Construction of PAC Codes with List-Search and Path-Splitting Critical Sets

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.