Quantum low-density parity-check (QLDPC) codes are among the most promising candidates for future quantum error correction schemes. However, a limited number of short to moderate-length QLDPC codes have been designed and their decoding performance is sub-optimal with a quaternary belief propagation (BP) decoder due to unavoidable short cycles in their Tanner graphs. In this paper, we propose a novel joint code and decoder design for QLDPC codes. The constructed codes have a minimum distance of about the square root of the block length. In addition, it is, to the best of our knowledge, the first QLDPC code family where BP decoding is not impaired by short cycles of length 4. This is achieved by using an ensemble BP decoder mitigating the influence of assembled short cycles. We outline two code construction methods based on classical quasi-cyclic codes and finite geometry codes. Numerical results demonstrate outstanding decoding performance over depolarizing channels.

翻译：量子低密度奇偶校验码（QLDPC码）是未来量子纠错方案中最具潜力的候选之一。然而，目前已设计的短中长QLDPC码数量有限，且因Tanner图中不可避免存在短环，采用四进制置信传播（BP）译码器时性能欠佳。本文提出一种新型的QLDPC码联合码本与译码器设计方法。所构造码字的最小距离约为分组长度的平方根。此外，据我们所知，这是首个在BP译码中不受长度为4的短环影响的QLDPC码族。该成果通过采用集成BP译码器来缓解聚合短环的影响得以实现。我们基于经典准循环码和有限几何码概述了两种码构造方法。数值结果表明，该方法在去极化信道下具有卓越的译码性能。