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IEEE Communications Letters

Iterative Soft Decoding of Reed-Solomon Codes Based on Deep Learning

Wei Zhang, Shuming Zou, Yanyan Liu

Published May 5, 2020• 13 citations
Publisher

Abstract

In this letter, a deep learning based iterative soft decision decoding algorithm for Reed-Solomon codes is proposed. This algorithm takes advantage of deep neural network and Stochastic Shifting based Iterative Decoding (SSID). By assigning weights to every edge in the Tanner graph and changing the architecture of SSID method, the proposed neural network decoder achieves better decoding performance. Compared with BM decoding, HDD-LCC and traditional SSID, simulation results show that for RS (15, 11), this algorithm provides coding gain up to 1.5dB, 1.1dB and 0.5dB, respectively when FER = 10-2.

DOI
10.1109/lcomm.2020.2992488

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This paper presents a soft decoding scheme based on the binary representations transferred from the parity-check matrices (PCMs) for Reed-Solomon (RS) codes. Referring to the modified binary PCM that has a systematic part and a high-density part corresponding to the least reliable variable nodes (LRVNs) and the most reliable variable nodes (MRVNs), respectively, an informed dynamic scheduling method, called Nested-Polling Residual Belief Propagation (NP-RBP), is applied to the corresponding Tanner graph. As with the popular adaptive BP (ABP) decoding approach, adaptation in a binary PCM based on the reliability of variable nodes is also conducted in the proposed NP-RBP decoding. The NP-RBP enables the LRVNs to receive significant updates and limits the correlation accumulation from the short cycles in the MRVNs. In order to enhance the error-rate performance for long codes, a bit-flipping (BF) technique is conducted in order to correct a selection of the errors in the MRVNs such that the propagation of these errors in the subsequent NP-RBP process can be avoided. The resultant decoder is termed NP-RBP-BF. For short codes such as the (31, 25) and (63, 55) RS codes, NP-RBP is able to provide an error-rate performance close to the maximum-likelihood (ML) bound. A more significant improvement can be observed for long codes. For instance, when the proposed NP-RBP-BF decoding is applied to the (255, 239) RS code, it can provide a gain of about 0.4 dB compared to the ABP decoding and the performance gap to the ML bound can be narrowed to about 0.25 dB at a frame error rate of2×10−32\times 10^{-3}2×10−3.
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.
Next-generation communication systems face challenges in meeting the growing demand of ultra-reliable low-latency communications (URLLC), which require advanced physical-layer designs, especially in channel coding. To satisfy the strict reliability and latency constraints of URLLC in 5G and emerging 6G networks, it is essential to use short codes with robust error-correction capabilities. This thesis explores the application of deep learning methodologies to develop advanced channel coding frameworks for short linear block codes. First, I propose a novel decoding algorithm for short block codes based on an edge-weighted graph neural network (EW-GNN). The EW-GNN decoder operates on the Tanner graph with an iterative message-passing structure, algorithmically aligning with conventional belief propagation (BP) decoding. The decoder is characterized by scalability, with trainable parameters independent of codeword length, and outperforms BP and existing deep-learning-based methods. I present a novel auto-encoder integrating deep reinforcement learning (DRL) and graph neural networks (GNN) for end-to-end channel coding. Code generation is modeled as a Markov decision process to optimize error rates and algebraic properties. An iterative joint training of the DRL-based code designer and the EW-GNN decoder is performed to optimise the end-to-end encoding and decoding process. Simulation results show significant improvements over traditional coding schemes including LDPC and BCH codes. Finally, I design a supervised learning framework using an integrated auto-encoder architecture with a systematic code generator and matrix-based adaptive double-weighted (MA-DW) decoder. This approach achieves superior performance compared to conventional systems while reducing training complexity through joint optimization of code design and decoding parameters.