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Luca Gallarini. Le molte vite di Aldo Buzzi. Letteratura, editoria e cultura del cibo. Pisa: Edizioni ETS, 2018. Dieci anni fa scompariva, quasi centenario, Aldo Buzzi (1910-2009). Autore prolifico, penna [...]

Claudio Moreschini. Rinascimento cristiano. Innovazioni e riforma religiosa nellTtalia del quindicesimo e sedicesimo secolo. Roma: Edizioni di storia e letteratura, 2017. Claudio Moreschini ha dedicato molti studi alie eta di [...]

Giulio Busi. Michelangelo. Mito e solitudine del Rinascimento. Milano: Mondadori, 2017. Se scrivere una biografia e sempre un compito arduo, cimentarsi con quella di Michelangelo Buonarroti e impresa quasi impossibile: [...]

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In this paper we propose a semi-random technique for the generation of a class of eIRA codes (a popular class of irregular LDPC codes that can be encoded in linear time) suited to partially parallel decoder implementations. The suggested technique tries to avoid both low-weight codewords and near-codewords, which limit the performance of the belief propagation decoder. Its effectiveness is verified by comparison with literature results. The obtained codes are versatile, in terms of code-rate and block length, and they are characterized by a low error floor. Index Terms--Low-density parity-check, LDPC, minimum distance, near-codewords, parallel decoders.

The practical relevance of the proposed joint decoding approach is demonstrated within the JPEG coding standard and an iterative channel and JPEG 2000 decoder is designed and tested in the case of image transmission across the AWGN channel.

This correspondence presents an upper bound on the minimum distance of serially concatenated codes with interleaver where the inner code is a systematic recursive convolutional encoder and the outer code is any convolutional encoder. The resulting expression shows that the minimum distance of the concatenated code cannot grow more than O([K.sup.1-1/[d.sup.(O).sub.f]]), where K is the information word length, and [d.sup.(O).sub.f]) is the free distance of the outer code. The obtained upper bound is shown to agree with and, in some cases, improve over previously known results. Index Terms--Combinatorial, concatenated, convolutional, minimum distance, performance bounds, serial.

In this paper, we present an all-analog implementation of the rate-l/3, block length 40, universal mobile telecommunications system (UMTS) turbo decoder. The prototype was designed and fabricated in 0.35 [micro]m complementary metal-oxide-semiconductor technology and operates at 3.3 V. We also introduce a discrete-time first-order model for analog decoders which allows fast bit-error rate simulations, while taking into account circuit transient behavior and component mismatch. The model is applied to the rate-l/3 analog turbo decoder for UMTS defined in the Third Generation Partnership Project standard, and the discrete-time model predictions are compared with the decoder experimental performance and the transistor-level simulations. These results demonstrated that this model can be successfully used as a tool to both predict analog decoder performance and give design guidelines for complex decoders, for which circuit-level simulations are impractical. Index Terms--Analog decoding, device mismatch, discrete-time model, iterative decoding, turbo codes.

In this paper, we propose two techniques to design good S-random interleavers, to be used in parallel and serially concatenated codes with interleavers. The interleavers designed according to these algorithms can be shortened, in order to support different block lengths in such a way that all the permutations obtained by pruning, when employed in a parallel turbo decoder, are collision-free. The first technique, suitable for short and medium interleavers, guarantees the same performance of non-parallel interleavers in terms of spreading properties, simulated frame-error probabilities, and obtainable minimum distance of the actual codes. The second algorithm, to be used for large block lengths, permits achieving high degrees of parallelism at the price of a slight degradation of the spread properties, and also to change the degree of parallelism on-the-fly. The operations of a parallel turbo decoder employing these interleavers are described, and an example of the advantages of the proposed techniques is provided in a realistic system framework. Index Terms--Parallel architecture, prunable interleavers, S-random interleavers.

We deal with the design of interleavers in a coded code-division multiple-access (CDMA) scenario, where at the receiver an iterative turbo-like structure to perform multiuser detection is employed. The choice of the interleavers affects both the maximum-likelihood (ML) performance and the impact of the suboptimality of the iterative receiver. First, heuristic criteria of goodness for a set of interleavers, each assigned to a given active user, are introduced and motivated. One of these criteria is based on the intersection between the equivalent codes seen after the interleavers for each user pair. The design rules are valid for any kind of channel code. In particular, when the channel code used by every user is a terminated convolutional code, a very simple design rule, in the subset of congruential interleavers, is specified. The suitability of an interleaver set to iterative decoding is also treated. The analysis leads to a design rule which is shown to have great importance on the performance of a turbo-like receiver. Numerical results assess the validity of the derived design rules by showing that, for iterative multiuser receivers and reasonable block lengths, the suitability to iterative decoding is more important than the performance optimization. Index Terms--Coded code-division multiple access (CDMA), interleaver design, iterative multiuser receivers, permutations.

In this paper, a new upper bound on the minimum distance of turbo codes is derived. The new bound is obtained by construction of an undirected graph which reflects the characteristics of the constituent codes and the interleaver. The resulting expression shows that the minimum distance of a turbo code grows approximately with the base-3 logarithm of the information word length. The new bound is easy to compute, applies to rate [k.sub.o]/[n.sub.o] constituent encoders, and often improves over existing results. Index Terms--Minimum distance, performance bounds, permutations, turbo codes.

