Quantum low-density parity-check (QLDPC) codes have been proven to achieve higher minimum distances at higher code rates than surface codes. However, this family of codes imposes stringent latency requirements and poor performance under iterative decoding, especially when the variable degree is low. In this work, we improve both the error correction performance and decoding latency of variable degree-3 (dv-3) QLDPC codes under iterative decoding. Firstly, we perform a detailed analysis of the structure of a well-known family of QLDPC codes, i.e., hypergraph product-based codes. Then, we propose a decoding approach that stems from the knowledge of harmful configurations apparent in these codes. Our decoding scheme is based on applying a modified version of bit flipping (BF) decoding, namely two-bit bit flipping (TBF) decoding, which adds more degrees of freedom to BF decoding. The granularity offered by TBF decoding helps us design sets of decoders that operate in parallel and can collectively decode error patterns appearing in harmful configurations of the code, thus addressing both the latency and performance requirements. Finally, simulation results demonstrate that the proposed decoding scheme surpasses other iterative decoding approaches for various dv-3 QLDPC codes.

翻译：量子低密度奇偶校验（QLDPC）码已被证明能在比表面码更高的码率下实现更大的最小距离。然而，这类码对译码延迟要求严苛，且在迭代译码下性能较差，特别是在变量节点度数较低时。本研究改进了变量节点度数为3（dv-3）的QLDPC码在迭代译码下的纠错性能和译码延迟。首先，我们对一类广为人知的QLDPC码（即基于超图积构造的码）的结构进行了详细分析。随后，基于对这些码中有害构型的认知，提出了一种译码方法。我们的译码方案采用改进型比特翻转（BF）译码，即双比特翻转（TBF）译码，其为BF译码提供了更多自由度。TBF译码提供的细粒度特性有助于我们设计并行操作的译码器集合，这些译码器能够协同译码出现在码有害构型中的错误模式，从而同时满足延迟和性能要求。最后，仿真结果表明，所提出的译码方案在多种dv-3 QLDPC码上均优于其他迭代译码方法。