Study of Polar Codes Based on Piecewise Gaussian Approximation

TL;DR

This paper introduces a piecewise Gaussian approximation method for constructing polar codes, significantly improving performance over traditional Gaussian approximation techniques.

Contribution

The paper proposes a novel piecewise Gaussian approximation approach for polar code construction, enhancing accuracy and performance compared to existing methods.

Findings

PGA outperforms standard GA in simulations

The method provides a more accurate approximation function

Performance gains are consistent across various code examples

Abstract

In this paper, we investigate the construction of polar codes by Gaussian approximation (GA) and develop an approach based on piecewise Gaussian approximation (PGA). In particular, with the piecewise approach we obtain a function that replaces the original GA function with a more accurate approximation, which results in significant gain in performance. The proposed PGA construction of polar codes is presented in its integral form as well as an alternative approximation that does not rely on the integral form. Simulations results show that the proposed PGA construction outperforms the standard GA for several examples of polar codes and rates.