This paper presents a refined analysis of the block error rate (BLER) of polar codes over symmetric binary-input discrete memoryless channels under successive cancellation (SC) and successive cancellation list (SCL) decoding. A novel expression for the BLER under SC decoding is derived directly in terms of the decoder's LLRs. Building on this formulation, we propose a polar code construction algorithm optimized for SC decoding and evaluate its performance under SC and dynamic SC flip (DSCF) decoding against established SC-optimized constructions, including Gaussian approximation (GA)-based and Tal-Vardy polar codes. Furthermore, by decomposing the BLER into path loss and path selection components, we derive a novel LLR-based expression for the path loss probability, which enables an SCL-optimized polar code construction method. The proposed constructions are evaluated under SCL decoding with list sizes 2, 4, and 8, and are compared with 5G standard polar codes, GA-based designs, and Reed-Muller polar codes. Simulation results show that the proposed SC-optimized polar codes achieve up to a 0.2 dB performance gain under DSCF decoding over the AWGN channel compared to benchmark constructions, and exhibit superior performance over binary symmetric channels. For SCL-optimized polar codes, the proposed method achieves comparable or improved performance across all considered list sizes, with gains of up to 0.4 dB relative to benchmark designs.

翻译：本文针对对称二进制输入离散无记忆信道下采用连续删除（SC）和连续删除列表（SCL）译码的极化码，提出了块误码率（BLER）的精确分析方法。通过直接利用译码器的对数似然比（LLR），推导出SC译码下BLER的新表达式。在此基础上，我们提出了一种针对SC译码优化的极化码构造算法，并在SC译码和动态SC翻转（DSCF）译码下，与基于高斯近似（GA）和Tal-Vardy极化码等现有SC优化构造方案进行了性能评估。进一步地，通过将BLER分解为路径损失和路径选择两部分，我们推导出基于LLR的路径损失概率新表达式，从而实现了面向SCL译码优化的极化码构造方法。针对列表大小为2、4和8的SCL译码场景，评估了所提构造方案，并与5G标准极化码、基于GA的设计以及里德-穆勒极化码进行了比较。仿真结果表明，在AWGN信道下采用DSCF译码时，所提SC优化极化码相较于基准构造方案可获得高达0.2 dB的性能增益，且在二进制对称信道上表现出更优性能。对于SCL优化极化码，所提方法在所有考虑的列表大小下均实现相当或更优的性能，相较基准设计最大增益达0.4 dB。