to marked differences in structure. Decoding is assumed to be by the VA, a maximum like lihood sequence estimation pro cedure for any trellis code. The complexity of such a de coder is roughly proportional to the number of encoder VIÖZET Bu tezde, sayısal İletişim sistemlerinin verici ve alıcıları arasında çeşitli bozucu etkenlerin sonucu olarak ortaya çıkan faz kaymasının kafes kodlamalı sistemlere etkisi ele alınmış, bu sistemlerin sözedilen etkilere olan duyarlılıkları azaltma amaçlı çalışmalar incelenmiştir. Karma modülasyon kullanılarak tasarım yöntemi 4/2-PSK ve 16/8-PSK sistemlerine uygulanarak literatürde 4/ 8-PSK. sis temi için verilen sonuçlar genelleştirilmiş, serbest Öklid uzaklığını maksimum yapan karma kafes yapılar tasarlanmış tır. Sabit faz kayması varsayımı altında ve istatistiksel bir modele dayanarak faz seyirmesi altında karma sistemlerin bata başarından incelenerek, klasik kafes kodlamalı ve kodlamasız sistemler ile karşılaştırmalar yapılmıştır. Oluşturulan bir bilgisayar benzetim modelinin yardımı ile klasik ve karma sistemlerin alıcılarına ilişkin faz izleme başarımını yansıtan S-eğrileri elde edilerek faz kaymasına ilişkin başarım araştırmaları bu doğrultuda yapılmıştır. 103

Multi-Frequency Modulation has been the topic of several papers at NPS. In past systems the majority of time required for the generation of the MFM signal was due to the software routine used to implement the FFT. In this report a Digital Signal Processor was used to reduce the time needed to generate the FFT. The use of Trellis coding and Viterbi decoding on a Digital Signal Processor was also investigated. Assembly language programs for three encoder/ decoder systems were developed. The first uses a 16 QAM signal, the second uses a 2/3 rate convolutional encoder and Viterbi decoder and the third uses the V.32 convolutional encoder and a Viterbi decoder. http://archive.org/details/implementationof1094530967 Lieutenant, United States Navy Approved for public release; distribution is unlimited.

ÖZET Bu tez çalışmasında çoklu kafes kodlamalı modülasyon tekniğinin dik genlik modülasyonlu (QAM) işaretlere uygulanması problemi ele alınmıştır. Tasarlanan iki durumlu çoklu kafes kodlamalı QAM sistemin, klasik kafes kodlamalı QAM sisteme göre üstünlükleri araştırılmış, her iki sistemin hata başarım sınırları analitik yöntemlerle hesaplanmıştır. Ayrıca bir bilgisayar benzetim modeli oluşturularak elde edilen sonuçlarla yukarda adı geçen sistemlerin hata başarım değerleri işaret - gürültü oranına göre çizilmiştir. Sonuç olarak çoklu kafes kodlamalı tekniğe göre tasarlanan 16-QAM sistemin hata başarımının kafes kodlamalı tekniğe göre daha iyi olduğu görülmüş ve elde edilen sonuçlar verilmiştir. SUMMARY DESIGN AND PERFORMANCE ANALYSIS OF QUADRATURE AMPLITUDE MODULATED SIGNALS BASED ON MULTIPLE TRELLIS CODED MODULATION TECHNIQUE In this thesis, multiple trellis coded modulation technique is applied to quadrature amplitude modulation (QAM) signals. The limits of error performance is computed for multiple trellis coded QAM signals with an analytical method. In addition, a computer simulation model is given to determine how much improvement of error performance is provided by multiple trellis coding technique with respect to classical trellis coding technique. In digital communication system design the main purpose is to increase the error performance in transmitting binary data sequences and the function of modulation and error-correction coding are separated. Conventional encoders and decoders for error correction operate on binary, code symbols transmitted over a discrete channel. With a code of rate k/n, n-k redundant check symbols are appended to every k information symbols. Since the decoder receives only discrete code symbols, Hamming distance is the appropriate measure of distance for decoding. The rate loss is occured by sending redundant check symbols. Generally, there exist two posibilities to compensate for the rate loss: increasing the modulation rate if the channel permits bandwidth expansion, or enlarging the signal set of the modulation system if the channel is band limited. However, when modulation and error- correction coding are performed in the clasical independent manner, dissappointing results are obtained. Trellis coded modulation (TCM) is envolved by Ungerboeck [1], [2], [3] as a combined coding and modulation technique for digital transmission over band limited channels. Its main attraction is the achievement of significant coding gains over conventional uncoded VImultilevel modulation without compromising bandwidth efficiency. TCM schemes employ redundant nonbinary modulation in combination with a finite state encoder which governs the selection of modulation signals to generate coded signal sequences. In the receiver, the noisy signals are decoded by a soft-decision maximum-likelihood sequence decoder. Simple TCM schemes can improve the robustness of digital transmission against additive noise by 3 dB compared to conventional uncoded modulation. With more complex TCM schemes, the coding gain can reach 6 dB or more. These gains are