In this paper, we first indicate that the block error event of polar codes under successive cancellation list (SCL) decoding is composed of path loss (PL) error event and path selection (PS) error event, where the PL error event is that correct codeword is lost during the SCL decoding and the PS error event is that correct codeword is reserved in the decoded list but not selected as the decoded codeword. Then, we simplify the PL error event by assuming the all-zero codeword is transmitted and derive the probability lower bound via the joint probability density of the log-likelihood ratios of information bits. Meanwhile, the union bound calculated by the minimum weight distribution is used to evaluate the probability of the PS error event. With the performance analysis, we design a greedy bit-swapping (BS) algorithm to construct polar codes by gradually swapping information bit and frozen bit to reduce the performance lower bound of SCL decoding. The simulation results show that the BLER performance of SCL decoding is close to the lower bound in the medium to high signal-to-noise ratio region and we can optimize the lower bound to improve the BLER performance of SCL decoding by the BS algorithm.

翻译：本文首先指出，在逐次消除列表（SCL）解码下，极化码的块错误事件由路径丢失（PL）错误事件和路径选择（PS）错误事件组成，其中PL错误事件指在SCL解码过程中正确码字丢失，PS错误事件指正确码字保留在解码列表中但未被选为解码码字。随后，我们通过假设传输全零码字简化PL错误事件，并利用信息比特对数似然比的联合概率密度推导其概率下界。同时，采用最小重量分布计算的联合界用于评估PS错误事件的概率。基于性能分析，我们设计了一种贪婪比特交换（BS）算法，通过逐步交换信息比特与冻结比特来降低SCL解码的性能下界。仿真结果表明，在中高信噪比区域，SCL解码的BLER性能接近该下界，且通过BS算法优化下界可提升SCL解码的BLER性能。