For high-data-rate applications, the implementation of iterative turbo-like decoders requires the use of parallel architectures posing some collision-free constraints to the reading/writing process from/into the memory. This consideration applies to the two main classes of turbo-like codes, i.e., turbo codes and low-density parity-check (LDPC) codes. Contrary to the literature belief, we prove in this paper that there is no need for an ad hoc code design to meet the parallelism requirement, because, for any code and any choice of the scheduling of the reading/writing operations, there is a suitable mapping of the variables in the memory that grants a collision-free access. The proof is constructive, i.e., it gives an algorithm that obtains the desired collision-free mapping. The algorithm is applied to two simple examples, one for turbo codes and one for LDPC codes, to illustrate how the algorithm works. Index Terms--Low-density parity-check (LDPC) codes, memory mapping, parallel implementation, turbo codes.

This correspondence deals with the design and decoding of high-rate convolutional codes. After proving that every (n, n - 1) convolutional code can be reduced to a structure that concatenates a block encoder associated to the parallel edges with a convolutional encoder defining the trellis section, the results of an exhaustive search for the optimal (n, n - 1) convolutional codes is presented through various tables of best high-rate codes. The search is also extended to find the "best" recursive systematic convolutional encoders to be used as component encoders of parallel concatenated "turbo" codes. A decoding algorithm working on the dual code is introduced (in both multiplicative and additive form), by showing that changing in a proper way the representation of the soft information passed between constituent decoders in the iterative decoding process, the soft-inpu soft-output (SISO) modules of the decoder based on the dual code become equal to those used for the original code. A new technique to terminate the code trellis that significantly reduces the rate loss induced by the addition of terminating bits is described. Finally, an inverse puncturing technique applied to the highest rate "mother" code to yield a sequence of almost optimal codes with decreasing rates is proposed. Simulation results applied to the case of parallel concatenated codes show the significant advantages of the newly found codes in terms of performance and decoding complexity. Index Terms--Block codes, convolutional codes, dual codes, high-rate codes, inverse puncturing, iterative decoding, puncturing, trellis termination, turbo-like codes.

The well-known uniform error property for signal constellations and codes is extended to encompass information bits. We introduce a class of binary labelings for signal constellations, called bit geometrically uniform (BGU) labelings, for which the uniform bit error property holds, i.e., the bit error probability does not depend on the transmitted signal. Strong connections between the symmetries of constellations and binary Hamming spaces are involved. For block-coded modulation (BCM) and trellis-coded modulation (TCM) Euclidean-space codes, BGU encoders are introduced and studied. The properties of BGU encoders prove quite useful for the analysis and design of codes aimed at minimizing the bit, rather than symbol, error probability. Applications to the analysis and the design of serially concatenated trellis codes are presented, together with a case study which realizes a spectral efficiency of 2 b/s/Hz. Index Terms--Coding, concatenated codes, constellations, encoding, labeling, trellis codes, uniform error property.

We present in this paper a novel accurate method to analyze the performance of an optical link where the amplified spontaneous emission noise, enhanced by a fiber nonlinear phenomenon called parametric gain, is the limiting factor. Our method allows us to compute the exact error probability given a generic noise spectral density at the input of a direct detection optical receiver, using arbitrary optical and electrical filters. We compare our results with those predicted using the standard Gaussian technique (based on the Q factor), showing that this approximation may lead to significant errors. Our method is then used to evaluate the impact of parametric gain on a realistic long-haul multiwavelength link operating at 10 Gb/s, showing both the system limitation imposed by this phenomenon and the inaccuracy of the Q factor method. Index Terms--BER evaluation, direct detection receiver, Karhunen-Loeve expansion, nonlinear phenomena, parametric gain, wavelength-division multiplexing.

Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the "best" recursive systematic convolutional encoders found are presented for various rates, together with the average bit-error probability performances of some turbo codes using them. Index Terms - Concatenated coding, convolutional codes, encoders, turbo codes.

A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codewords bits, and an inner encoder whose input words are the permuted outer codewords. The construction can be generalized to h cascaded encoders separated by h - 1 interleavers. We obtain upper bounds to the average maximum-likelihood bit error probability of serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer and inner encoders that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a new, low-complexity iterative decoding algorithm. Throughout the paper, extensive comparisons with parallel concatenated convolutional codes known as "turbo codes" are performed, showing that the new scheme can offer superior performance. Index Terms - Concatenated codes, iterative decoding, serial concatenation, turbo codes.

For the first time, a solution to the problem of recovering and tracking the signal constellation at the receiver side for binary and octonary digital optical transmission systems employing the modulation of polarization (POLSK) is proposed and analyzed. The effect of two recovery algorithms on the system performance is evaluated in terms of power penalty induced at P(e) = [10.sup.-9], acquisition and tracking speed, and hardware complexity. The results show that very small penalties are obtainable in practical situations by properly designing the recovery algorithms. Index Terms - Optical communications, state of polarization, synchronization recovery.

We present a theoretical framework for rotational invariance of trellis codes. The distinction between codes and encoders plays a pivotal role. Necessary and sufficient conditions for rotational invariance are derived under general assumptions, and a construction is presented that obtains a rotationally invariant encoder for almost any rotationally invariant code, independent of the code's algebraic structure. Encoders that use a differential precoder are considered as a separate case, where a system-theoretic characterization of precoding is used to find two alternative and slightly less general encoder constructions. Index Terms - Trellis codes, rotational invariance, symbolic dynamics, encoders, differential precoding.

In Part I, general results on rotationally invariant codes and encoders were derived assuming no algebraic structure. In Part II, trellis codes based on group systems are considered as a special case for which code and encoder constructions are particularly simple. Rotational invariance is expressed as an algebraic constraint on a group code, and algebraic constructions are found for both "absorbed precoder" encoders and for encoders with separate differential precoders. Finally, the various encoder forms used to achieve rotational invariance are compared based on their performance on an AWGN channel. Index Terms - Trellis codes, rotational invariance, group systems, encoders, differential precoding

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