Nonasymptotic Oblivious Relaying and Variable-Length Noisy Lossy Source Coding
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908991265701888 |
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| author | Liu, Yanxiao Advary, Sepehr Heidari Li, Cheuk Ting |
| author_facet | Liu, Yanxiao Advary, Sepehr Heidari Li, Cheuk Ting |
| contents | The information bottleneck channel (or the oblivious relay channel) concerns a channel coding setting where the decoder does not directly observe the channel output. Rather, the channel output is relayed to the decoder by an oblivious relay (which does not know the codebook) via a rate-limited link. The capacity is known to be given by the information bottleneck. We study finite-blocklength achievability results of the channel, where the relay communicates to the decoder via fixed-length or variable-length codes. These two cases give rise to two different second-order versions of the information bottleneck. Our proofs utilize the nonasymptotic noisy lossy source coding results by Kostina and Verdú, the strong functional representation lemma, and the Poisson matching lemma. Moreover, we also give a novel nonasymptotic variable-length noisy lossy source coding result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13582 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonasymptotic Oblivious Relaying and Variable-Length Noisy Lossy Source Coding Liu, Yanxiao Advary, Sepehr Heidari Li, Cheuk Ting Information Theory The information bottleneck channel (or the oblivious relay channel) concerns a channel coding setting where the decoder does not directly observe the channel output. Rather, the channel output is relayed to the decoder by an oblivious relay (which does not know the codebook) via a rate-limited link. The capacity is known to be given by the information bottleneck. We study finite-blocklength achievability results of the channel, where the relay communicates to the decoder via fixed-length or variable-length codes. These two cases give rise to two different second-order versions of the information bottleneck. Our proofs utilize the nonasymptotic noisy lossy source coding results by Kostina and Verdú, the strong functional representation lemma, and the Poisson matching lemma. Moreover, we also give a novel nonasymptotic variable-length noisy lossy source coding result. |
| title | Nonasymptotic Oblivious Relaying and Variable-Length Noisy Lossy Source Coding |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.13582 |