We present a novel framework for applying deep neural networks (DNN) to soft decoding of linear codes at arbitrary block lengths. Unlike other approaches, our framework allows unconstrained DNN design, enabling the free application of powerful designs that were developed in other contexts. Our method is robust to overfitting that inhibits many competing methods, which follows from the exponentially large number of codewords required for their training. We achieve this by transforming the channel output before feeding it to the network, extracting only the syndrome of the hard decisions and the channel output reliabilities. We prove analytically that this approach does not involve any intrinsic performance penalty, and guarantees the generalization of performance obtained during training. Our best results are obtained using a recurrent neural network (RNN) architecture combined with simple preprocessing by permutation. We provide simulation results that demonstrate performance that sometimes approaches that of the ordered statistics decoding (OSD) algorithm.

We provide a rigorous mathematical analysis of two communication strategies: soft decode-and-forward (soft-DF) for relay channels and soft partial interference-cancelation (soft-IC) for interference channels. Both strategies involve soft estimation, which assists the decoding process. We consider LDPC codes, not because of their practical benefits, but because of their analytic tractability, which enables an asymptotic analysis similar to random coding methods of information theory. Unlike some works on the closely-related demodulate-and-forward, we assume non-memoryless, code-structure-aware estimation. With soft-DF, we develop simultaneous density evolution to bound the decoding error probability at the destination. This result applies to erasure relay channels. In one variant of soft-DF, the relay applies Wyner-Ziv coding to enhance its communication with the destination, borrowing from compress-and-forward. To analyze soft-IC, we adapt existing techniques for iterative multiuser detection, and focus on binary-input additive white Gaussian noise interference channels. We prove that optimal point-to-point codes are unsuitable for soft-IC, as well as for all strategies that apply partial decoding to improve upon single-user detection and multiuser detection, including Han-Kobayashi.

A two-user interference channel is considered where each transmitter has access to a part of the information intended to the other destination. A primary objective is to maximize the information rates, by exploring the cooperation between the transmitters for interference mitigation, based on the partial side information. It is clear that full cooperation between the transmitters is not possible since each transmitter has only a part of the side information. With this insight, several “layered coding” schemes, consisting of binning and superposition at different stages, are developed. These schemes are are carefully built on coding strategies for the classical interference channel and node cooperation mechanisms. In particular, two layered coding schemes, which are based on a combination of MIMO broadcast coding and the Han-Kobayashi (HK) coding, are thoroughly studied : The first one, namely layered coding with binning, makes heavy use of the Gelfand-Pinsker binning and the HK coding and the second one, namely layered superposition coding, involves superposition coding over different tiers. Rate regions corresponding to the proposed schemes are derived. Then the application of these coding schemes are illustrated for the Gaussian case and numerical results corroborate that the proposed layered coding schemes yield substantial gains at high SNR.

Results for Gaussian relay channels typically focus on maximizing transmission rates for given locations of the source, relay, and destination. We introduce an alternative perspective, where the objective is maximizingcoveragefor a given rate. The new objective captures the problem of how to deploy relays to provide a given level of service to a particular geographic area, where the relay locations become a design parameter that can be optimized. We evaluate the decode-and-forward (DF) and compress-and-forward (CF) strategies for the relay channel with respect to the new objective of maximizing coverage. When the objective is maximizing rate, different locations of the destination favor different strategies. When the objective is coverage for a given rate, and the relay is able to decode, DF is uniformly superior in that it provides coverage at any point served by CF. When the channel model is modified to include random fading, we show that the monotone ordering of coverage regions is not always maintained. While the coverage provided by DF is sensitive to changes in the location of the relay and the path loss exponent, CF exhibits a more graceful degradation with respect to such changes. The techniques used to approximate coverage regions are new and may be of independent interest.

