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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/2410.20020 |
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| _version_ | 1866912087723212800 |
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| author | Pernice, Francisco Sprumont, Oscar Wootters, Mary |
| author_facet | Pernice, Francisco Sprumont, Oscar Wootters, Mary |
| contents | It is known that the Shannon capacity of the q-ary symmetric channel (qSC) is the same as the list-decoding capacity of an adversarial channel, raising the question of whether there is a formal (and black-box) connection between the two. We show that there is: Any linear code $C\subseteq \mathbb{F}_q^n$ that has minimum distance $d_{\min}=ω(q^3)$ and achieves list-decoding capacity also achieves capacity on the qSC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20020 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | List-Decoding Capacity Implies Capacity on the q-ary Symmetric Channel Pernice, Francisco Sprumont, Oscar Wootters, Mary Information Theory It is known that the Shannon capacity of the q-ary symmetric channel (qSC) is the same as the list-decoding capacity of an adversarial channel, raising the question of whether there is a formal (and black-box) connection between the two. We show that there is: Any linear code $C\subseteq \mathbb{F}_q^n$ that has minimum distance $d_{\min}=ω(q^3)$ and achieves list-decoding capacity also achieves capacity on the qSC. |
| title | List-Decoding Capacity Implies Capacity on the q-ary Symmetric Channel |
| topic | Information Theory |
| url | https://arxiv.org/abs/2410.20020 |