Multiple-Bases Belief Propagation List Decoding for Quantum LDPC Codes

Sheida Rabeti and Hessam Mahdavifar · 2026 · arXiv.org

| 编号 QE285 | 主题 译码算法 | 链接 arXiv:2605.14170 |

摘要

摘要保留原文（英文）

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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 $[[88

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