We study the decoding problem for quantum Tanner codes and propose to exploit the underlying local code structure by grouping check nodes into more powerful generalized check nodes for enhanced iterative belief propagation (BP) decoding by decoding the generalized checks using a maximum a posteriori (MAP) decoder as part of the check node processing of each decoding iteration. We mainly study the finite-length setting and show that the proposed enhanced generalized BP decoder for quantum Tanner codes significantly outperforms the standard quaternary BP decoder with memory effects, as well as the recently proposed Relay-BP decoder, even outperforming generalized bicycle (GB) codes with comparable parameters in some cases. For other classes of quantum low-density parity-check (qLDPC) codes, we propose a greedy algorithm to combine checks for generalized BP decoding. However, for GB codes, bivariate bicycle codes, hypergraph product codes, and lifted-product codes, there seems to be limited gain by combining simple checks into more powerful ones. To back up our findings, we also provide a theoretical cycle analysis for the considered qLDPC codes.

翻译：我们研究了量子坦纳码的解码问题，提出通过将校验节点分组为更强大的广义校验节点，以利用其底层局部码结构，从而增强迭代置信传播解码性能。具体方法是在每次解码迭代的校验节点处理中，使用最大后验解码器对广义校验进行解码。我们主要研究有限码长场景，结果表明：所提出的增强型广义置信传播解码器在量子坦纳码上的性能显著优于具有记忆效应的标准四进制置信传播解码器以及近期提出的中继置信传播解码器，在某些情况下甚至优于具有可比参数的广义自行车码。对于其他类别的量子低密度奇偶校验码，我们提出一种贪心算法来合并校验以进行广义置信传播解码。然而，对于广义自行车码、双变量自行车码、超图乘积码和提升乘积码，将简单校验合并为更强大的校验似乎增益有限。为支撑研究结论，我们还对所考虑的量子低密度奇偶校验码进行了理论上的循环分析。