Identification for ISI Gaussian Channels

Abstract

We establish lower and upper bounds for the identification capacity of discrete-time Gaussian channels subject to inter-symbol interference (ISI), a canonical model in wireless communication. Our analysis accounts for deterministic encoders under peak power constraint. A principal finding is that, even when the number of ISI taps scales sub-linearly with the codeword length $n$ as $\sim n^{\kappa }$ with $\kappa \in [0,1/2),$ the number of messages that can be reliably identified grows super-exponentially in $n$ as $\sim 2^{(n\log n)R},$ where $R$ denotes the coding rate.

arXiv comment11 pages, 1 figure; general refinements, with particular emphasis on the exposition of Lemmas 2 and 3 across the asymptotic regimes of K