Study of Non-Uniform Channel Polarization and Design of Polar Codes with Arbitrary Rates

TL;DR

This paper introduces non-uniform channel polarization and a rate-compatible polar code design method for arbitrary lengths using Gaussian Approximation, enhancing flexibility and efficiency in polar coding over AWGN channels.

Contribution

It proposes a novel non-uniform polarization scheme based on Gaussian Approximation and a rate-compatible design technique for arbitrary codeword lengths.

Findings

NUPGA outperforms existing rate-compatible techniques in simulations

Efficient re-polarization process adapts to desired code lengths

Improved flexibility in polar code design for AWGN channels

Abstract

In this paper, we present the concept of non-uniform channel polarization and a scheme for rate-compatible polar code construction for any codeword length using additive white Gaussian noise (AWGN) channels and the successive cancellation (SC) decoder. A Non-Uniform Polarization technique based on the Gaussian Approximation (NUPGA) is developed and an efficient rate-compatible design technique is devised to choose the best channels for transmission by a process of re-polarization of the codeword with the desired length. Simulations illustrate the proposed NUPGA design against existing rate-compatible techniques.