The recent success in constructing asymptotically good quantum low-density parity-check (QLDPC) codes makes this family of codes a promising candidate for error-correcting schemes in quantum computing. However, conventional belief propagation (BP) decoding of QLDPC codes does not yield satisfying performance due to the presence of unavoidable short cycles in their Tanner graph and the special degeneracy phenomenon. In this work, we propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency. Furthermore, we propose a novel neural belief propagation decoder based on the quaternary BP decoder of QLDPC codes which leads to further decoding performance improvements.

翻译：近年来，渐近好量子低密度奇偶校验（QLDPC）码的成功构造，使得此类码成为量子计算中纠错方案的有力候选。然而，由于Tanner图中不可避免的短环以及特殊的简并现象，传统的置信传播（BP）译码方法在处理QLDPC码时性能欠佳。本文提出利用原始校验矩阵各行的线性组合生成具有冗余行的校验矩阵，并基于此进行QLDPC码译码。该方法在实现极低译码延迟的同时，显著提升了译码性能。此外，我们基于QLDPC码的四进制BP译码器提出了一种新型神经置信传播译码器，进一步改善了译码性能。