On identification capacity of infinite alphabets or continuous-time channels

Abstract

Two kinds of channels are considered: (1) discrete-time channel with additive noise, and (2) Poisson and white Gaussian (i.e., continuous-time) channels. For the type (1) channel there are given some sufficient conditions when the Shannon and identification capacities coincide. It is shown that the identification capacity of Poisson and Gaussian channels without bandwidth constraint is infinite. Conversely, for a white Gaussian channel with bandwidth constraint, the identification capacity coincides with the Shannon capacity.