Coding capacity for a class of additive channels

Coding capacity is considered for a class of additive dimension-limited channels. The channels may be with or without memory, stationary or nonstationary. The constraint is partially given in terms of an increasing family of finite-dimensional subspaces. A general expression for the capacity is obtained, which depends on the family of subspaces and the relation between the noise covariance and the covariance giving the energy-frequency constraint on the transmitted signal. This result holds for all classical discrete-time Gaussian channels and for continuous-time Gaussian channels with fixed time of transmission, so long as a peak energy constraint is used on the codewords. The expression also provides upper bounds for a class of non-Gaussian channels. Several results are obtained that aid in calculation of capacity for specific applications. For this class of channels, it is shown that coding capacity is equal to information capacity. Error bounds are given for Gaussian channels