Polarization-adjusted convolutional (PAC) codes can approach the theoretical bound for block error rate (BLER) performance at short-to-medium codeword length. PAC codes have excellent BLER performance using Monte Carlo (MC) rate-profiles and Weighted Sum (WS) rate-profiles, but the BLER performances of the constructed codes still fall away from the dispersion bound at high signal-to-noise ratios (SNR). This paper proposes a List-Search (LS) construction method for PAC codes, which considers the influence of weight spectrum on BLER performance and the condition that sequence decoding for PAC codes having a finite mean computational complexity. The proposed construction method using LS can reduce the number of minimum weight codewords of PAC codes. The BLER performance of the constructed codes is better than that of the constructed codes using MC rate-profiles or WS rate-profiles, and can approach the dispersion bound at high SNR. Moreover, the BLER performance of successive cancellation list (SCL) decoding PAC codes using LS rate-profiles can approach the theoretical bound, but SCL decoding requires a large number of sorting operations. To reduce the number of sorting operations, a path-splitting critical sets (PSCS) construction method is proposed. The PSCS obtained by this method are the information bits subset that have the greatest influence on the number of minimum weight codewords. The simulation results show that this method can significantly reduce the number of sorting operations during SCL-type decoding.

翻译：极化调整卷积码（PAC码）在短至中码长范围内能以接近理论界的误块率（BLER）性能逼近理论界。采用蒙特卡洛（MC）速率剖面和加权和（WS）速率剖面的PAC码虽具有优异BLER性能，但所构造码字在高信噪比（SNR）条件下仍偏离色散界。本文提出一种基于列表搜索（LS）的PAC码构造方法，该方法综合考虑了权重谱对BLER性能的影响，以及PAC码序列译码具有有限平均计算复杂度的约束条件。所提出的LS构造方法可减少PAC码最小权重码字数量。采用该方法构造的码字其BLER性能优于基于MC速率剖面或WS速率剖面的构造结果，且在高SNR下可逼近色散界。此外，采用LS速率剖面的连续消除列表（SCL）译码PAC码其BLER性能可逼近理论界，但SCL译码需要大量排序操作。为降低排序操作次数，本文提出基于路径分裂关键集（PSCS）的构造方法。该方法获得的PSCS是对最小权重码字数量影响最大的信息比特子集。仿真结果表明，该方法能显著减少SCL类译码过程中的排序操作次数。