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In recent trends, digital systems in the light of power dissipation are a crucial issue. In computing, the computational process of reversible logic is bijective and can decrease the rising issue of power dissipation. In reversible circuit design, Peres gate considered as one of the fundamental reversible gate. Therefore, a Peres gate using Add/Drop Multiplexer (ADM) and Reflective Semiconductor Optical Amplifier (RSOA) is proposed in this paper. Frequency encoding scheme and dibit-based logic are incorporated here. In long range transmission, frequency encoding bears huge benefits in respect with the other encoding techniques. This encoding technique may decrease the probability of bit error. Due to the high gain and low noise property of RSOA, the proposed design can perform operations like computation, data processing, etc. at ultra-high speed with low noise. MATLAB Simulink (R2018a) software has been used to verify the operation of the proposed design. [ABSTRACT FROM AUTHOR]

A long-standing vision of backscatter networks is to provide long-range connectivity and high-speed transmissions for batteryless Internet-of-Things (IoT). Recent years have seen major innovations in designing backscatter networks toward this goal. Yet, they either operate at a very short range, or experience extremely low throughput. This paper takes one step further towards breaking this stalemate, by presenting PolarScatter that exploits channel polarization in long-range backscatter networks. We transform backscatter channels into nearly noiseless virtual channels through channel polarization, and convey bits with extremely low error probability. Specifically, we propose a new polar code scheme that automatically adapts itself to different channel quality, and design a low-cost encoder to accommodate polar codes on resource-constrained backscatter tags. Furthermore, we devise a new metric to calculate log-likelihood ratio for accurate decoding, and present a stopping criterion of iterations to reduce decoding latency. We build a prototype PCB tag, and our experiments show that it achieves up to 11.5× throughput improvement over the state-of-the-art long-range backscatter solution. We also simulate an IC design in TSMC 65 nm LP CMOS process. Compared with traditional encoders, our encoder reduces storage overhead by three orders of magnitude, and lowers the power consumption to tens of microwatts. [ABSTRACT FROM AUTHOR]

The DNA storage channel is considered, in which a codeword is comprised of $M$ unordered DNA molecules. At reading time, $N$ molecules are sampled with replacement, and then each molecule is sequenced. A coded-index concatenated-coding scheme is considered, in which the $m$ th molecule of the codeword is restricted to a subset of all possible molecules (an inner code), which is unique for each $m$. The decoder has low-complexity, and is based on first decoding each molecule separately (the inner code), and then decoding the sequence of molecules (an outer code). Only mild assumptions are made on the sequencing channel, in the form of the existence of an inner code and decoder with vanishing error. The error probability of a random code as well as an expurgated code is analyzed and shown to decay exponentially with $N$. This establishes the importance of increasing the coverage depth $N/M$ in order to obtain low error probability. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of relaying a single bit of information across a series of binary symmetric channels, and the associated trade-off between the number of hops $m$ , the transmission time $n$ , and the error probability. We introduce a simple, efficient, and deterministic protocol that attains positive information velocity (i.e., a non-vanishing ratio $\frac {m}{n}$ and small error probability) and is significantly simpler than existing protocols that do so. In addition, we characterize the optimal low-noise and high-noise scaling laws of the information velocity, and we adapt our 1-bit protocol to transmit $k$ bits over $m$ hops with $\mathcal {O}(m+k)$ transmission time. [ABSTRACT FROM AUTHOR]

Quantum readout provides a general framework for formulating statistical discrimination of quantum channels. Several paths have been taken for such this problem. However, there is much to be done in the avenue of optimizing channel discrimination using classical codes. At least two open questions can be pointed out: how to construct low complexity encoding schemes that are interesting for channel discrimination and, more importantly, how to develop capacity-achieving protocols. This paper aims at presenting a solution to these questions using polar codes. Firstly, we characterize the information rate and reliability parameter of the channels under polar encoding. We also show that the error probability of the scheme proposed decays exponentially with the square root of the code length. Secondly, an analysis of the optimal quantum states to be used as probes is given. [ABSTRACT FROM AUTHOR]

We propose a novel approach to optimization of irregular nonbinary (NB) quasi-cyclic (QC)-LDPC codes over small alphabets. In this approach, first, the base parity-check matrices are constructed by a simulated annealing method, and then these matrices are labeled by the field elements while maximizing the so- called generalized girth of the Tanner graph. In order to analyze the performance of the constructed irregular NB LDPC codes, a new ensemble of irregular NB LDPC codes over the extensions of the binary Galois field is introduced. A finite-length random coding bound on the error probability of the maximum-likelihood (ML) decoding over the binary phase shift keying (BPSK) input AWGN channel for the new code ensemble is derived. The frame error rate (FER) performance of the sum-product belief-propagation (BP) decoding of the constructed NB QC-LDPC block codes is compared to that of both the optimized binary QC-LDPC block codes in the 5G standard and the best known NB QC-LDPC codes as well as to the derived random coding bound on the ML decoding error probability. It is shown that the obtained bound predicts the behavior of BP decoding performance of practical NB QC-LDPC codes more accurately than the BP decoding thresholds do. [ABSTRACT FROM AUTHOR]

