Computing the Low-Weight codewords of Punctured and Shortened Pre-Transformed polar Codes
Information Theory
2024-11-11 v1 math.IT
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.
Keywords
Cite
@article{arxiv.2411.05433,
title = {Computing the Low-Weight codewords of Punctured and Shortened Pre-Transformed polar Codes},
author = {Malek Ellouze and Romain Tajan and Camille Leroux and Christophe Jégo and Charly Poulliat},
journal= {arXiv preprint arXiv:2411.05433},
year = {2024}
}