obtained without bandwidth expansion or reduction of the effective information rate as required by traditional error-correction schemes. Signal waveforms representing information sequences are most impervious to noise-induced detection errors if the are very different from each other. Mathematically, this translates into the requirement that signal sequences should have large distance in Euclidean signal space. The essential new concept of TCM that led to the above mentioned gains was to use signal-set expansion to provide redundancy for coding and to design coding and signal-mapping functions jointly so as to maximize directly the `free distance` (minimum Euclidean distance) between coded sequences. This allowed the construction of modulation codes whose free distance significantly exceeded the minimum distance between uncoded modulation signals at the same information rate, bandwidth and signal power. In TCM schemes, the trellis branches are labeled with redundant nonbinary modulation signals rather than with binary code symbols. Divsalar, Simon and Yuen [4], [5], [6] envolved trellis coding with asymmetric modulation technique by designing the signal constellations to be asymmetric. This technique provides a performance gain over the traditional symmetric constellations combined with trellis coding. Divsalar and Simon [7], demonstrated trellis coded modulation technique referred to as multiple trellis coded modulation (MTCM) which is capable of achieving asymptotic performance gains without resorting to modulation asymmetry. In addition this technique circumvents the problem of code catastrope. The principle is to design a rate nk/(n + l)k (k=2,3,4,...) encoder and combine it a suitable mapping function with a 2n+1 point VII -signal constellation outputting k of these signal points in each transmission interval. Since, in each transmission interval, kn bits enter the encoder and k symbols leave the modulator, thre exist a unity bandwidth expansion relative to an uncoded 2n-point uncoded systems. It is important that values of k greater than 1 (k = 1 corresponds to the conventional TCM systems) for certain cases produce increased values of dfree with symmetric modulations. Trellis coded modulation (TCM) refers to the technique wherein a rate n/(n + l) trellis code is combined with an 2n+ point signal constellation to produce a coded modulation which has no bandwith expansion relative to an uncoded 2n point modulation of the same type yet gives significant performance improvement. Traditionnally, TCM systems have employed symmetric signal constellations, uniformly spaced signal points. Although symmetric signal constellations are optimum for uncoded systems, the same is not necessarily true for TCM. In fact, it has been shown [4], [5], [6] that by designing the signal constellations to be asymmetric, in many instances, obtain a performance gain over the traditional symmetric TCM designs. The measure of performance gain and the amount of it achieved is, in general, a function of many factors, namely, signals to noise ratio (SNR), complexity of the trellis encoder (number of trellis code states), and the number of modulation levels. For TCM systems, an asymptotic measure of performance gain is the comparison of the minimum free Euclidean distance d of the trellis code relative to the minimum distance d. of the uncoded modulation. In certain cases of asymmetry, the asymptotic improvement as measured d can only be achieved in free the limit as points in the signal constellation merge together. Trellis code becomes catastrophic. Multiple trellis coding, wherein more than one channel symbol per trellis branch is transmitted, has been shown to yield a performance gain with symmetric signal sets, comparable to that previously achieved only with signal constellation asymmetry. The advantage of multiple trellis coding over the conventional trellis coded asymmetric modulation technique is that the potential for code catastrophe associated with the latter has been eliminated. VIIIBiglieri [9] presented a generating function method which enumarates all possible incorrect paths for all possible correct paths, for trellis codes. The generalized generating function can be obtained as the transfer function of a state diagram regarded as a signal flow graph. The state diagram is defined over an expanded set of states, namely 2 v, where 2V is the number of states in the trellis and v is the memory of the code. Since the number of the states grows exponentially with 2v rather than v, this method is only useful for very simple codes. Zehavi and Wolf [10] designed a generating function method which can be applied to a special class of trellis codes. For this class of codes the error weight distribution, the error event probability, and the bit-error event probability can be bounded by a generating function of a state diagram containing 2V states. The generating function usually denoted by T(W,L,I), is derived from the state diagram of the code and contains in a closed form all of the weight distribution properties of the code. This method can be applied to many