On the Weight Distribution of Weights Less than $2w_{\min}$ in Polar Codes
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913338492977152 |
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| author | Ye, Zicheng Li, Yuan Zhang, Huazi Wang, Jun Yan, Guiying Ma, Zhiming |
| author_facet | Ye, Zicheng Li, Yuan Zhang, Huazi Wang, Jun Yan, Guiying Ma, Zhiming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10024 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Weight Distribution of Weights Less than $2w_{\min}$ in Polar Codes Ye, Zicheng Li, Yuan Zhang, Huazi Wang, Jun Yan, Guiying Ma, Zhiming Information Theory 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. |
| title | On the Weight Distribution of Weights Less than $2w_{\min}$ in Polar Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2308.10024 |