Belief propagation (BP) decoding of quantum low density parity check (QLDPC) codes is often implemented using overcomplete stabilizer (OS) representations, where redundant parity checks are introduced to improve finite length performance. Decoder behavior for such representations is governed primarily by finite iteration dynamics rather than asymptotic code properties. These dynamics are known to critically depend on the initialization of the decoder. In this paper, we investigate the impact of mismatched log likelihood ratios (LLRs) used for BP initialization on the performance of QLDPC codes with OS representations. Our results demonstrate that initial LLR mismatch has a strong influence on the frame error rate (FER), particularly in the low noise regime. We also show that the optimal performance is not sharply localized: the FER remains largely insensitive over an extended region of mismatched LLRs. This behavior motivates an interpretation of LLR mismatch as a regularization control parameter rather than a quantity that must be precisely matched to the quantum channel.

翻译：量子低密度奇偶校验（QLDPC）码的置信传播（BP）解码常采用过完备稳定子（OS）表示实现，即引入冗余奇偶校验以改善有限码长性能。此类表示下的解码器行为主要受有限迭代动力学而非渐近码特性支配。已知这些动力学关键取决于解码器的初始化方式。本文研究了BP初始化所用对数似然比（LLR）失配对采用OS表示的QLDPC码性能的影响。结果表明：初始LLR失配对帧错误率（FER）具有显著影响，尤其在低噪声区域。我们还发现最优性能并非尖锐定位：在较宽的LLR失配区间内，FER基本保持不敏感。该现象促使我们将LLR失配解释为一种正则化控制参数，而非必须与量子信道精确匹配的物理量。