Min-Sum (MS) decoding is a popular low-complexity alternative to belief propagation (BP), retaining only the minimum incoming message magnitude during check-node (CN) processing, at the cost of systematic message magnitude overestimation. The scaled MS (SMS) decoder compensates for this effect using a fixed scaling factor. We propose the syndrome adaptive gain Min-Sum (SAGMS) decoder for quantum low-density parity-check (QLDPC) codes, which adapts the message gain online based on the fraction of unsatisfied stabilizers, requiring no per-code or per-noise level optimization. We show that the scaling factor required for SMS to match belief propagation decreases with the CN degree, so any fixed scaling optimized for one degree incurs into a growing penalty as the CN degree varies. SAGMS avoids this limitation by adapting the gain during decoding. Simulations on generalized bicycle QLDPC codes demonstrate that SAGMS matches or outperforms the frame error rate (FER) of an offline optimized SMS decoder. Moreover, SAGMS approaches BP performance and, under certain conditions outperforms it while retaining MS-level complexity.

翻译：最小和译码是置信传播的一种低复杂度替代方案，在检查节点处理过程中仅保留最小传入消息幅度，但会导致系统性的消息幅度高估。缩放最小和译码器通过固定缩放因子补偿这一效应。我们针对量子低密度奇偶校验码提出伴随自适应增益最小和译码器，该译码器基于未满足稳定子的比例在线调整消息增益，无需针对每种码或噪声水平进行优化。研究表明，缩放最小和译码匹配置信传播所需的缩放因子随检查节点度数的增加而降低，因此针对某一度数优化的固定缩放因子在检查节点度数变化时会产生递增的性能损失。伴随自适应增益最小和译码通过在译码过程中自适应调整增益规避了这一限制。基于广义自行车量子低密度奇偶校验码的仿真表明，伴随自适应增益最小和译码在帧错误率上匹配或优于离线优化的缩放最小和译码器。此外，伴随自适应增益最小和译码接近置信传播性能，并在特定条件下超越置信传播，同时保持最小和级别的复杂度。