New Upper Bounds for Noisy Permutation Channels
Lugaoze Feng, Baoji Wang, Guocheng Lv, Xunan Li, Lühua Wang, Jin Ye · IEEE Transactions on Communications · 2025
Thenoisy permutation channelis 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 thefinite blocklengthregime. To do this, we present a modified minimax meta-converse for noisy permutation channels by symbol relaxation and construct an auxiliary distribution for this bound usingdivergence covering. We then show the strong converse and refined asymptotic expansions. 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, and the$\epsilon $-capacityresult. Finally, numerical results show that the normal approximation shows remarkable precision, and our new converse bound is stronger than existing bounds.