Computer Science > Information Theory
[Submitted on 15 May 2024]
Title:Identification via Binary Uniform Permutation Channel
View PDF HTML (experimental)Abstract:We study message identification over the binary uniform permutation channels. For DMCs, the number of identifiable messages grows doubly exponentially. Identification capacity, the maximum second-order exponent, is known to be the same as the Shannon capacity of a DMC. We consider a binary uniform permutation channel where the transmitted vector is permuted by a permutation chosen uniformly at random. Permutation channels support reliable communication of only polynomially many messages. While this implies a zero second-order identification rate, we prove a soft converse result showing that even non-zero first-order identification rates are not achievable with a power-law decay of error probability for identification over binary uniform permutation channels. To prove the converse, we use a sequence of steps to construct a new identification code with a simpler structure and then use a lower bound on the normalized maximum pairwise intersection of a set system on {0, . . . , n}. We provide generalizations for arbitrary alphabet size.
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