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

TL;DR

This paper demonstrates that the computational cutoff rate in sequential decoding of PAC codes polarizes, enabling improved rate-profile construction and reduced complexity while maintaining near-theoretical error-correction performance.

Contribution

It proves the polarization of the computational cutoff rate and introduces a tamed-RM rate-profile construction for PAC codes with lower complexity.

Findings

The computational cutoff rate in sequential decoding polarizes.

Tamed-RM rate-profile construction achieves near-theoretical performance.

Reduced computational complexity compared to traditional RM rate-profile.

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 computational 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 computational cutoff rate in sequential decoding of pre-transformed polar codes polarizes. The polarization of the computational cutoff rate affects the criteria for the rate-profile construction of the pre-transformed polar codes. 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.