Study of Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

TL;DR

This paper introduces a new method called NUPGA for designing rate-compatible polar codes of arbitrary lengths using non-uniform channel polarization, improving performance over existing techniques for AWGN channels.

Contribution

The paper presents a novel NUPGA method that enables efficient construction of arbitrary-length polar codes through re-polarization, enhancing flexibility and performance.

Findings

NUPGA outperforms existing rate-compatible techniques in simulations.

The method effectively handles arbitrary code lengths with lower complexity.

Simulation results demonstrate improved error performance.

Abstract

We propose a novel scheme for rate-compatible arbitrary-length polar code construction for the additive white Gaussian noise (AWGN) channel. The proposed scheme is based on the concept of non-uniform channel polarization. The original polar codes can only be designed with code lengths that are powers of two. Puncturing, shortening and extension are three strategies to obtain arbitrary code lengths and code rates for polar codes. There are other ways to design codes with arbitrary length but which have encoding and decoding with higher complexity such as multi-kernel, concatenated codes and specific constructions for Belief propagation (BP) or Successive Cancellation (SC) decoding. In general, the quality of the projected bit channels by these arbitrary-length techniques differs from that of the original bit channels, which can greatly affect the performance of the constructed polar codes. The proposed Non-Uniform Polarization based on Gaussian Approximation (NUPGA) is an efficient construction technique for rate-compatible arbitrary-length polar codes, which chooses the best channels (i.e., selects the positions of the information bits) by re-polarization of the codeword with desired length. A generalization of the Gaussian Approximation is devised for both polarization and re-polarization processes. We also present shortening and extension techniques for design polar codes. Simulations verify the effectiveness of the proposed NUPGA designs against existing rate-compatible techniques.