We introduce an algorithm for approximating the codebook probability that is compatible with all successive cancellation (SC)-based decoding algorithms, including SC list (SCL) decoding. This approximation is based on an auxiliary distribution that mimics the dynamics of decoding algorithms with an SC decoding schedule. Based on this codebook probability and SCL decoding, we introduce soft-output SCL (SO-SCL) to generate both blockwise and bitwise soft-output (SO). Using that blockwise SO, we first establish that, in terms of both block error rate (BLER) and undetected error rate (UER), SO-SCL decoding of dynamic Reed-Muller (RM) codes significantly outperforms the CRC-concatenated polar codes from 5G New Radio under SCL decoding. Moreover, using SO-SCL, the decoding misdetection rate (MDR) can be constrained to not exceed any predefined value, making it suitable for practical systems. Proposed bitwise SO can be readily generated from blockwise SO via a weighted sum of beliefs that includes a term where SO is weighted by the codebook probability, resulting in a soft-input soft-output (SISO) decoder. Simulation results for SO-SCL iterative decoding of product codes and generalized LDPC (GLDPC) codes, along with information-theoretical analysis, demonstrate significant superiority over existing list-max and list-sum approximations.

翻译：我们提出了一种与所有基于连续消除（SC）的译码算法（包括SC列表（SCL）译码）兼容的码本概率近似算法。该近似基于一个辅助分布，该分布模拟了采用SC译码调度的译码算法的动态特性。基于此码本概率及SCL译码，我们引入软输出SCL（SO-SCL）以同时生成分组级与比特级软输出（SO）。利用该分组级软输出，我们首先证明：在分组误码率（BLER）与未检测误码率（UER）方面，动态里德-穆勒（RM）码的SO-SCL译码性能显著优于5G新空口标准中采用SCL译码的CRC级联极化码。此外，通过SO-SCL译码，可将译码漏检率（MDR）约束在不超过任何预设值的范围内，使其适用于实际系统。所提出的比特级软输出可直接通过加权求和信念从分组级软输出生成，其中包含软输出以码本概率加权的项，从而构成软输入软输出（SISO）译码器。针对乘积码与广义LDPC（GLDPC）码的SO-SCL迭代译码仿真结果及信息论分析表明，其性能显著优于现有的列表最大与列表求和近似方法。