Identification for ISI Gaussian Channels

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 $\kappa \in [0,1\mathrm{/}2),$ the number of messages that can be reliably identified grows super-exponentially in $n$ as $\sim 2^{(n\log n)R},$ where $R$ is the coding rate.