Computing the Low-Weight codewords of Punctured and Shortened Pre-Transformed polar Codes

TL;DR

This paper introduces a deterministic algorithm for efficiently counting low-weight codewords in punctured and shortened polar codes, applicable to various configurations and outperforming existing methods in computational complexity.

Contribution

The paper presents a novel, general algorithm for counting low-weight codewords in punctured and shortened polar codes, regardless of pattern or pretransformation.

Findings

Algorithm reduces computational complexity compared to state-of-the-art methods.

Method is applicable to any frozen bit set, puncturing/shortening pattern, or pretransformation.

Results demonstrate efficiency and broad applicability of the proposed approach.

Abstract

In this paper, we present a deterministic algorithm to count the low-weight codewords of punctured and shortened pure and pre-transformed polar codes. The method first evaluates the weight properties of punctured/shortened polar cosets. Then, a method that discards the cosets that have no impact on the computation of the low-weight codewords is introduced. A key advantage of this method is its applicability, regardless of the frozen bit set, puncturing/shortening pattern, or pretransformation. Results confirm the method's efficiency while showing reduced computational complexity compared to stateof-the-art algorithms.