Identification for ISI Gaussian Channels
This provides fundamental limits for identification in wireless communication channels, though it appears incremental to existing channel capacity theory.
The paper tackles the problem of determining identification capacity for Gaussian channels with inter-symbol interference under peak power constraints, finding that the number of reliably identifiable messages grows super-exponentially with codeword length even when interference scales sub-linearly.
We establish non-asymptotic 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, \(n\), i.e., \(\sim n^κ\) with \(κ\in [0,1/2),\) the number of messages that can be reliably identified grows super-exponentially in \(n\), i.e., \(\sim 2^{(n \log n)R}\), where \(R\) denotes the coding rate.