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IEEE Transactions on Machine Learning in Communications and Networking

A Neural Network Empowered Belief Propagation Algorithm Optimized for Short-Cycles in Tanner Graph

Hao Xu, Ying Li, Bin Tan, Jun Hui Wu, Die Hu

Published Jan 1, 2023• 7 citations

Abstract

Short-cycles in Tanner graphs have a direct impact on the accuracy and effectiveness of the belief propagation (BP) algorithm, as they diverge the BP algorithm by disrupting the independency of message transmission. In this paper, we present a Neural Network Empowered BP (NNE-BP) algorithm as an alternative to the conventional BP algorithm, which can approach the optimum form of BP in short-cycles. The earlier deep learning (DL) based decoder treated the entire decoding process as a classification issue, making it effective only in short block lengths and with limited generalization. In the proposed NNE-BP, we design two neural networks, namely the horizontal network and vertical network, to learn, respectively, the optimized horizontal and vertical processes for single nodes in the presence of cycles. These two networks operate in an iterative fashion, allowing them to approach a theoretical message propagation equation without assuming independent message transmission. Compared to the classification based DL decoder, the proposed network topology is no longer bundled with any specific Tanner graph, and the number of network parameters are greatly reduced. The obtained experimental results show that the proposed NNE-BP outperforms the conventional BP decoder, especially in the case of short-cycles.

DOI: 10.1109/tmlcn.2023.3279051

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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.

In this work, we 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, which algorithmically aligns with the conventional belief propagation (BP) decoding method. In each iteration, the “weight” on the message passed along each edge is obtained from a fully connected neural network that has the reliability information from nodes/edges as its input. Compared to existing deep-learning-based decoding schemes, the EW-GNN decoder is characterised by its scalability, meaning that 1) the number of trainable parameters is independent of the codeword length, and 2) an EW-GNN decoder trained with shorter/simple codes can be directly used for longer/sophisticated codes of different code rates. Furthermore, simulation results show that the EW-GNN decoder outperforms the BP and deep-learning-based BP methods from the literature in terms of the decoding error rate.

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