important codes, including Ungerboeck codes and Calderbank-Mazo codes. The basic principles of TCM were published in 1982. Further descriptions followed in 1984 and coincided with a rapid transition of TCM from the research stage to practical use. In 1984, a TCM scheme with a coding gain of 4 dB was adapted by the International Telegraph and Telephone Consultative Committee (CCITT) for use in new high speed voiceband modems. Prior to TCM, uncoded transmission at 9.6 kbit/s over voiceband channels was often considered as a practical limit for data modems. Since 1984, data modems have appeared on the market which employ TCM along with other improvements in equalization, synchronization, and so forth, to transmit reliably over voiceband channels at rates of 14.4 kbit/s and higher. Similar advances are being achieved in transmission over other bandwith - constrained channels. The common use of TCM techniques in such applications, as satellite, terrestrial microwave and mobile communications, in order to increase throughput rate or to permit satisfactory operation at lower signal to noise ratios, can be safely predicted for the near future. In section 2 the trellis coded modulation technique is presented and the basic principles are determined. The IXdifferences of this technique from the classical error correction coding are explained. The design of PSK and QAM signals based on TCM technique are shown. In section 3 the multiple trellis coded modulation technique and the improvement with respect to the classical trellis coded modulation are explained. In section 4 the design of 16-QAM system based on the multiple trellis method is given and compared to the classical trellis coded 16-QAM system. In section 5 upper bounds on the error event and the bit error probabilities for multiple and classical trellis coded 16-QAM systems are obtained with an analytical method and a comparision is given. For the same error probability a reduction of 1.25 dB in the signal to noise ratio (SNR) is provided by the MTCM method. In section 6 a computer simulation model is given for systems mentioned in section 5. The error performance obtained in the simulation study show that the multiple TCM technique provides an improvement for the 16-QAM signals with respect to the classical TCM. 88

İV ÖZET Bu çalışmada ilk olarak» daha yüksek hızda veri iletim olanağı sağlayan kafes kodlu modül asyon tekniğinin gelişimi kısaca anlatılmıştır. Modemler hakkında genel bir bilgi verilmiş ve tipleri hakkında açıklamalar yapılmıştır. CCITT V32 modeminin özellikleri verilmiş ve modül asyon ve demodülasyon işlemleri anlatılmıştır. Daha sonra, kafes kodlu modül asyonun yapısı ve temel kavramları anlatılmıştır. 9600 bps'lik V32 modeminde seçimli olarak kullanılmakta olan 90 'lik dönmeyle değişmeyen geri beslemeli kodlar için kurallar verilmiş, tasarım adımları açıklanmıştır. Alıcıda demodülasyon sırasında oluşan işaret elemanları dönmelerinin giderilmesinde kullanılan farksal kodlama yöntemi an latı lmı ştı r. İdeal olmayan iletim kanalı nedeniyle oluşan simgelerarası girişim anlatılmış ve giderme çaresi olarak uyar 1 amali dengeleyicilere giriş yapılmıştır. Bu çalışmada kullanılan ve dengeleyici çıkışında oluşan karesel ortalama hatayı en aza indirmeye çalışan» iki boyutlu en küçük ortalama karesel hata algoritması açıklanmıştır. Benzetim modelinde ilk olarak kanal etkisi gözönüne alınmadan çeşitli işaret gürültü oranlarına göre vi terbi kod çözme tekniği kullanılarak hata başarım eğrisi çıkarılmıştır. Daha sonra sisteme kanal eklenmiş ve getirdiği bozucu etkiyi giderebilmek için ayrıca bir uyar lamalı dengeleyici alıcı girişine yerleştirilmiştir. Bu durumda karar devresinde elde edilen hatanın iterasyon sayısına göre değişim eğrileri, kanal ve dengeleyici çıkış işaret eğrileri çizdirilmiş ve dengeleyicin sistemin çeşitli işaret gürültü oranları için hata başarım eğrisi çıkarılmıştır. SUMMARY PERFORMANCE ANALYSIS OF V.32 MODEM Developments in semiconductor technology cause many theoretical digital signal processing techniques be used in practice and as a result of this, digital systems are preferred to analogue systems. Low speed modems desi gned accor di ng to phase and frequency modulation principle at the beginning» are developed according to ways having higher error per for mance. In this study, the structure of a CCITT V32 modem using trellis coded modulation technique is investigated and a communication system consisting this modem is studied for error performance by computer simulation. The trellis coded modulation technique in channels with limited bands had been first introduced by Ungerboeck, which gives better results, has taken its place in today's data communication systems. In this way, coding and modulation processes are considered as a whole. The excess obtained by expanding the signal set to be transmitted, as in con vol uti onal encoders, is used to enlarge the free Euclid distance between signal sequences. In receiver, by using Vi terbi decoder, trellis coded modulation signals are directly processed. State transitions in encoder structure are determined from modulated