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）译码下，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错误事件是指正确的码字在SCL译码过程中丢失，而PS错误事件是指正确的码字保留在译码列表中但未被选为译码码字。随后，我们通过假设全零码字被发送来简化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出其概率下界。同时，利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。基于该性能分析，我们设计了一种贪心比特交换（BS）算法，通过逐步交换信息比特和冻结比特来降低SCL译码的性能下界，从而构造极化码。仿真结果表明，在中高信噪比区域，SCL译码的误块率性能接近该下界，并且我们可以通过BS算法优化该下界以提高SCL译码的误块率性能。