Multiple-Bases Belief Propagation List Decoding for Quantum LDPC Codes

2026-05-13

AI Summary

This work addresses the performance limitations of conventional belief propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes by introducing, for the first time, a classical multi-basis BP framework into the quantum domain. By decomposing the Tanner graph into acyclic subtrees, the method constructs multiple redundant parity-check representations to generate structured decoding diversity, enabling efficient list decoding through parallel BP executions. The approach retains linear time complexity and avoids superlinear post-processing overhead. Evaluated on [[144,12,12]] and [[288,12,18]] QLDPC codes, it significantly outperforms existing BP-based decoders, achieving up to 20% and 30% lower error rates compared to BPGD and BP-OSD, respectively, while requiring fewer total BP iterations.

Abstract

In this paper, we propose a belief-propagation (BP)-based decoder, termed the Multiple-Bases Belief-Propagation List Decoder (MBBP-LD), for quantum low-density parity-check (QLDPC) codes. The key idea is to generate \emph{structured decoding diversity} by constructing multiple redundant parity-check representations via cycle-free subtree decompositions of the Tanner graph, and running BP decoding in parallel across these representations. This extends the classical Multiple-Bases Belief-Propagation (MBBP) framework to the quantum setting while preserving the linear-time complexity and efficiency of standard BP decoding, and avoids the need for super-linear post-processing. Simulation results demonstrate that MBBP-LD improves upon existing BP-based decoders, including BP with ordered statistics decoding (BP-OSD) and belief propagation with guided decimation (BPGD) across several QLDPC codes, while requiring substantially fewer total BP iterations. For bivariate bicycle codes $[[144,12,12]]$ and $[[288,12,18]]$, MBBP-LD achieves up to $20\%$ reduction in error rate compared to BPGD and up to $30\%$ compared to BP-OSD in the low- and moderate-error regimes. For the larger B1 code $[[882, 24, 18 \leq d \leq 24]]$, MBBP-LD attains comparable or improved performance relative to BPGD while maintaining BP-like decoding latency under parallel implementation.

Problem

• Quantum LDPC codes
• Belief Propagation decoding
• Decoding performance
• Error rate reduction
• QLDPC decoding

Innovation

• Multiple-Bases Belief Propagation
• Quantum LDPC Codes
• Structured Decoding Diversity
• Cycle-Free Subtree Decomposition
• List Decoding