channel signals and, thus, instead of free Hamming distance, free Euclid distance is becoming the measure for performance.. Ungerboeck, has shown that, for PSK and QAM systems, with trellis structures increasing transmitted signal set element number by double, 3-4 dB coding gains can be obtained.VI Lee-Fang Wei, by designing binary encoders transparent to 90* 180*270° phase ambiguities, matching binary sequences in accordance with channel signals has shown that those ambiguities can be eliminated. By using such coding techniques it is possible to transmit data in higher speeds with the same band width. In recommandations published by CCITT, the error performance of high speed modems are increased in this way. It is true that the telephone network is the most common network today. Therefore, this network is also used for other communication means other than telephone conversations. Most important among them is no doubt, the data communication. But telephone network is not suitable for digital systems to be connected directly. This is because, that this network is suitable for transmitting only the frequency band 300-3400 Hz, cannot transmit direct current and due to the group delay properties the impulse shapes are disturbed. The modems are used to convert digital signals to voiee frequency signals. By using various techniques, the bit speed can be hold faster than line transmission speed. Basis of information packaging is corresponding one modulation step to a sequence of bits, instead of one bit. Information packed like this shall be decoded on the receiving side. Modulation being multilevel causes modulation steps to be reduced and as a result the signal to noise ratio is reduced. It becomes possible to reach data speeds, which are under normal conditions not transmit t able on telephone channels, by keeping speed low on line. Such procedures are used in modems working% at 2400 bps or higher speeds. In CCITT V32 modem, coming 4 bits data sequence is changed into a two-dimension transmission signal by using trellis coding modulation technique. In order to supply the uniform distribution of signal to frequency area before this transformation, the data coming to modem is put through a scrambler. In this modem, where data speed is 9600 bps and transmission speed is 2400 symbol /s, the transmitted signal occupies the whole telephone band and therefore the seperation of channels is supplied by echo cancelling techniques.vıı In part three, the trellis coded modulation technique is investigated and basic notions are given. In technique of trellis coded modulation, information is modulated by an encoder with finite states and the signal received at receiver is turned to its original state by a sequance of decoders. In this modulation technique, by using expanded signal sets, coding and signal mapping processes are applied making the minimum Euclid distance between signal sequences the largest. Using this type of sturueture causes the distances between signals grow significantly even the same information speed, band width and signal power is used. The reason for use of trellis term is that those systems can be described with similar state transition diagrams to trellis diagrams in binary con vol uti onal codes. The difference in trellis ceded modulation is that modulation signals are corresponded to trellis branches instead of binary numbers. Convol uti onal channel coding with expanded signal space is a technique improving error performance of synchronous data transmission without limiting data speed or requiring broad band width. Generally speaking, this coding technique consist of applying m data bit groups to the Input of a finite state machine. This machine expands each input group to m+1 bit groups by keeping some specific bits stored in encoder and being in conformity with predetermined logical combi nati ons. This coding technique, being a special case of convol uti onal codes, is realized by mapping on grouped signal sets. Signal subsets are determined so that the distance between them is largest. This process depends on the principle of dividing signal set into smaller subsets and thus increasing distance between elements in set. Vi terbi algoritm used in decoding binary convol uti onal codes is also used in trellis coded modulation procedure. In this algoritm, decoding operation is started after a certain sequence length of signals are received. This means, a decision operation is not done as soon as the signal is received. This sequence length is called code decoding depth and determined by designer. It is clear that to choose this parameter as big as possible shall reduce the error during decoding.VI 1 1 Since the minimum Euclid distance between valid signal elements is increased, coding gain occours. Against this advantage, phase ambiguities during obtaining carrier signal in receiver demodulation cause received signal elements be rotated according to transmitted ones. This causes errors in sequentially received data and system's performance is reduced. As it is used to be, the problem of phase ambi qui ties can be solved by differential