New Upper Bounds for Noisy Permutation Channels
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913399955259392 |
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| author | Feng, Lugaoze Wang, Baoji Lv, Guocheng Li, Xvnan Wang, Luhua jin, Ye |
| author_facet | Feng, Lugaoze Wang, Baoji Lv, Guocheng Li, Xvnan Wang, Luhua jin, Ye |
| contents | The noisy permutation channel is a useful abstraction introduced by Makur for point-to-point communication networks and biological storage. While the asymptotic capacity results exist for this model, the characterization of the second-order asymptotics is not available. Therefore, we analyze the converse bounds for the noisy permutation channel in the finite blocklength regime. To do this, we present a modified minimax meta-converse for noisy permutation channels by symbol relaxation. To derive the second-order asymptotics of the converse bound, we propose a way to use divergence covering in analysis. It enables the observation of the second-order asymptotics and the strong converse via Berry-Esseen type bounds. These two conclusions hold for noisy permutation channels with strictly positive matrices (entry-wise). In addition, we obtain computable bounds for the noisy permutation channel with the binary symmetric channel (BSC), including the original computable converse bound based on the modified minimax meta-converse, the asymptotic expansion derived from our subset covering technique, and the ε-capacity result. We find that a smaller crossover probability provides a higher upper bound for a fixed finite blocklength, although the ε-capacity is agnostic to the BSC parameter. Finally, numerical results show that the normal approximation shows remarkable precision, and our new converse bound is stronger than previous bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Upper Bounds for Noisy Permutation Channels Feng, Lugaoze Wang, Baoji Lv, Guocheng Li, Xvnan Wang, Luhua jin, Ye Information Theory The noisy permutation channel is a useful abstraction introduced by Makur for point-to-point communication networks and biological storage. While the asymptotic capacity results exist for this model, the characterization of the second-order asymptotics is not available. Therefore, we analyze the converse bounds for the noisy permutation channel in the finite blocklength regime. To do this, we present a modified minimax meta-converse for noisy permutation channels by symbol relaxation. To derive the second-order asymptotics of the converse bound, we propose a way to use divergence covering in analysis. It enables the observation of the second-order asymptotics and the strong converse via Berry-Esseen type bounds. These two conclusions hold for noisy permutation channels with strictly positive matrices (entry-wise). In addition, we obtain computable bounds for the noisy permutation channel with the binary symmetric channel (BSC), including the original computable converse bound based on the modified minimax meta-converse, the asymptotic expansion derived from our subset covering technique, and the ε-capacity result. We find that a smaller crossover probability provides a higher upper bound for a fixed finite blocklength, although the ε-capacity is agnostic to the BSC parameter. Finally, numerical results show that the normal approximation shows remarkable precision, and our new converse bound is stronger than previous bounds. |
| title | New Upper Bounds for Noisy Permutation Channels |
| topic | Information Theory |
| url | https://arxiv.org/abs/2406.15031 |