This paper investigates the secrecy achievable region of multiple access wiretap (MAC-WT) channels where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver (or Bob for brevity) but only the confidential messages need to be protected from the eavesdropper (Eve). We first consider a discrete memoryless (DM) MAC-WT channel where both Bob and Eve jointly decode their interested messages. By using random coding, we find an achievable rate region, within which perfect secrecy can be realized, i.e., all users can communicate with Bob with arbitrarily small probability of error, while the confidential information leaked to Eve tends to zero. Due to the high implementation complexity of joint decoding, we also consider the DM MAC-WT channel where Bob simply decodes messages independently while Eve still applies joint decoding. We then extend the results in the DM case to a Gaussian vector (GV) MAC-WT channel. Based on the information theoretic results, we further maximize the sum secrecy rate of the GV MAC-WT system by designing precoders for all users. Since the problems are non-convex, we provide iterative algorithms to obtain suboptimal solutions. Simulation results show that compared with existing schemes, secure communication can be greatly enhanced by the proposed algorithms, and in contrast to the works which only focus on the network secrecy performance, the system spectrum efficiency can be effectively improved since open messages can be simultaneously transmitted. [ABSTRACT FROM AUTHOR]

Noncoherent two- and three-phase two-way relaying (TWR) techniques are bandwidth efficient and entail no pilot symbol–related rate loss. However, noncoherent two-phase TWR (2P-TWR) has not been compared with three-phase TWR (3P-TWR), and several unanswered questions remain. In this paper, we focus on the noncoherent detection of the relay with the decode-and-forward technique. For the noncoherent maximum-likelihood detector at the relay, we propose a distance measure for the transmitted signals of the two terminal nodes. For 2P-TWR, we propose that the signal constellation of one terminal node is the signal constellation of the other terminal node rotated by an angle. Using the proposed distance measure, we obtain the optimal angles and thus resolve those unanswered questions pertaining to 2P-TWR. Finally, noncoherent 3P-TWR was found to significantly outperform noncoherent 2P-TWR in simulations and distance analyses. [ABSTRACT FROM AUTHOR]

The challenge in massive Machine Type Communication (mMTC) is to support reliable and instant access for an enormous number of machine-type devices (MTDs). In some particular applications of mMTC, the access point (AP) only has to know the messages received, but not where they source from, thus giving rise to the concept of unsourced random access (URA). In this paper, we propose a novel URA scheme exploiting the elegant properties of Reed-Muller (RM) sequences. Specifically, after dividing the message of an active user into several information chunks, RM sequences are used to carry those chunks, for exploiting the vast sequence space to improve the spectral efficiency, and their nested structure to enable reliable and efficient sequence detection. Next, we further explore a novel structural property of RM sequences for designing sparse patterns which carry part of the information and serve as the hints of coupling the information chunks of a single user. The factors affecting the performance of our slot-based RM detection are characterized. Besides, the complexity of the proposed message stitching method is analyzed and compared to the commonly used tree coding approach. Our simulation results verify the enhanced performance of the proposed URA scheme in error probability and computational complexity compared to the existing counterpart. [ABSTRACT FROM AUTHOR]

It is known that continuous variable quantum information cannot be protected against naturally occurring noise using Gaussian states and operations only. Noh et al. proposed bosonic oscillator-to-oscillator codes relying on non-Gaussian resource states as an alternative, and showed that these encodings can lead to a reduction of the effective error strength at the logical level as measured by the variance of the classical displacement noise channel. An oscillator-to-oscillator code embeds K logical bosonic modes (in an arbitrary state) into N physical modes by means of a Gaussian N-mode unitary and N-K auxiliary one-mode Gottesman-Kitaev-Preskill-states. Here we ask if – in analogy to qubit error-correcting codes – there are families of oscillator-to-oscillator codes with the following threshold property: They allow to convert physical displacement noise with variance below some threshold value to logical noise with variance upper bounded by any (arbitrary) constant. We find that this is not the case if encoding unitaries involving a constant amount of squeezing and maximum likelihood error decoding are used. We show a general lower bound on the logical error probability which is only a function of the amount of squeezing and independent of the number of modes. As a consequence, any physically implementable family of oscillator-to-oscillator codes combined with maximum likelihood error decoding does not admit a threshold. [ABSTRACT FROM AUTHOR]

This study investigates the fundamental limits of variable-length compression in which prefix-free constraints are not imposed (i.e., one-to-one codes are studied) and non-vanishing error probabilities are permitted. Due in part to a crucial relation between the variable-length and fixed-length compression problems, our analysis requires a careful and refined analysis of the fundamental limits of fixed-length compression in the setting where the error probabilities are allowed to approach either zero or one polynomially in the blocklength. To obtain the refinements, we employ tools from moderate deviations and strong large deviations. Finally, we provide the third-order asymptotics for the problem of variable-length compression with non-vanishing error probabilities. We show that unlike several other information-theoretic problems in which the third-order asymptotics are known, for the problem of interest here, the third-order term depends on the permissible error probability. [ABSTRACT FROM AUTHOR]

Distributed Arithmetic Coding (DAC) is an interesting realization of Slepian-Wolf coding that performs nonlinear coset-like partition for equiprobable binary sources. Just as in other coding problems, it is a very important issue to theoretically predict the decoding error probability of DAC. This letter proposes a plausible solution to this difficult issue. Our analyses are based on the concept of coexisting interval introduced in our previous work. Specifically, we use it to deduce the probability that two given codewords coexist in the same coset. Experimental results confirm the correctness of our theoretical analyses. [ABSTRACT FROM AUTHOR]

Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error performance of polar codes in the case of block mapping and random mapping. For both the mappings, by introducing the new concept, named split polar spectrum, we derive the upper bound on the error probability of polarized channel which explicitly reveals the relationship between the diversity order $L$ and the block-wise weight distribution of the codeword. For the special case $L=2$ in the block mapping, we design the enumeration algorithm to calculate the exact split polar spectrum based on the general MacWilliams identities. For arbitrary diversity order in the random mapping, with the help of uniform interleaving, we derive the approximate split polar spectrum by combining the polar spectrum and the probability of fading pattern for a specific weight. Furthermore, we propose the design criteria to construct polar codes over the block fading channel. The full diversity criterion is the primary target to achieve the diversity gain and the product distance criterion requires to maximize the product of the block-wise Hamming distance whereby obtain the coding gain. Guided by these design criteria, the construction metrics, respectively named polarized diversity weight (PDW) and simplified PDW (SPDW) are proposed to designpolar codes in both mappings. Such simple metrics can construct polar codes with similar or better performance over those based on traditional methods in block fading channel. [ABSTRACT FROM AUTHOR]

We consider a point–to–point communication system, where in addition to the encoder and the decoder, there is a helper that observes non–causally the realization of the noise vector and provides a (lossy) rate– $ {R}_{{ \text { h}}}$ description of it to the encoder ($ {R}_{{ \text { h}}} < \infty $). In continuation to Lapidoth and Marti (2020), who derived the capacity of this model, here our focus is on error exponents. We consider both continuous–alphabet, additive white Gaussian channels and finite–alphabet, modulo–additive channels, and for each one of them, we study the cases of both fixed–rate and variable–rate noise descriptions by the helper. Our main finding is that, as long as the channel–coding rate, R, is below the helper–rate, $ {R}_{{ \text { h}}}$ , the achievable error exponent is unlimited (i.e., it can be made arbitrarily large), and in some of the cases, it is even strictly infinite (i.e., the error probability can be made strictly zero). However, in the range of coding rates $({R}_{{ \text { h}}}, {R}_{{ \text { h}}}+ {C}_{0})$ , C0 being the ordinary channel capacity (without help), the best achievable error exponent is finite and strictly positive, although there is a certain gap between our upper bound (converse bound) and lower bound (achievability) on the highest achievable error exponent. This means that the model of encoder–assisted communication is essentially equivalent to a model, where in addition to the noisy channel between the encoder and decoder, there is also a parallel noiseless bit–pipe of capacity $ {R}_{{ \text { h}}}$. We also extend the scope to the Gaussian multiple access channel (MAC) and characterize the rate sub–region, where the achievable error exponent is unlimited or even infinite. [ABSTRACT FROM AUTHOR]

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated with the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a closed-form analytical expression. For the case of having only a total-power constraint, the optimal code structure is obtained, provided that the blocklength is greater than the memory length of the channel. For the case of having only a peak-power constraint, the optimal code is derived for arbitrary memory and blocklength in the high-power regime. For the case of having both the peak-power and total-power constraints, the optimal code is derived for memoryless Poisson channels when both the total-power and the peak-power bounds are large. [ABSTRACT FROM AUTHOR]

We present the first hardware design that supports operations over the Fano–Elias encoding (FE-encoding). Our design is a combinational circuit (i.e., single clock cycle) that supports insertions, deletions, and queries. FE-encoding allows one to store f binary strings, each of length ℓ + log m using a string that is m + f + f ℓ bits long (rather than f (ℓ + log m)). The asymptotic gate-count of the circuit is Θ ((m + f) ⋅ lg m + f ⋅ ℓ). The asymptotic delay is Θ (lg m + lg f + lg ℓ). We implemented our design on an FPGA with four combinations of parameters in which the FE-encoding fits in 512 or 1024 bits. We present the first hardware design for a dynamic filter that maintains a set subject to insertions, deletions, and approximate membership queries. The design contains four main blocks: two memory banks that store FE-encodings and two combinational circuits for FE-encoding. Additional logic deals with double buffering and forwarding. We implemented the dynamic filter on an FPGA with the following parameters: (1) Elements in the dataset are 32-bit strings. (2) The supported dataset can contain up to n m a x = 45 ⋅ 2 14 = 737 , 280 elements. (3) The latency is 2-4 clock cycles. (4) Fixed (i.e., constant and stable) throughput. A new operation can be issued every clock cycle. (5) We prove that the probability of a false-positive error is bounded by 0. 385 ⋅ 1 0 − 2 . (6) We prove that the expected number of insertion failures is less than 1 for every 75 million insertions. Synthesis of our filter on a Xilinx Alveo U250 FPGA achieves a clock rate of 100 MHz (the critical path is due to the memory access). We measure a fixed throughput of 97.7 million operations per second (the loss of 2.3% in the throughput is due to instabilities in the bandwidth of the AXI4 Lite I/O channel). A unique feature of our filter implementation is that the throughput is stable and constant for all benchmarks and loads. Namely, the combination of operations does not influence the throughput and the throughput does not depend on the number of elements in the dataset (as long as the cardinality of the dataset is bounded by n m a x). Previous dynamic filter implementations in software (implemented on x86 or GPU's) do not exhibit stable and constant throughputs. [ABSTRACT FROM AUTHOR]

