On the Weight Distribution of Weights Less than $2w_{\min}$ in Polar Codes Article Swipe

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Zicheng Ye , Yuan Li , Huazi Zhang , Jun Wang , Guiying Yan , Zhi-Ming Ma ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2308.10024

The number of low-weight codewords is critical to the performance of error-correcting codes. In 1970, Kasami and Tokura characterized the codewords of Reed-Muller (RM) codes whose weights are less than $2w_{\min}$, where $w_{\min}$ represents the minimum weight. In this paper, we extend their results to decreasing polar codes. We present the closed-form expressions for the number of codewords in decreasing polar codes with weights less than $2w_{\min}$. Moreover, the proposed enumeration algorithm runs in polynomial time with respect to the code length.

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Polar Weight distribution Enumeration Mathematics Code (set theory) Minimum weight Combinatorics Discrete mathematics Polynomial Computer science Physics Mathematical analysis Astronomy Set (abstract data type) Thermodynamics Programming language

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2308.10024
PDF: https://arxiv.org/pdf/2308.10024
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Related Works: 10
OpenAlex ID: https://openalex.org/W4386081015

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DOI: https://doi.org/10.48550/arxiv.2308.10024

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Title: On the Weight Distribution of Weights Less than $2w_{\min}$ in Polar Codes

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-08-19

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Authors: Zicheng Ye, Yuan Li, Huazi Zhang, Jun Wang, Guiying Yan, Zhi-Ming Ma

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Landing page: https://arxiv.org/abs/2308.10024

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PDF URL: https://arxiv.org/pdf/2308.10024

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Concepts: Polar, Weight distribution, Enumeration, Mathematics, Code (set theory), Minimum weight, Combinatorics, Discrete mathematics, Polynomial, Computer science, Physics, Mathematical analysis, Astronomy, Set (abstract data type), Thermodynamics, Programming language

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