On Puncturing Strategies for Polar Codes

TL;DR

This paper proposes symmetric puncturing patterns for polar codes, developed from generator matrix rows, optimized via density evolution, and shown to outperform existing rate-compatible code constructions.

Contribution

It introduces a novel class of symmetric puncturing patterns for polar codes, with a low-complexity generation method and improved performance over existing techniques.

Findings

Symmetric puncturing patterns outperform state-of-the-art methods.

A low-complexity search tree algorithm effectively generates these patterns.

Optimized patterns via density evolution enhance code performance.

Abstract

This paper introduces a class of specific puncturing patterns, called symmetric puncturing patterns, which can be characterized and generated from the rows of the generator matrix $G_N$. They are first shown to be non-equivalent, then a low-complexity method to generate symmetric puncturing patterns is proposed, which performs a search tree algorithm with limited depth, over the rows of $G_N$. Symmetric patterns are further optimized by density evolution, and shown to yield better performance than state-of-the-art rate compatible code constructions, relying on either puncturing or shortening techniques.