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IEEE/CIC International Conference on Communications in China (ICCC)

Deep Learning Methods for Channel Decoding: A Brief Tutorial

Kai Niu, Jincheng Dai, Kailin Tan, Jian Shu Gao

Published Jul 28, 2021• 8 citations
Publisher

Abstract

The recent development of deep learning methods demonstrates a new insight to optimize the decoding of linear codes. In this paper, we survey the typical neural network decoding methods, including data-driven and model-driven schemes. We investigate the design principle, algorithm mechanism, parameter assignment, and training process of these neural decoders for high-density parity check (HDPC), low-density parity-check (LDPC), and polar codes. Finally, we summarize the advantages of neural network decoding and point out some research directions in the future.

DOI
10.1109/iccc52777.2021.9580304

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Neural network decoding algorithms are recently introduced by Nachmani et al. to decode high-density parity-check (HDPC) codes. In contrast with iterative decoding algorithms such as sum-product or min-sum algorithms in which the weight of each edge is set to 1, in the neural network decoding algorithms, the weight of every edge depends on its impact in the transmitted codeword. In this paper, we provide a novel feed-forward neural network lattice decoding algorithm suitable to decode lattices constructed based on Construction A, whose underlying codes have HDPC matrices. We first establish the concept of feed-forward neural network for HDPC codes and improve their decoding algorithms compared to Nachmani et al. We then apply our proposed decoder for a Construction A lattice with HDPC underlying code, for which the well-known iterative decoding algorithms show poor performances. The main advantage of our proposed algorithm is that instead of assigning and training weights for all edges, which turns out to be time-consuming especially for high-density parity-check matrices, we concentrate on edges which are present in most of 4-cycles and removing them gives a girth -6 Tanner graph. This approach, by slight modifications using updated LLRs instead of initial ones, simultaneously accelerates the training process and improves the error performance of our proposed decoding algorithm.
Neural network decoding algorithms are recently introduced by Nachmani et al. to decode high-density parity-check (HDPC) codes. In contrast with iterative decoding algorithms such as sum-product or min-sum algorithms in which the weight of each edge is set to 111, in the neural network decoding algorithms, the weight of every edge depends on its impact in the transmitted codeword. In this paper, we provide a novel \emph{feed-forward neural network lattice decoding algorithm} suitable to decode lattices constructed based on Construction A, whose underlying codes have HDPC matrices. We first establish the concept of feed-forward neural network for HDPC codes and improve their decoding algorithms compared to Nachmani et al. We then apply our proposed decoder for a Construction A lattice with HDPC underlying code, for which the well-known iterative decoding algorithms show poor performances. The main advantage of our proposed algorithm is that instead of assigning and training weights for all edges, which turns out to be time-consuming especially for high-density parity-check matrices, we concentrate on edges which are present in most of 444-cycles and removing them gives a girth-666 Tanner graph. This approach, by slight modifications using updated LLRs instead of initial ones, simultaneously accelerates the training process and improves the error performance of our proposed decoding algorithm.
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BP decoding algorithm is one of the commonly used decoding algorithms for LDPC codes. To adapt LDPC codes to different 5G scenarios and further improve the decoding performance of short LDPC codes, a scheme combining model-driven deep learning with a traditional BP decoding algorithm is proposed. With the advantages of model-driven, this solution expands the decoding iteration process between the check node and the variable node into a neural network and proposes a parameter normalization optimization solution to solve the problem of the program with many training parameters, the edge weights of the optimized Tanner graph are re-assigned and bound. Simulation results show that the proposed scheme can improve the decoding performance of LDPC codes with short lengths.
LDPC code is a widely-used high-performance error correction code. In recent years, LDPC decoding based on deep learning and neural networks becomes a research hotspot. Based on the (512,256) LDPC code of the CCSDS standard, this paper firstly studies the traditional decoding algorithms of SP, MS, NMS, and OMS, laying a foundation for the construction of neural networks. Then a data-driven (DD) decoding method is studied which adopts the information with its encoded, modulated and noise-added LDPC code as the training data within a Multi-layer Perceptron (MLP) neural network. In order to solve the problem of high bit error rate (BER) in data-driven method, the Neural Normalized Min-sum (NNMS) decoding in which the NMS algorithm is mapped to the neural network structure is proposed, achieving more excellent BER performance than that of NMS. The BER declines by 85.19% when channel SNR equals to 3.5 dB. Finally, improved training methods to enhance the SNR generalization ability of the NNMS network is studied.
In this paper, we analyze the performance of neural belief propagation (BP) decoding on the additive white Gaussian noise (AWGN) channel, compared to the traditional BP algorithm. Previous investigations have shown that assigning pre-trained weights to BP messages can significantly improve the decoding performance in case of high-density parity-check (HDPC) codes, by reducing the negative impact of short cycles. These weights are trained by a neural network whose structure matches the trellis of the decoder. Specifically, we show that medium-density paritycheck (MDPC) codes decoded with neural BP algorithm can achieve lower bit error rate versus HDPC codes with the same codeword length and the same code rate.