Coding Capacity of Generalized Additive Channels

摘要

The generalized additive channel was introduced. It is described by an additive noise process with sample functions inducing a measure on a linear topological vector space, and by a constraint which includes dimensionality. The coding capacity of the matched channel was analyzed, with an exact value obtained for the Gaussian channel and an upper bound for a class of nonGaussian channels. Bounds on the coding capacity for the mismatched Gaussian generalized channel were obtained. In this paper, the exact coding capacity of the mismatched Gaussian generalized channel is determined, along with an upper bound for a class of nonGaussian mismatched channels. The set of admissable constraints is also greatly increased over that considered. Although the treatment here is restricted to noise measures induced on a separable Hilbert space, it can readily be seen that the results extended immediately to the class of linear topological vector spaces considered. The results of the present paper are partly based on the Hilbert space results on information capacity given, for the extension of linear topological vector spaces, one would use the corresponding results given. The focus on Hilbert space is useful for application of the results given here to the discrete-time or continuous-time additive channel.