We consider the problem of (almost) lossless source coding of two correlated memoryless sources using separate encoders and a joint decoder, that is, Slepian-Wolf (S-W) coding. In our setting, the encoding and decoding are asynchronous, i.e., there is a certain relative delay between the two sources. Neither the source parameters nor the relative delay are known to the encoders and the decoder. Since we assume that both encoders implement standard random binning, which does not require such knowledge anyway, the focus of this work is on the decoder. Our main contribution is in proposing a universal decoder, that independent of the unknown source parameters and the relative delay, and at the same time, is asymptotically as good as the optimal maximum a posteriori probability (MAP) decoder in the sense of the random coding error exponent achieved. Consequently, the achievable rate region is also the same as if the source parameters and the delay were known to the decoder. [ABSTRACT FROM AUTHOR]

This letter presents a modified low-complexity chase (LCC) algorithm, where a fewer number of vectors can be tested with minor error correction performance degradation. The proposed LCC decoding pre-determines whether the number of errors in the received codeword is even or odd, and it processes only necessary test vectors. As a result, the number of test vectors can be reduced by half compared to the conventional LCC decoding. The Reed-Solomon (255,239) decoder with the proposed LCC algorithm has been implemented using 65nm CMOS process. The hardware implementation results show that the proposed decoder shows 48.5% reduced latency with 0.06 dB of coding gain decrease at 10−6 codeword error rate compared to the state-of-the-art LCC decoder. [ABSTRACT FROM AUTHOR]

We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error on the translated channel implies a mismatched-decoding error in the original channel. In particular, it is shown that if the rate exceeds the upper-bound, the probability of error tends to one exponentially when the block-length tends to infinity. We also show that the underlying optimization problem is a convex-concave problem and that an efficient iterative algorithm converges to the optimal solution. In addition, we show that, unlike achievable rates in the literature, the multiletter version of the bound cannot not improve. A number of examples are discussed throughout the paper. [ABSTRACT FROM AUTHOR]

The group testing problem consists of determining a small set of defective items from a larger set of items based on tests on groups of items, and is relevant in applications such as medical testing, communication protocols, pattern matching, and many more. While rigorous group testing algorithms have long been known with runtime at least linear in the number of items, a recent line of works has sought to reduce the runtime to ${\mathrm{ poly}}({k} \log {n})$ , where n is the number of items and k is the number of defectives. In this paper, we present such an algorithm for non-adaptive group testing termed bit mixing coding (BMC), which builds on techniques that encode item indices in the test matrix, while incorporating novel ideas based on erasure-correction coding. We show that BMC achieves asymptotically vanishing error probability with ${O}({k} \log {n})$ tests and ${O}({k}^{2} \cdot \log {k} \cdot \log {n})$ runtime, in the limit as ${n} \to \infty $ (with k having an arbitrary dependence on n). This closes an open problem of simultaneously achieving ${\mathrm{ poly}}({k} \log {n})$ decoding time using ${O}({k} \log {n})$ tests without any assumptions on k. In addition, we show that the same scaling laws can be attained in a commonly-considered noisy setting, in which each test outcome is flipped with constant probability. [ABSTRACT FROM AUTHOR]

In this article, we consider a distributed antenna system to enable the downlink ultrareliable and low-latency communications (URLLC) for the industrial Internet of Things. To satisfy the low latency, the short packet length is exploited and accordingly, the achievable rate under the finite blocklength codes is considered in the analysis of the packet loss probability in downlink URLLC distributed antenna system. Specifically, the packet loss probability is approximated as a sum of the channel OP and the finite blocklength coding error probability. By using a stochastic geometry approach, we analytically derive the packet loss probability in terms of the system parameters (i.e., the densities of the DA ports and the receiving sensor nodes, the number of receive antennas, and the packet size/duration, etc.), when the sensor nodes and the DA ports are randomly distributed in a given area. From the analytic results, we show how to optimize the short blocklength coding error probability to minimize the overall packet loss probability. Furthermore, we also derive the required DA port density to satisfy the packet loss probability constraint for a given distributed antenna system parameters, which gives us a useful insight into the design of downlink distributed antenna system for URLLC. [ABSTRACT FROM AUTHOR]

We propose a novel multipath multi-hop adaptive and causal random linear network coding (AC-RLNC) algorithm with forward error correction. This algorithm generalizes our joint optimization coding solution for point-to-point communication with delayed feedback. AC-RLNC is adaptive to the estimated channel condition, and is causal, as the coding adjusts the retransmission rates using a priori and posteriori algorithms. In the multipath network, to achieve the desired throughput and delay, we propose to incorporate an adaptive packet allocation algorithm for retransmission, across the available resources of the paths. This approach is based on a discrete water filling algorithm, i.e., bit-filling, but, with two desired objectives, maximize throughput and minimize the delay. In the multipath multi-hop setting, we propose a new decentralized balancing optimization algorithm. This balancing algorithm minimizes the throughput degradation, caused by the variations in the channel quality of the paths at each hop. Furthermore, to increase the efficiency, in terms of the desired objectives, we propose a new selective recoding method at the intermediate nodes. We derive bounds on the throughput and the mean and maximum in-order delivery delay of AC-RLNC, both in the multipath and multipath multi-hop case. In the multipath case, we prove that in the non-asymptotic regime, the suggested code may achieve more than 90% of the channel capacity with zero error probability under mean and maximum in-order delay constraints, namely a mean delay smaller than three times the optimal genie-aided one and a maximum delay within eight times the optimum. In the multipath multi-hop case, the balancing procedure is proven to be optimal with regards to the achieved rate. Through simulations, we demonstrate that the performance of our adaptive and causal approach, compared to selective repeat (SR)-ARQ protocol, is capable of gains up to a factor two in throughput and a factor of more than three in mean delay and eight in maximum delay. The improvements on the throughput delay trade-off are also shown to be significant with regards to the previously developed singlepath AC-RLNC solution. [ABSTRACT FROM AUTHOR]

