1. New Upper Bounds for Noisy Permutation Channels
- Author
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Feng, Lugaoze, Wang, Baoji, Lv, Guocheng, Li, Xvnan, Wang, Luhua, and jin, Ye
- Subjects
Computer Science - Information Theory - Abstract
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 {\epsilon}-capacity result. We find that a smaller crossover probability provides a higher upper bound for a fixed finite blocklength, although the {\epsilon}-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., Comment: 24 Pages, Submitted to IEEE Transactions on Communications
- Published
- 2024