Learning to Decode Quantum LDPC Codes via Cluster-Based Sequential Belief Propagation

2026-07-22

AI Summary

This work addresses the limitations of belief propagation (BP) decoding for quantum low-density parity-check (LDPC) codes—namely, performance degradation due to short cycles, degeneracy, and convergence failure—and the trade-offs inherent in existing reinforcement learning (RL)-based variable-node scheduling, which improves error-rate performance at the cost of parallelism and increased latency. To overcome these challenges, the authors propose a clustering-based RL scheduling approach that partitions variable nodes into fixed clusters and enables an agent to select one cluster per iteration for parallel update. By representing cluster states via permutation-invariant quantized histograms, the method decouples state complexity from cluster size and formulates a cluster-level Markov decision process with Q-learning. Evaluated on representative quantum LDPC codes, the proposed scheme achieves error-rate performance close to per-node RL scheduling while substantially reducing the number of scheduling steps, thereby effectively balancing decoding performance, parallel efficiency, and low latency.

Abstract

Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is attractive due to its low complexity, but its performance is often limited by short cycles, degeneracy, and convergence failures. Recently, reinforcement-learning-based sequential variable-node (VN) scheduling (RL-S) was shown to improve BP decoding by learning state-dependent update orders. However, the VN-by-VN nature of that approach offers limited within-iteration parallelism, since only one VN is updated at a time. In this paper, we propose a cluster-based extension of RL-S for QLDPC codes. The VNs are partitioned into fixed clusters, and at each scheduling step the RL agent selects one cluster to update, after which all VNs in that cluster are updated in parallel using the same pre-update incoming messages. To keep the tabular state space practical for large cluster sizes, we introduce a permutation-invariant cluster state based on a normalized histogram of local mismatch weights, followed by quantization. This representation makes the number of cluster states depend on the quantization resolution rather than the cluster size. We also develop the corresponding cluster-level Markov decision process, reward function, and Q-learning update. Numerical results on representative QLDPC codes show that the proposed clustered learned scheduling preserves most of the error-rate benefit of VN-level learned sequential scheduling while substantially reducing the number of scheduling decisions per BP iteration, thereby providing an attractive latency-parallelism tradeoff.

Problem

• quantum LDPC codes
• belief propagation decoding
• sequential scheduling
• parallelism
• reinforcement learning

Innovation

• cluster-based scheduling
• reinforcement learning
• quantum LDPC codes
• belief propagation
• permutation-invariant state representation