A Comparative Study of Polar Code Constructions for the AWGN Channel

TL;DR

This paper compares various polar code construction algorithms for the AWGN channel, showing that optimizing the design-SNR makes all algorithms produce similarly good codes, despite their differences.

Contribution

It provides a comprehensive survey of existing polar code constructions and introduces a heuristic algorithm to optimize the design-SNR for improved performance.

Findings

All construction algorithms perform equally well when the design-SNR is optimized.

The proposed heuristic effectively identifies the optimal design-SNR for each construction.

Extensive simulations validate that optimized constructions yield comparable performance.

Abstract

We present a comparative study of the performance of various polar code constructions in an additive white Gaussian noise (AWGN) channel. A polar code construction is any algorithm that selects $K$ best among $N$ possible polar bit-channels at the design signal-to-noise-ratio (design-SNR) in terms of bit error rate (BER). Optimal polar code construction is hard and therefore many suboptimal polar code constructions have been proposed at different computational complexities. Polar codes are also non-universal meaning the code changes significantly with the design-SNR. However, it is not known which construction algorithm at what design-SNR constructs the best polar codes. We first present a comprehensive survey of all the well-known polar code constructions along with their full implementations. We then propose a heuristic algorithm to find the best design-SNR for constructing best possible polar codes from a given construction algorithm. The proposed algorithm involves a search among several possible design-SNRs. We finally use our algorithm to perform a comparison of different construction algorithms using extensive simulations. We find that all polar code construction algorithms generate equally good polar codes in an AWGN channel, if the design-SNR is optimized.