Improving Uniquely Decodable Codes in Binary Adder Channels
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909894402113536 |
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| author | Balogh, József Nguyen, The Ostergard, Patric R. J. White, Ethan Patrick Wigal, Michael |
| author_facet | Balogh, József Nguyen, The Ostergard, Patric R. J. White, Ethan Patrick Wigal, Michael |
| contents | We present a general method to modify existing uniquely decodable codes in the $T$-user binary adder channel. If at least one of the original constituent codes does not have average weight exactly half of the dimension, then our method produces a new set of constituent codes in a higher dimension, with a strictly higher rate. Using our method we improve the highest known rate for the $T$-user binary adder channel for all $T \geq 2$. This information theory problem is equivalent to co-Sidon problems initiated by Lindstr{ö}m in the 1960s, and also the multi-set union-free problem. Our results improve the known lower bounds in these settings as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11723 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improving Uniquely Decodable Codes in Binary Adder Channels Balogh, József Nguyen, The Ostergard, Patric R. J. White, Ethan Patrick Wigal, Michael Combinatorics Information Theory 05D40, 05C65, 05D05, 94A40, 05B10 We present a general method to modify existing uniquely decodable codes in the $T$-user binary adder channel. If at least one of the original constituent codes does not have average weight exactly half of the dimension, then our method produces a new set of constituent codes in a higher dimension, with a strictly higher rate. Using our method we improve the highest known rate for the $T$-user binary adder channel for all $T \geq 2$. This information theory problem is equivalent to co-Sidon problems initiated by Lindstr{ö}m in the 1960s, and also the multi-set union-free problem. Our results improve the known lower bounds in these settings as well. |
| title | Improving Uniquely Decodable Codes in Binary Adder Channels |
| topic | Combinatorics Information Theory 05D40, 05C65, 05D05, 94A40, 05B10 |
| url | https://arxiv.org/abs/2312.11723 |