In this paper, we analyze classical data compression with quantum side information (also known as the classical-quantum Slepian–Wolf protocol) in the so-called large and moderate deviation regimes. In the non-asymptotic setting, the protocol involves compressing classical sequences of finite length $n$ and decoding them with the assistance of quantum side information. In the large deviation regime, the compression rate is fixed, and we obtain bounds on the error exponent function, which characterizes the minimal probability of error as a function of the rate. Devetak and Winter showed that the asymptotic data compression limit for this protocol is given by a conditional entropy. For any protocol with a rate below this quantity, the probability of error converges to one asymptotically and its speed of convergence is given by the strong converse exponent function. We obtain finite blocklength bounds on this function, and determine exactly its asymptotic value. In the moderate deviation regime for the compression rate, the latter is no longer considered to be fixed. It is allowed to depend on the blocklength $n$ , but assumed to decay slowly to the asymptotic data compression limit. Starting from a rate above this limit, we determine the speed of convergence of the error probability to zero and show that it is given in terms of the conditional information variance. [ABSTRACT FROM AUTHOR]

We present an upper bound on the error probability achievable using variable-length stop feedback (VLSF) codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. Numerical evaluation of our bound suggests that, for fixed latency and reliability constraints, noise in the feedback link may increase the minimum average service time for the VLSF scheme considered in this paper, to the extent that fixed-length codes without feedback may be preferable in some scenarios. [ABSTRACT FROM AUTHOR]

A method for construction of polar subcodes with reduced error coefficient is presented. The proposed approach relies on explicit enumeration of low-weight non-zero codewords in a polar code, and construction of dynamic freezing constraints which define a subcode not containing most of these codewords. The obtained codes provide a large performance gain in the high-SNR region compared to non-optimized polar subcodes and polar codes with CRC. [ABSTRACT FROM AUTHOR]

This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the TRC exponent is exponentially small; upper and lower bounds for this exponent are given, which coincide in some cases. In addition, the probability of randomly drawing a codebook whose error exponent is larger than the TRC exponent is shown to be double–exponentially small; upper and lower bounds to the double–exponential exponent are given. The results suggest that codebooks whose error exponent is larger than the error exponent of the TRC are extremely rare. The key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel method, called doubly-recursive block Markov superposition transmission (DrBMST), to construct high-performance spatially coupled codes. An important characteristic of DrBMST codes is that the degrees of the constraint nodes in their normal graphs are at most three. As a result, DrBMST codes can be decoded with low complexity. We first prove that the error probability of an enlarged DrBMST code ensemble can be made arbitrarily small under windowed maximum-likelihood decoding (MLD) by increasing the decoding window size. This result partially explains the superior performances of DrBMST codes. Then we propose to use the extrinsic information transfer (EXIT) chart analysis to estimate the iterative windowed decoding thresholds of DrBMST codes. The EXIT chart analyses show that, with such a simple structure, DrBMST codes are comparable to BMST codes with large encoding memories in terms of decoding thresholds. Finally, we carry out comparisons to validate the advantages of DrBMST codes in terms of error performances and decoding complexities. In particular, for a decoding latency of 20,000 bits, the DrBMST code performs better than the (4, 8)-regular spatially coupled low-density parity-check (SC-LDPC) code, but with lower computational complexity. Hence, DrBMST codes can be used in communication systems with limited computational resources. In addition, we show that DrBMST can be used to construct multiple-rate codes. [ABSTRACT FROM AUTHOR]

The Slepian-Wolf (SW) coding system is a source coding system with two encoders and a decoder, where these encoders independently encode source sequences from two correlated sources into codewords, and the decoder reconstructs both source sequences from the codewords. In this paper, we consider the situation in which the SW coding system is asynchronous, i.e., each encoder samples a source sequence with some unknown delay. We assume that delays are unknown but maximum and minimum values of possible delays are known to encoders and the decoder. We also assume that sources are discrete stationary memoryless and the probability mass function (PMF) of the sources is unknown but the system knows that it belongs to a certain set of PMFs. For this asynchronous SW coding system, we clarify the achievable rate region which is the set of rate pairs of encoders such that the decoding error probability vanishes as the blocklength tends to infinity. We show that this region does not always coincide with that of the synchronous SW coding system in which each encoder samples a source sequence without any delay. [ABSTRACT FROM AUTHOR]

In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more. [ABSTRACT FROM AUTHOR]

A Lagrange–dual (Gallager–style) lower bound is derived for the error exponent function of the typical random code (TRC) pertaining to the i.i.d. random coding ensemble and mismatched stochastic likelihood decoding. While the original expression, derived from the method of types (the Csiszár–style expression) involves minimization over probability distributions defined on the channel input–output alphabets, the new Lagrange–dual formula involves optimization of five parameters, independently of the alphabet sizes. For both stochastic and deterministic mismatched decoding (including maximum likelihood decoding as a special case), we provide a rather comprehensive discussion on the insight behind the various ingredients of this formula and describe how its behavior varies as the coding rate exhausts the relevant range. Among other things, it is demonstrated that this expression simultaneously generalizes both the expurgated error exponent function (at zero rate) and the classical random coding exponent function at high rates, where it also meets the sphere–packing bound. [ABSTRACT FROM AUTHOR]

