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arXiv:2304.08868 · IEEE Globecom Workshops (GC Wkshps)

Soft-Output Deep Neural Network-Based Decoding

Dmitry Artemasov, Kirill Andreev, Pavel S. Rybin, Alexey Frolov

Published Dec 4, 2023• 4 citations

Abstract

Deep neural network (DNN)-based channel decoding is widely considered in the literature. The existing solutions are investigated for the case of hard output, i.e. when the decoder returns the estimated information word. At the same time, soft output decoding is of critical importance for iterative receivers and decoders. In this paper, we focus on the soft-output DNN-based decoding problem. We start with the syndrome-based approach proposed by Bennatan et al. (2018) and modify it to provide soft output in the additive white Gaussian noise (AWGN) channel. The new decoder can be considered as an approximation of the maximum a-posteriori (MAP) decoder with smaller computation complexity. We discuss various regularization functions for joint DNN-MAP training and compare the resulting distributions for [64], [45] (extended Bose-Chaudhuri-Hocquenghem) eBCH code. Finally, to demonstrate the soft-output quality we consider the turbo-product code with [64], [45] eBCH codes as row and column codes. We show that the resulting DNN-based scheme is very close to the MAP-based performance and significantly outperforms the solution based on the Chase decoder. We come to the conclusion that the new method is prospective for the challenging problem of DNN-based decoding of long codes consisting of short component codes.

DOI: 10.1109/gcwkshps58843.2023.10465120

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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.

In this letter, we introduce a new syndrome-based decoder where a deep neural network (DNN) estimates the error pattern from the reliability and syndrome of the received vector. The proposed algorithm works by iteratively selecting the most confident positions to be the error bits of the error pattern, updating the vector received when a new position of the error pattern is selected. Simulation results for the (63,45) and (63,36) BCH codes show that the proposed approach outperforms existing neural network decoders. In addition, the new decoder is flexible in that it can be applied on top of any existing syndrome-based DNN decoder without retraining.

In modern communication systems, multiple types of error-correcting codes can be utilized for different transmission scenarios. Therefore, the receiver should include the decoder compatible with multiple codes used in the transmission scheme, which results in the increase of the resources required for its implementation. In this paper, we investigate the possibility of training a single syndrome-based DNN decoder to solve the problem of unified decoding. We observe, that the syndrome-based approach allows to extend the unified decoding capabilities to the codes with considerably larger lengths in comparison to the initially described by Wang et al. (2018) method. Through numerical experiments, we show that the model trained for decoding a pair of moderate lengths codes (BCH and CRC-Aided Polar) achieves performance results comparable with classical decoding solutions, while sharing the same architecture and the set of trainable weights. We note, that the unification of a syndrome-based DNN decoder does not lead to large performance degradation, in comparison to the decoder trained on a single code. The approach described in the paper is promising in terms of reducing the hardware resources required to implement the decoder.

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We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code families and for short codeword lengths, we observe that (i) structured codes are easier to learn and (ii) the neural network is able to generalize to codewords that it has never seen during training for structured, but not for random codes. These results provide some evidence that neural networks can learn a form of decoding algorithm, rather than only a simple classifier. We introduce the metric normalized validation error (NVE) in order to further investigate the potential and limitations of deep learning-based decoding with respect to performance and complexity.