One-Shot Coding over General Noisy Networks
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908491170447360 |
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| author | Liu, Yanxiao Li, Cheuk Ting |
| author_facet | Liu, Yanxiao Li, Cheuk Ting |
| contents | We present a unified one-shot coding framework designed for the communication and compression of messages among multiple nodes across a general acyclic noisy network. Our setting can be seen as a one-shot version of the acyclic discrete memoryless network studied by Lee and Chung, and noisy network coding studied by Lim, Kim, El Gamal and Chung. We design a proof technique, called the exponential process refinement lemma, that is rooted in the Poisson matching lemma by Li and Anantharam, and can significantly simplify the analyses of one-shot coding over multi-hop networks. Our one-shot coding theorem not only recovers a wide range of existing asymptotic results, but also yields novel one-shot achievability results in different multi-hop network information theory problems, such as compress-and-forward and partial-decode-and-forward bounds for a one-shot (primitive) relay channel, and a bound for one-shot cascade multiterminal source coding. In a broader context, our framework provides a unified one-shot bound applicable to any combination of source coding, channel coding and coding for computing problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-Shot Coding over General Noisy Networks Liu, Yanxiao Li, Cheuk Ting Information Theory We present a unified one-shot coding framework designed for the communication and compression of messages among multiple nodes across a general acyclic noisy network. Our setting can be seen as a one-shot version of the acyclic discrete memoryless network studied by Lee and Chung, and noisy network coding studied by Lim, Kim, El Gamal and Chung. We design a proof technique, called the exponential process refinement lemma, that is rooted in the Poisson matching lemma by Li and Anantharam, and can significantly simplify the analyses of one-shot coding over multi-hop networks. Our one-shot coding theorem not only recovers a wide range of existing asymptotic results, but also yields novel one-shot achievability results in different multi-hop network information theory problems, such as compress-and-forward and partial-decode-and-forward bounds for a one-shot (primitive) relay channel, and a bound for one-shot cascade multiterminal source coding. In a broader context, our framework provides a unified one-shot bound applicable to any combination of source coding, channel coding and coding for computing problems. |
| title | One-Shot Coding over General Noisy Networks |
| topic | Information Theory |
| url | https://arxiv.org/abs/2402.06021 |