Luby transform (LT) codes suffer from undesired error floors since a certain amount of input symbols may remain uncovered by output symbols due to the uniformly random encoding process. Several variants of LT codes presented previously aiming at removing low-degree input symbols assure that all input symbols can be covered by output symbols after encoding in high probability and have been verified to effectively reduce error floors for short and moderate block lengths. However, in this work, we show that those variants might not be asymptotically good even with the removal of low-degree input symbols in the encoding process. [ABSTRACT FROM AUTHOR]

The edge-removal problem addresses the loss in capacity obtained by the removal of an edge of capacity $\lambda $ from a given network. In the context of network coding, the edge-removal problem has been solved for certain families of networks (such as instances with co-located sources). However, the problem is open for general instances. This work ties the edge-removal problem to two additional problems in the context of network communication: (a) the “ zero-error” network coding problem, which asks whether the zero-error network coding capacity differs from the capacity when error probability is allowed to tend to zero as the blocklength grows; and (b) the “ $\delta $ -dependence” problem, which measures the advantage of message dependence in network coding capacity. [ABSTRACT FROM AUTHOR]

We consider the secure quantum communication over a network with the presence of a malicious adversary who can eavesdrop and contaminate the states. The network consists of noiseless quantum channels with the unit capacity and the nodes which applies noiseless quantum operations. As the main result, when the maximum number $m_{1}$ of the attacked channels over the entire network uses is less than a half of the network transmission rate $m_{0}$ (i.e., $m_{1} < m_{0}/2$), our code implements secret and correctable quantum communication of the rate $m_{0}-2m_{1}$ by using the network asymptotic number of times. Our code is universal in the sense that the code is constructed without the knowledge of the specific node operations and the network topology, but instead, every node operation is constrained to the application of an invertible matrix to the basis states. Moreover, our code requires no classical communication. Our code can be thought of as a generalization of the quantum secret sharing. [ABSTRACT FROM AUTHOR]

The error exponent of the typical random code is defined as the asymptotic normalized expectation of the logarithm of the probability of error, as opposed to the traditional definition of the random coding exponent as the normalized logarithm of the expectation of the probability of error with respect to a given ensemble of codes. For a certain ensemble of independent codewords, with a given power spectrum, and a generalized stochastic mismatched decoder, we characterize the error exponent of the typical random codes (TRC) for the colored Gaussian channel, with emphasis on the range of low rates, where the TRC error exponent differs in value from the ordinary random coding error exponent. The error exponent formula, which is exponentially tight at some range of low rates, is presented as the maximum of a certain function with respect to one parameter only (in the spirit of Gallager’s formulas) in the case of matched decoding, and two parameters in the case of mismatched decoding. Several aspects of the main results are discussed. These include: general properties, a parametric representation, critical rates, phase transitions, optimal input spectrum (water pouring), and comparison to the random coding exponent. [ABSTRACT FROM AUTHOR]

Due to the spectrum scarcity in the space information networks, non-orthogonal multiple access (NOMA) is envisioned as a promising technique in satellite-terrestrial communications networks as its improved system capacity and spectral efficiency. In this paper, to further improve the spectrum utilization efficiency in satellite-terrestrial networks, bandwidth compression (BC) design is embedded in the NOMA scheme, which contributes to the non-orthogonality both in power and frequency domains, named BC-NOMA. However, with such advantages provided by BC-NOMA, the inter-carrier interference (ICI) and the intra-group interference (IGI) are severe, which degrade the reliability and the capacity. Therefore, the impacts of BC and power domain multiplexing on the system capacity are first investigated. To cancel the mixed internal interference, an iterative and successive interference cancellation (ISIC) approach is proposed. Secondly, the symmetrical coding (SC) is designed with BC-NOMA to avoid the error propagation when using ISIC, which benefits much for the low power user (LUE). Furthermore, the closed-form expression of error probability for SCNOMA is derived and the system and individual capacities are also analyzed. Results show that the BC-NOMA system can achieve a quasi-optimal performance compared with the orthogonal subcarrier NOMA (ONOMA) system and balance the fairness. [ABSTRACT FROM AUTHOR]

Multilevel flash memories enable multiple bits to be stored in a single memory cell and hence a significant increase of the storage capacity. The multiple bits that are used for labeling the threshold voltage level of a memory cell belong to different pages. A multilevel flash memory channel resembles a multi-user channel with asymmetric noise, while the data of different pages, which are encoded independently, resembles data of multiple users. In this paper, performance analyses are proposed for this channel by using the union bound technique. In particular, we investigated two different binary labeling schemes of a cell level, the Gray labeling and non-Gray labeling with three maximum-likelihood (ML)-based decoding schemes, which are the joint multi-page ML decoding, page-separate ML decoding, and default setting ML decoding. Our analysis reveals an asymptotic diminishing rate of decoding errors as the channel noise approaches zero, based on which the code design criteria are proposed. It is shown theoretically that the Gray mapping has no joint (i.e., multi-page) decoding gain. The corresponding diminishing decoding error rate is dominated by the weakest code in each page and hence a separate decoding scheme is adequate. On the other hand, the non-Gray mapping has a joint decoding gain which means the weak code can exploit the decoding of the strong code and the diminishing rate of its decoding errors is not subject to the cask effect. Therefore, for Gray mapping, a symmetric coding scheme using equal-strength code for each page achieves better error performance, while for non-Gray mapping with joint decoding, the symmetric coding is not necessary. Moreover, by using the asymmetric coding scheme through assigning different code rates to different pages, the non-Gray mapping can achieve higher overall sum rate than Gray mapping with a similar decoding error rate performance. [ABSTRACT FROM AUTHOR]

