Multiple-Bases Belief Propagation List Decoding for Quantum LDPC Codes

TL;DR

This paper introduces a novel belief-propagation list decoder for quantum LDPC codes that enhances decoding performance by using multiple parity-check representations, achieving better error rates with efficient parallel processing.

Contribution

It extends the classical MBBP framework to quantum codes, providing a structured diversity approach that improves decoding accuracy without increasing complexity.

Findings

MBBP-LD reduces error rates by up to 20-30% compared to existing BP decoders.

It maintains linear-time complexity and is suitable for parallel implementation.

The method shows significant improvements on several quantum LDPC codes in simulations.

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.