Fully Parallelized BP Decoding for Quantum LDPC Codes Can Outperform BP-OSD

TL;DR

This paper introduces a fully parallelizable, hardware-efficient decoder for quantum LDPC codes that outperforms traditional BP-OSD in latency and is suitable for real-time quantum error correction.

Contribution

It proposes a novel BP-SF decoding method that eliminates Gaussian elimination, enabling high parallelism and reduced latency in quantum LDPC decoding.

Findings

Achieves comparable or better logical error rates than BP-OSD.

Reduces average latency to approximately 70% of BP-OSD.

Parallel post-processing further reduces latency by 55%.

Abstract

This work presents a hardware-efficient and fully parallelizable decoder for quantum LDPC codes that leverages belief propagation (BP) with a speculative post-processing strategy inspired by classical Chase decoding algorithm. By monitoring bit-level oscillation patterns during BP, our method identifies unreliable bits and generates multiple candidate vectors to selectively flip syndromes. Each modified syndrome is then decoded independently using short-depth BP, a process we refer to as BP-SF (syndrome flip). This design eliminates the need for costly Gaussian elimination used in the current BP-OSD approaches. Our implementation achieves logical error rates comparable to or better than BP-OSD while offering significantly lower latency due to its high degree of parallelism for a variety of bivariate bicycle codes. Evaluation on the [[144,12,12]] bivariate bicycle code shows that the proposed decoder reduces average latency to approximately $70\%$ of BP-OSD. When post-processing is parallelized the average latency is reduced by $55\%$ compared to the single process implementation, with the maximum latency reaching as low as $18\%$. These advantages make it particularly well-suited for real-time and resource-constrained quantum error correction systems.