This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the classic privacy amplification results, but also achieve secrecy under the stronger semantic-security metric. [ABSTRACT FROM AUTHOR]

We consider data transmission across discrete memoryless channels (DMCs) using variable-length codes with feedback. We consider the family of such codes whose rates are $\rho _{N}$ below the channel capacity $C$ , where $\rho _{N}$ is a positive sequence that tends to zero slower than the reciprocal of the square root of the expectation of the (random) blocklength $N$. This is known as the moderate deviations regime, and we establish the optimal moderate deviations constant. We show that in this scenario, the error probability decays sub-exponentially with speed $\exp (-(B/C)N\rho _{N})$ , where $B$ is the maximum relative entropy between output distributions of the DMC. [ABSTRACT FROM AUTHOR]

In recent years, communicating information using molecules via diffusion has attracted significant interest in bio-medical applications. To date, most of the studies have concentrated on point-to-point molecular communication (MC), whereas in a realistic environment, multiple MC transmitters are likely to transmit molecular messages simultaneously sharing the same propagation medium, resulting in significant performance variation of the MC system. In this type of large-scale MC system, the collective signal strength at the desired receiver can be impaired by the interference caused by other MC transmitters, which may degrade the system reliability and efficiency. This paper presents the first tractable analytical framework for the collective signal strength at a partially absorbing receiver due to the desired transmitter under the impact of a swarm of interfering transmitters in a 3D large-scale MC system using stochastic geometry. To combat the multi-user interference and the intersymbol interference (ISI) in the multi-user environment, we propose Reed–Solomon (RS) error correction coding, due to its high effectiveness in combating burst and random errors, as well as the two types of information molecule modulating scheme, where the transmitted bits are encoded using two types of information molecules at consecutive bit intervals. We derive analytical expressions for the bit error probability (BEP) of the large-scale MC system with the proposed two schemes to show their effectiveness. The results obtained using Monte Carlo simulations, match exactly with the analytical results, justifying the accuracy of the derivations. Results reveal that both schemes improve the BEP by a factor of 3–4 compared with that of a conventional MC system without using any ISI mitigation techniques. Due to the implementation simplicity, the two-type molecule encoding scheme is better than the RS error correction coding scheme, as the RS error correction coding scheme involves additional encoding and decoding process at both the transmitter and receiver nodes. Furthermore, the proposed analytical framework can be generalized to the analysis of other types of receiver designs and performance characterization in multi-user large-scale MC systems. Also, the two types of information molecule modulating scheme can be extended to M-type of information molecule modulating scheme without loss of generality. [ABSTRACT FROM AUTHOR]

This paper contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two different methods of code expurgation will be used, that will provide two competing error exponents. The second is the derivation of expurgated exponents under the generalized stochastic likelihood decoder (GLD). We prove that the expurgated exponents achieved for the hierarchical ensemble under GLD decoding are at least as good as the maximum between the random coding error exponents derived in an earlier work by Averbuch and Merhav (2018) and one of our ML–based expurgated exponents. [ABSTRACT FROM AUTHOR]

Consider the problem of constructing a polar code of block length $N$ for a given transmission channel $W$. Previous approaches require one to compute the reliability of the $N$ synthetic channels and then use only those that are sufficiently reliable. However, we know from two independent works by Schürch and by Bardet et al. that the synthetic channels are partially ordered with respect to degradation. Hence, it is natural to ask whether the partial order can be exploited to reduce the computational burden of the construction problem. We show that, if we take advantage of the partial order, we can construct a polar code by computing the reliability of roughly a fraction $1/\log ^{3/2} N$ of the synthetic channels. In particular, we prove that $N/\log ^{3/2} N$ is a lower bound on the number of synthetic channels to be considered and such a bound is tight up to a multiplicative factor $\log \log N$. This set of roughly $N/\log ^{3/2} N$ synthetic channels is universal, in the sense that it allows one to construct polar codes for any $W$ , and it can be identified by solving a maximum matching problem on a bipartite graph. Our proof technique consists of reducing the construction problem to the problem of computing the maximum cardinality of an antichain for a suitable partially ordered set. As such, this method is general, and it can be used to further improve the complexity of the construction problem, in case a refined partial order on the synthetic channels of polar codes is discovered. [ABSTRACT FROM AUTHOR]

We use stochastic network calculus to investigate the delay performance of a multiuser MISO system with zero-forcing beamforming. First, we consider ideal assumptions with long codewords and perfect CSI at the transmitter, where we observe a strong channel hardening effect that results in very high reliability with respect to the maximum delay of the application. We then study the system under more realistic assumptions with imperfect CSI and finite blocklength channel coding. These effects lead to interference and to transmission errors, and we derive closed-form approximations for the resulting error probability. Compared to the ideal case, imperfect CSI and finite length coding cause massive degradations in the average transmission rate. Surprisingly, the system nevertheless maintains the same qualitative behavior as in the ideal case: as long as the average transmission rate is higher than the arrival rate, the system can still achieve very high reliability with respect to the maximum delay. [ABSTRACT FROM AUTHOR]

