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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.05433 |
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| _version_ | 1866912111227043840 |
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| author | Ellouze, Malek Tajan, Romain Leroux, Camille Jégo, Christophe Poulliat, Charly |
| author_facet | Ellouze, Malek Tajan, Romain Leroux, Camille Jégo, Christophe Poulliat, Charly |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing the Low-Weight codewords of Punctured and Shortened Pre-Transformed polar Codes Ellouze, Malek Tajan, Romain Leroux, Camille Jégo, Christophe Poulliat, Charly Information Theory 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. |
| title | Computing the Low-Weight codewords of Punctured and Shortened Pre-Transformed polar Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2411.05433 |