Learning Variable Node Selection for Improved Multi-Round Belief Propagation Decoding

TL;DR

This paper introduces a neural network-based method inspired by syndrome decoding to identify problematic variable nodes in multi-round belief propagation decoding, significantly improving error correction performance for short LDPC codes.

Contribution

It proposes a novel SBND-inspired neural network architecture for variable node selection in MRBP decoding, outperforming heuristic rules and reducing decoding attempts.

Findings

Outperforms existing heuristic methods in fewer decoding rounds.

Achieves near-MLD performance on short LDPC codes.

Demonstrates the effectiveness of neural networks in decoding error correction.

Abstract

Error correction at short blocklengths remains a challenge for low-density parity-check (LDPC) codes, as belief propagation (BP) decoding is suboptimal compared to maximum-likelihood decoding (MLD). While BP rarely makes errors, it often fails to converge due to a small number of problematic, erroneous variable nodes (VNs). Multi-round BP (MRBP) decoding improves performance by identifying and perturbing these VNs, enabling BP to succeed in subsequent decoding attempts. However, existing heuristic approaches for VN identification may require a large number of decoding rounds to approach ML performance. In this work, we draw a connection between identifying candidate VNs to perturb in MRBP and estimating channel output errors, a problem previously addressed by syndrome-based neural decoders (SBND). Leveraging this insight, we propose an SBND-inspired neural network architecture that learns to predict which VNs MRBP needs to focus on. Experimental results demonstrate that the proposed learning approach outperforms expert rules from the literature, requiring fewer MRBP decoding attempts to reach near-MLD performance. This makes it a promising lead for improving the decoding of short LDPC codes.