This paper investigates the probability that the delay and the peak-age of information exceed a desired threshold in a point-to-point communication system with short information packets. The packets are generated according to a stationary memoryless Bernoulli process, placed in a single-server queue and then transmitted over a wireless channel. A variable-length stop-feedback coding scheme—a general strategy that encompasses simple automatic repetition request (ARQ) and more sophisticated hybrid ARQ techniques as special cases—is used by the transmitter to convey the information packets to the receiver. By leveraging finite-blocklength results, the delay violation and the peak-age violation probabilities are characterized without resorting to approximations based on larg-deviation theory as in previous literature. Numerical results illuminate the dependence of delay and peak-age violation probability on system parameters such as the frame size and the undetected error probability, and on the chosen packet-management policy. The guidelines provided by our analysis are particularly useful for the design of low-latency ultra-reliable communication systems. [ABSTRACT FROM AUTHOR]

With the growing popularity of delay-sensitive applications (e.g., real-time conversational video, online gaming, and augmented reality) and future trends toward ultra-reliable low-latency communications such as the tactile Internet, performance analysis of wireless systems under the finite code blocklength constraint becomes extremely important. In this paper, we investigate the maximum achievable throughput of incremental redundancy-hybrid automatic repeat request (IR-HARQ) over the (correlated) Rayleigh fading channel under finite blocklength and delay-violation probability constraints as a function of the modulation scheme. The maximum number of HARQ rounds together with the transport block size specifies the underlying coding latency of the IR-HARQ scheme. A framework, namely the HARQ Markov model (HARQ-MM), is introduced to track the throughput and the probability of error of IR-HARQ over the Rayleigh fading channel as a function of the modulation scheme. The dispersion of parallel additive white Gaussian noise channels with finite input alphabets (e.g., pulse amplitude modulation) is analytically characterized. It is used to identify the state transition probabilities of the underlying HARQ-MM. An algorithm is developed to efficiently compute the steady-state distribution of the HARQ-MM. Extensive performance evaluation is conducted, which shows a good match between the throughput performance characterized by the theoretical framework and that achieved by the practical channel codes. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity $({1}/{2})\log (1+ \mathop {\mathrm {\mathsf {SNR}}}\nolimits)$ of the additive white Gaussian-noise (AWGN) channel. Our construction follows the multilevel approach of Forney et al., where we construct a capacity-achieving polar code on each level. The component polar codes are shown to be naturally nested, thereby, fulfilling the requirement of the multilevel lattice construction. We prove that the polar lattices are AWGN-good. Furthermore, using the technique of source polarization, we propose discrete Gaussian shaping over the polar lattice to satisfy the power constraint. Both the construction and shaping are explicit, and the overall complexity of encoding and decoding is $O(N\log N)$ for any fixed target error probability. [ABSTRACT FROM AUTHOR]

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no a priori channel state information available at the transmitter or at the receiver. An upper bound built upon the min–max converse is compared with two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver and the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, in Rayleigh fading, for the case when a coded packet of 168 symbols is transmitted using a channel code of rate 0.48-bits/channel use, over a block-fading channel with block size equal to eight symbols, PAT requires an additional 1.2 dB of energy per information bit to achieve a packet error probability of 10−3 compared with a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered-statistics decoding, whose performance is close (1-dB gap at 10−3 packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the performance of the Viterbi decoding algorithm with/without Automatic Repeat reQuest (ARQ) over a Rician flat fading channel with unlimited interleaving. We show that the decay rate of the average bit error probability with respect to the bit energy to noise ratio is at least equal to $d_{f}$ at high-bit energy to noise ratio for both cases (with ARQ and without ARQ), where $d_{f}$ is the free distance of the convolutional code. The Yamamoto-Itoh flag helps to reduce the average bit error probability by a factor of $4^{d_{f}}$ with a negligible retransmission rate. We also prove an interesting result that the average bit error probability decays exponentially fast with respect to the Rician factor for any fixed bit energy per noise ratio. In addition, the average bit error exponent with respect to the Rician factor is shown to be $d_{f}$. [ABSTRACT FROM AUTHOR]

Using the Thompson circuit complexity model, it is shown that fully parallel encoding and decoding schemes with asymptotic block error probability that scales as $O(f(n))$ have energy that scales as $\Omega (n{-\ln f(n)}^{1/2})$. In addition, it is shown that the number of clock cycles [ $T(n)$ ] required for any encoding or decoding scheme that reaches this bound must scale as $T(n)\ge {-\ln f(n)}^{1/2}$. Similar scaling results are extended to serialized computation. A similar approach is extended to three dimensions by generalizing the Grover information-friction energy model. Within this model, it is shown that encoding and decoding schemes with probability of block error $P_{\mathrm {e}}(n)$ consume at least $\Omega (n(-\ln P_{\mathrm {e}}(n))^{({1}/{3})})$ energy. [ABSTRACT FROM AUTHOR]

We propose two classes of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast, and we identify an explicit lower bound on the error exponent. The other class attains the epsilon-capacity of the channel, and we also identify the second-order term in the asymptotic expansion. The proposed encoder is essentially based on the packing lemma of the method of types. For the decoder, we first derive a Rényi-relative-entropy version of Clarke and Barron’s formula the distance between the true distribution and the Bayesian mixture, which is of independent interest. The universal decoder is stated in terms of this formula and quantities used in the information spectrum method. The methods contained herein allow us to analyze universal codes for channels with continuous and discrete output alphabets in a unified manner and to analyze their performances in terms of the exponential decay of the error probability and the second-order coding rate. [ABSTRACT FROM AUTHOR]