coding technique. Here differential coding technique is applied to convol uti onal channel coding technique and by this, obtained cedes are not effected by signal element rotations. If it is supposed that the Gauss noi se is added to the channel, si nee at the receiver decoding operation is done by Vi terbi algoritm, system's error probability is limited by free distance from bottom. In part four, disturbances in signals due to non -ideal transmission channel and eliminating methods are given. In telephone networks, characteristics of line to be connected and the number of exchanges are not known previously. When the trasnsmission speed rises, the changes in average characteristics in used channel may prevent healthy transmission. For this reason in high speeds, in order to prevent inter symbol interference adaptive equalizers shall be used. Adaptive equalizers in basic are digital filters, whose cofficient can be adjusted according to a determined a proximity measure. By using such filters, the opposite of telephone channel characteristic is approached and the total frequency characteristic of transmission media is straightened. Intersymbol interference is reduced to minimum. For this reason various adapted stabilizing methods are developed. Before starting data transmission, by sending a suitable signal sequence the stabilizer coefficients are determined. Since the channel properties are not known previously, by measures in receiver it is possible to proximate the stabilizer coefficients to most suitable values step by step. According to different ways of calculating coefficients, different stabilizing methods are obtained. In method of the least mean square error, the mean square error occured at the output of equalizer is tried to be minimized. In systems quadrature amplitude modulation is used, the signal is divided among twoIX carriers which has QO° phase difference. For this reason in systems using this modulation technique, channel and equalizer are modeled as a complex function. In part five, in order to study the error performance of this this modem a simulation model is constructed. First of all, by using this model, error performance of channels with Gauss noise is examined. In this examination modulation and demodulation operations and channel 's disturbing effect have not been considered. In second part of simulation, effect of transmission channel has been considered and by using an adaptive equalizer this disturbing effect has been tried to be eliminated. After adding channel and adaptive equalizer to the system, for ideal and disturb channel, the change of equalizer's mean square error with iteration number is studied and equalizer's input and output signals has been plotted in two dimensional plane. In the system with channel and equalizer, for ideal and disturbing channel, the change of error performance with signal to noise ratio has been examined. 108

ÖZET Bu tezde, sayısal haberleşme sistemlerinin hata ba şarımlarının yükseltilmesine yönelik olarak son yıllarda ortaya atılan kafes kodlamalı modülasyon yöntemi hat kod- lamalı temelband sayısal sistemlere uygulanmaktadır. R=n/n+l (n=l,2,3,) kodlama oranları için, kaynaktan üreti len her ikili teri dizisine, kodlayıcı kafes yapısına bağ lı olarak, 2 elemanlı hat kodu alfabesinden n+1 uzun luklu bir üçlü (+,0,-) hat kodu karşı düşürülmektedir. Kodlayıcı sonlu durumlu bir sistem olarak ele alınmakta, kod sözcükleri temelband iletişim gereksinimlerinin sağ lanması amacıyla tasarlanan bir durum geçiş modeline göre seçilerek durumlara atanmaktadır. Viterbi algoritmasıyla kod çözüleceği varsayılarak sistemin hata başarımı, kodla yıcının ürettiği üçlü simge dizileri arasındaki Öklid uzaklığı artırılarak düzeltilmekte, kafes kodlamasız duru ma göre 3-4.77 dB lik kodlama kazançları sağlanmaktadır. Kafes yapıda hat kodlarının analitik olarak ifade edilebi lecekleri gösterilmekte, serbest Öklid uzaklıklarının he saplanmasını sağlayan bir algoritma verilmektedir. Doğru sal olmayan R=l/2 ve R=3/4 oranlı hat kodlarının, hata ağırlıkları açısından simetrik bir yapıya sahip oldukları ortaya çıkarılmakta, buna dayanarak hata olasılıkları için analitik üst sınır ifadeleri verilmektedir. Kodlar, güç spektral yoğunlukları ve seyirme başarımları açısından in celenmektedir. SUMMARY DESIGN OF NEW LINE CODES IN BASEBAND TRANSMISSION SYSTEMS BASED ON TRELLIS CODING TECHNIQUE In recent years, `trellis coded modulation` (TCM) method for improving the error performance of band-limited digital communication systems has found a large application area in M-AM, PSK and QAM systems. The detection errors caused by the channel noise can be lowered by increasing the distance between channel signals. The trellis coded modulation method assumes the coding and modulation operations as an entity and uses the redundancy obtained by expanding the signal set in order to increase the minimum distance between coded channel signal sequences. At the receiver, the Viterbi decoder operates directly on the received channel signal sequences instead of the corresponding binary sequences. Then, the code design problem turns