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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2501.05748 |
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| _version_ | 1866909511517732864 |
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| author | Pfister, Henry D. Sprumont, Oscar Zémor, Gilles |
| author_facet | Pfister, Henry D. Sprumont, Oscar Zémor, Gilles |
| contents | We provide a general framework for bounding the block error threshold of a linear code $C\subseteq \mathbb{F}_2^N$ over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight of any $r$-dimensional subcode of $C$, for all small values of $r$. As a proof of concept, we use our machinery to obtain a new proof of the celebrated result that Reed-Muller codes achieve capacity on the erasure channel with respect to block error probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Bit to Block: Decoding on Erasure Channels Pfister, Henry D. Sprumont, Oscar Zémor, Gilles Information Theory We provide a general framework for bounding the block error threshold of a linear code $C\subseteq \mathbb{F}_2^N$ over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight of any $r$-dimensional subcode of $C$, for all small values of $r$. As a proof of concept, we use our machinery to obtain a new proof of the celebrated result that Reed-Muller codes achieve capacity on the erasure channel with respect to block error probability. |
| title | From Bit to Block: Decoding on Erasure Channels |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.05748 |