Application of Guessing to Sequential Decoding of Polarization-Adjusted Convolutional (PAC) Codes

Abstract

Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the cutoff rate denotes the region between rates whose average computational complexity of decoding is finite and those which is infinite. In this paper, by benefiting from the polarization and guessing techniques, we prove that the required computation in sequential decoding of pre-transformed polar codes polarizes, and this polarization determines which set of bit positions within the rate profile may result in high computational complexity. Based on this, we propose a technique for taming the Reed-Muller (RM) rate-profile construction, and the performance results demonstrate that the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed-RM rate-profile construction and requires a significantly lower computational complexity than the RM rate-profile construction.