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

2025-07-04

AI Summary

Short-length LDPC codes suffer from poor convergence under belief propagation (BP) decoding, primarily due to a small number of error-prone variable nodes (VNs) that trigger decoding failure. Method: We propose a learnable multi-round BP (MRBP) decoding framework that unifies VN selection and channel error estimation—inspired by syndrome-based neural decoding. A lightweight neural network is designed to directly predict vulnerable VNs from the syndrome and node-wise reliability metrics, enabling end-to-end learning of targeted perturbations. Contribution/Results: Unlike existing MRBP methods relying on handcrafted heuristics, our approach significantly reduces the number of decoding iterations required to approach maximum-likelihood performance. On short codes (e.g., blocklengths N = 128–256), it improves decoding success probability by one to two orders of magnitude, without increasing per-iteration computational complexity.

Technology Category

Natural Language Processing: Learning & Optimization for NLPMachine Learning: Multi-instance/Multi-view LearningCognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsEconomics, Online Markets and Human Computation: Social networks and social learning

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.

Problem

• Improving error correction for short LDPC codes
• Enhancing multi-round BP decoding efficiency
• Reducing decoding rounds for near-MLD performance

Innovation

• Neural network predicts problematic variable nodes
• Syndrome-based learning improves MRBP decoding
• Fewer rounds needed for near-MLD performance