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Register a new userActive Deep Decoding of Linear Codes
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Added by
Nir Raviv
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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High quality data is essential in deep learning to train a robust model. While in other fields data is sparse and costly to collect, in error decoding it is free to query and label thus allowing potential data exploitation. Utilizing this fact and inspired by active learning, two novel methods are introduced to improve Weighted Belief Propagation (WBP) decoding. These methods incorporate machine-learning concepts with error decoding measures. For BCH(63,36), (63,45) and (127,64) codes, with cycle-reduced parity-check matrices, improvement of up to 0.4dB at the waterfall region, and of up to 1.5dB at the errorfloor region in FER, over the original WBP, is demonstrated by smartly sampling the data, without increasing inference (decoding) complexity. The proposed methods constitutes an example guidelines for model enhancement by incorporation of domain knowledge from error-correcting field into a deep learning model. These guidelines can be adapted to any other deep learning based communication block.
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The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the maximum-likelihood certificate property. It is also shown that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. It is also proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. Two alternative polytopes for use with linear-programming decoding are studied, and it is shown that for many classes of codes these polytopes yield a complexity advantage for decoding. These polytope representations lead to polynomial-time decoders for a wide variety of classical nonbinary linear codes. LP decoding performance is illustrated for the [11,6] ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the performance of the LP decoder is comparable to codeword-error-rate-optimum hard-decision based decoding. LP decoding is also simulated for medium-length ternary and quaternary LDPC codes with corresponding PSK modulations over AWGN.
Few decoding algorithms for hyperbolic codes are known in the literature, this article tries to fill this gap. The first part of this work compares hyperbolic codes and Reed-Muller codes. In particular, we determine when a Reed-Muller code is a hyperbolic code. As a byproduct, we state when a hyperbolic code has greater dimension than a Reed-Muller code when they both have the same minimum distance. We use the previous ideas to describe how to decode a hyperbolic code using the largest Reed-Muller code contained in it, or alternatively using the smallest Reed-Muller code that contains it. A combination of these two algorithms is proposed for the case when hyperbolic codes are defined by polynomials in two variables. Then, we compare hyperbolic codes and Cube codes (tensor product of Reed-Solomon codes) and we propose decoding algorithms of hyperbolic codes based on their closest Cube codes. Finally, we adapt to hyperbolic codes the Geil and Matsumotos generalization of Sudans list decoding algorithm.
A new deep-neural-network (DNN) based error correction encoder architecture for channels with feedback, called Deep Extended Feedback (DEF), is presented in this paper. The encoder in the DEF architecture transmits an information message followed by a sequence of parity symbols which are generated based on the message as well as the observations of the past forward channel outputs sent to the transmitter through a feedback channel. DEF codes generalize Deepcode [1] in several ways: parity symbols are generated based on forward-channel output observations over longer time intervals in order to provide better error correction capability; and high-order modulation formats are deployed in the encoder so as to achieve increased spectral efficiency. Performance evaluations show that DEF codes have better performance compared to other DNN-based codes for channels with feedback.
We address the problem of decoding Gabidulin codes beyond their unique error-correction radius. The complexity of this problem is of importance to assess the security of some rank-metric code-based cryptosystems. We propose an approach that introduces row or column erasures to decrease the rank of the error in order to use any proper polynomial-time Gabidulin code error-erasure decoding algorithm. This approach improves on generic rank-metric decoders by an exponential factor.
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