Towards Weight Distribution-Aware Polar Codes

TL;DR

This paper proposes a novel method for designing polar codes with improved weight distribution by leveraging the weight-contribution partial order, avoiding search-based optimization, and demonstrating superior numerical performance.

Contribution

It introduces a structure-based design approach for polar codes that enhances weight distribution without using search or optimization algorithms.

Findings

Improved weight distribution over traditional polar codes.

Enhanced performance demonstrated through numerical results.

Effective design method without search or optimization.

Abstract

Polar codes are constructed based on the reliability of sub-channels resulting from the polarization effect. However, this information-theoretic construction approach leads to a poor weight distribution. To address this issue, pre-transformed polar codes, such as CRC-polar codes and PAC codes, have been employed. In this paper, we focus on the structure of polar codes without applying any pre-transformations and explore methods, guided by the weight-contribution partial order, to design polar-like codes with enhanced weight distribution, notably without employing any search or optimization algorithms. Numerical results demonstrate improvement over a range of codes both with and without pre-transformation.