Capacity of dimension-limited channels

Abstract

Capacity is deremined for a class of communication channels containing additive noise. Gaussian noise processes and a large class of non-Gaussian processes are included. The constraint on the transmitted signals is given in terms of an increasing family of finite-dimensional subspaces. For this class of channels, it is shown that coding capacity is equal to the average information capacity. A general expression for the capacity is given, along with results that facilitate its calculation in applications. The results apply to the classical discrete-time channel and to continuous-time channels with fixed signal duration.