Fast Enumeration of Minimum Weight Codewords of PAC Codes

The number of minimum weight codewords, a.k.a error coefficient, is a good comparative measure for the block error rate (BLER) of a linear block code, in particular in a high SNR regime. The smaller the error coefficient, the lower the BLER. Unlike polar codes, the error coefficient of polarization-adjusted convolutional (PAC) codes cannot be determined easily due to the precoding stage. In this work, we propose an enumeration method that considers the impact of convolutional precoding on the minimum weight codewords of polar codes. This relative enumeration method simplifies the process significantly compared with conventional methods as the complexity analysis shows.