On Convolutional Precoding in PAC Codes

In polarization-adjusted convolutional (PAC) codes, a convolutional transform is employed as a precoding stage before the polar transform. It turned out that the precoding stage improves the weight distribution of polar codes according. That could be the main reason for the superiority of error correction performance of PAC codes relative to polar codes. In this work, we explicitly show why the convolutional precoding reduces the number of minimum-weight codewords. Furthermore, we show where the precoding stage is not effective in the improvement of weight distribution. Eventually, to evaluate the FER gain obtainable from reducing the number of min-weight codewords, we assess the performance and the number of minimum-weight codewords resulted from an irregular convolutional precoding process.