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arXiv · 2411.05433

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

Malek Ellouze·Romain Tajan·Camille Leroux·Christophe Jégo·Charly Poulliat
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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.

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Malek Ellouze, Romain Tajan, Camille Leroux, Christophe Jégo, Charly Poulliat. 2024-11-08. Computing the Low-Weight codewords of Punctured and Shortened Pre-Transformed polar Codes. https://arxiv.org/abs/2411.05433

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