Identification for ISI Gaussian Channels

TL;DR

This paper derives bounds on the identification capacity of Gaussian channels with ISI, showing super-exponential growth in message count under certain conditions.

Contribution

It provides the first bounds on identification capacity for ISI Gaussian channels with sub-linear ISI tap scaling.

Findings

Identification capacity grows super-exponentially with code length.

Bounds are established for channels with ISI scaling as n^κ, κ in [0,1/2).

Reliable identification is possible at rates involving n log n.

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 $R$ is the coding rate.