We consider a fading version of the dirty-paper problem, as proposed by Grover and Sahai. In this formulation, the various signals involved are complex-valued, and the interference (known only to the transmitter) is multiplied by a random complex-valued coefficient, whose phase is known only to the receiver. We focus on a compound channel formulation, and seek to maximize the worst-case performance. We present an achievable strategy modeled on the lattice-based approach of Erez, Shamai and Zamir and propose heuristic methods to optimize its parameters. We also derive an upper bound on the maximum achievable transmission rates. Our bounds are shown to be tight in some settings, yielding a complete characterization of capacity. We also provide simulation results, indicating the practical effectiveness of our approaches.

We consider transmission over the ergodic fading multiple-antenna broadcast (MIMO-BC) channel with partial channel state information at the transmitter and full information at the receiver. Over the equivalent non-fading channel, capacity has recently been shown to be achievable using transmission schemes that were designed for the "dirty paper" channel. We focus on a similar "fading paper" model. The evaluation of the fading paper capacity is difficult to obtain. We confine ourselves to the linear-assignment capacity, which we define, and use convex analysis methods to prove that its maximizing distribution is Gaussian. We compare our fading-paper transmission to an application of dirty paper coding that ignores the partial state information and assumes the channel is fixed at the average fade. We show that a gain is easily achieved by appropriately exploiting the information. We also consider a cooperative upper bound on the sum-rate capacity as suggested by Sato. We present a numeric example that indicates that our scheme is capable of realizing much of this upper bound.

Results for Gaussian relay channels typically focus on maximizing transmission rates for given locations of the source, relay and destination. We consider an alternative approach, focusing on maximizing coverage for a given rate. This novel perspective enables treatment of the relay location as a design parameter, producing an extra degree of freedom that may be optimized. Focusing on coverage, we evaluate existing approaches, like decode and forward (DF), compress and forward (CF) and compare them with upper bounds. In the process, we obtain some surprising insights on the performance of these approaches.

We present an analysis under the iterative decoding of coset low-density parity-check (LDPC) codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random- coset analysis to produce an effect that is similar to output symmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q-1-dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop extrinsic information transfer (EXIT) charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the additive white Gaussian noise (AWGN) channel, including results within 0.56 dB of the unrestricted Shannon limit (i.e., not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.

We present simple, practical codes designed for the binary and Gaussian dirty-paper channels. We show that the dirty-paper decoding problem can be transformed into an equivalent multiple-access decoding problem, for which we apply superposition coding. Our concept is a generalization of the nested lattices approach of Zamir, Shamai, and Erez. In a theoretical setting, our constructions are capable of achieving capacity using random component codes and maximum-likelihood decoding. We also present practical implementations of the constructions, and simulation results for both dirty-paper channels. Our results for the Gaussian dirty-paper channel are on par with the best known results for nested lattices. We discuss the binary dirty- tape channel, for which we present a simple, effective coding technique. Finally, we propose a framework for extending our approach to general Gel'fand-Pinsker channels.

We consider coset LDPC codes over GF(q), designed for use over arbitrary channels (particularly nonbinary and asymmetric channels). We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the messages produced by the decoder. We use this property to show that under a Gaussian approximation, the entire q - 1 dimensional distribution of the vector messages is described by a single scalar parameter. We apply this result to develop EXIT charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present results for the AWGN channel at 0.56 dB of the unconstrained Shannon limit (i.e. not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz

We discuss three structures of modified low-density parity-check (LDPC) code ensembles designed for transmission over arbitrary discrete memoryless channels. The first structure is based on the well-known binary LDPC codes following constructions proposed by Gallager and McEliece, the second is based on LDPC codes of arbitrary (q-ary) alphabets employing modulo-q addition, as presented by Gallager, and the third is based on LDPC codes defined over the field GF(q). All structures are obtained by applying a quantization mapping on a coset LDPC ensemble. We present tools for the analysis of nonbinary codes and show that all configurations, under maximum-likelihood (ML) decoding, are capable of reliable communication at rates arbitrarily close to the capacity of any discrete memoryless channel. We discuss practical iterative decoding of our structures and present simulation results for the additive white Gaussian noise (AWGN) channel confirming the effectiveness of the codes.