out to be searching the encoders with good Euclidean distance properties instead of the encoders with good Hamming distance properties. At the same information rate, important coding gains were obtained without bandwidth expansion. Signal set con taining twice the necessary channel signals is used according to a finite-state encoder, thus, for M-AM, PSK and QAM systems, coding gains of 3-4 dB are obtained by means of simple trellis structure. Coding gains up to 6 dB are possible using more complex trellis codes. In this thesis, the trellis coded modulation method is applied to the line coded baseband transmission systems. In baseband digital transmission systems, the signal to be transmitted must have zero direct-current (dc) component in order to avoid any dc power feeding over the line, must have small power spectral components a.t low frequencies to reduce low-frequency noise and ufficient timing content to provide the extraction of lock information. If the baseband digital signal is a1 si c. transmitted as a binary unipolar sequence, these requirements are not satisied. For this purpose, line requirements are not satısıea. tor tnxs purpose, line coding techniques are used. A line encoder transforms binary sequences feeded at rate R bit/sec, to its input, to R' symbol/sec rate L-level (L>2) sequences at its out put and provides a redundancy of R'log~ L-Rİog2 2 in information rate. This redundancy is used in order to fulfil the basic requirements cited above. Existing line encoders provide the desirable properties due to their finite-state structure without increasing the free Euclidean distance between sequences they produce. If theViterbi decoding is assumed, the system error performance is lower-bounded relative to the free Euclidean distance of the encoder as follows: P(e) â N(ds)Q(ds/2a) 2 where a represents the variance of Gaussian noise process and K the average number of errors with distance dc, Q(.) is the Gaussian error function. s` The free Euclidean distance of a trellis encoder is the minimum Euclidean distance between sequence of pairs starting at a common state in the trellis and going over distinct states until ending at a common state, k. mi denoting i th symbol of the codeword km at the m th step, the free distance is given as -m d_ = min {Z ( £ d2(k., k*.))}1/2 s r i i /r t f i - t mı m:L {^m}^m} m 1=1 2 Here d (...) is the squared Euclidean distance between two channel symbol. In this work, the basic requirements for baseband digital signal transmission and the error performance improvement by increasing the number of channel signals are considered together. The design of the new line codes based on trellis coded modulation includes the following steps: and the restriction of the consecutive symbols w same polarity). The code alphabet must contain 2 words with zero polarity, 2n codewords with +1 codewords with -1 oolarities. and 2 2. The partitioning of the codeword alphabet to the subsets with maximum Euclidean distance, with respect to the proposed trellis encoder model. 3. The assignment of the codewords of each state- subset to the state transitions in order to maximize the minimum distance between codewords leading to the same state. On the other hand, the equally use of each codeword and the symmetric distance structure of the trellis encoder is important in order to reach the codes with optimum free distance. But, augmenting the state number of the encoder does not always leads to the codes with better distance properties. - vi -In the second chapter, a codeword assignment model for the branchs of the trellis encoder is proposed. According to this model, only codewords with disparities equal to -1,0 or 1 is used and the value of the running digital sum is restricted to values -1,0,1. For R=n/n+l, (n=l,2,3) coding rates, according to the trellis structure of the encoder, each n-length binary data sequence is encoded into a n+1 length ternary (+,0,-) line codeword chosen among the line code alphabet with 2n elements. For R=l/2 and R=3/4 rate line coding, codewords are chosen as ternary sequences produced at the output of the known paired-selected ternary (PST) encoder, in one and two steps, respectively. For R=2/3 rate, selected codewords satisfy the symmetry and distance properties best. In all cases, some codewords are used twice. This leads to partially overlapping subsets in set partitioning and to better codes than the distinct subsets case. Thus, for the same bandwidth, with some loss in data rate, the free Euclidean distance is increased by appropriate assignments of codeword subsets to the branchs of the trellis encoder. For R=l/2 rate line code, the maximum value of the free distance (d =8) is reached for four-state encoder and a coding gain of 3 dB is obtained compared to the paired- selected ternary `code. For R=2/3 rate, an eight-state encoder give the optimum solution. The reached value of the squared free Euclidean distance is equal to 6 and a coding gain of 4.77 dB is obtained compared to the uncoded case. In R=3/4 rate design, the maximum value of the free distance (d~=6) is realized with an eight-state