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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., Comment: The first two authors contributed equally to this work. A shortened version was submitted to the ISIT 2018 conference

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 {\it 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 (BIAWGN) 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 (SUD) and multiuser detection (MUD), including Han-Kobayashi (HK)., Comment: Accepted to the IEEE Transactions on Information Theory. This is a major revision of a paper originally submitted in August 2010

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 maximizing coverage for 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., Comment: 17 pages,8 figures, Submitted to IEEE Trans. Inf. Th, Oct. 2007

We consider transmission over the ergodic fading multi-antenna broadcast (MIMO-BC) channel with partial channel state information at the transmitter and full information at the receiver. Over the equivalent {\it 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 {\it 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., Comment: Manuscript submitted to IEEE Transactions on Information Theory: June 2006, revised: July 2007, accepted: October 2007. The material in this paper was presented at the 44th Annual Allerton Conference on Communications, Control and Computing, Monticello, IL, September 2006

We present an analysis, under iterative decoding, of coset 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 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 AWGN channel, including results within 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., Comment: To appear, IEEE Transactions on Information Theory, (submitted October 2004, revised and accepted for publication, November 2005). The material in this paper was presented in part at the 41st Allerton Conference on Communications, Control and Computing, October 2003 and at the 2005 IEEE International Symposium on Information Theory