Informed Dynamic Scheduling for QLDPC Codes

TL;DR

This paper introduces an informed dynamic scheduling method for quantum LDPC codes that significantly improves decoding performance by addressing residual errors and trapping sets, outperforming previous layered scheduling techniques.

Contribution

It proposes a novel predict-and-reduce-error mechanism for residual belief propagation, enhancing quantum LDPC decoding beyond existing layered scheduling methods.

Findings

Over one order of magnitude performance gain on bicycle and hypergraph codes

Effective mitigation of quantum trapping sets

Improved convergence speed compared to sLBP

Abstract

Recent research has shown that syndrome-based belief propagation using layered scheduling (sLBP) can not only accelerate the convergence rate but also improve the error rate performance by breaking the quantum trapping sets for quantum low-density parity-check (QLDPC) codes, showcasing a result distinct from classical error correction codes. In this paper, we consider edge-wise informed dynamic scheduling (IDS) for QLDPC codes based on syndrome-based residual belief propagation (sRBP). However, the construction of QLDPC codes and the identical prior intrinsic information assignment will result in an equal residual in many edges, causing a performance limitation for sRBP. Two heuristic strategies, including edge pool design and error pre-correction, are introduced to tackle this obstacle and quantum trapping sets. Then, a novel sRBP equipped with a predict-and-reduce-error mechanism (PRE-sRBP) is proposed, which can provide over one order of performance gain on the considered bicycle codes and symmetric hypergraph (HP) code under similar iterations compared to sLBP.