encoder with parallel transitions. Parallel transitions mean that the last bits of binary 3-bit length sequences are not affected by the trellis coding. These last bits determine which of the two codewords in the corresponding subset will be chosen. The coding gain obtained with respect to the uncoded case is 4.77 dB and 3.52 dB with respect to the PST encoder. Further in the same chapter, it is shown that the designed line codes can be analytically expressed and a new algorithm for the calculation of free Euclidean distance between line coded sequences is developed. A com puter simulation is made for the baseband communication system with R=n/n+l rate TCM line encoders operating in an additive white Gaussian noise environment. When using the Viterbi decoding, the error-event probability is assumed as a performance criterion. It is assumed that an error event occurs if the Viterbi algorithm decides to a state which does not belong to the correct path. In terms of the error curves, it is shown that R=n/n+l (n=l,2,3) rate TCM line encoded systems have better error performance than the corresponding uncoded cases. For the convolutional codes, the free Hamming distance and the upper bounds on the error probabilities are determinated based on the state transition diagram of the encoder. Because of the linearity of these binary codes the all-zero sequence can be assumed as the correct code sequence. The generating function obtained from the state transition diagram provide the distance, step length - vii -and the number of bit errors of any incorrect sequence compared to the correct sequence. For the nonlinear trellis codes, these properties can not be obtained by the same simple approach. For a nonlinear encoder, the Euclidean distance between any incorrect sequence and the correct sequence is generally dependent upon the correct sequence. In other words, the all-zero sequence can not be assumed as the correct sequence without loss of generality. Then, the evaluation of. the upper bounds on error probabilities necessitates the analysis of very complex diagrams specially at high encoder state numbers. In Chapter 3, a method for computation of the upper bounds on error-event and bit-error probabilities of non linear trellis codes with the same complexity as the linear trellis codes is generalized for the new line encoders which have partially distinct and partially over lapping state-subsets. It is shown that R=l/2 and R=3/4 rate line encoders satisfy the error weight profile equivalency condition necessitated by this method. For these encoders, the modified generating functions are nese encoders, cne moaxriea generating xuncrions are btained from a signal-flow graph with state number equal _o the state number of their trellis diagram and the analytical expressions for the error upper bounds are O to Chapter 4 is concerned with the evaluation of power spectral densities for the new line codes proposed. For each R=n/n+l (n=l,2,3) rate, it is aimed at determine the code with minimum spectral components at low frequencies among codes having equal and maximum free distances. For R=l/2 rate, the encoder having minimal components at low frequencies is chosen among four encoders with equal and maximum free distance. For R=2/3 and R=3/4 rates, in spite of the fact that there are more than one encoder with maximum free distance, their power spectras are equal. The TCM line encoders are also compared with known line encoders. The bipolar encoder power spectra is the best at low frequencies. The new line encoders have smaller spectral components at these frequencies with respect to 4B3T, FOMOT, MS43 encoders. Only R=l/2 rate TCM encoder has smaller components than the PST encoder at frequencies around zero. In Chapter 5, the jitter performance of the base band transmission systems with line encoders based on trellis coded modulation method, is analysed. Usually, the analytical approach is not practical for the codes having complex statistical properties such as our case. There fore, in order to obtain the clock information, the base band transmission system including the TCM line encoders and a timing circuit is simulated by a computer program. The timing circuit is formed by a square-law device - viii -- IX - 91

Date of Conference: 15-18 October 1989 Conference Name: IEEE Military Communications Conference, Bridging the Gap: Interoperability, Survivability, Security, MILCOM 1989 It is known that under energy constraints it is best to have each code word of a code satisfy the constraint with equality, rather than have the constraint satisfied only in an average sense over all code words. This suggests the use of fixed-composition codes on additive Gaussian noise channels, for which the coding gains achievable by this method are significant, especially in the high signal-to-noise-ratio case. The author examines the possibility of achieving these gains by using fixed-composition trellis codes. Shell-constrained trellis codes are promising in this regard, since they can be decoded by sequential decoding at least at rates below the computational cutoff rate.