Information Capacity of Channels with Partially Unknown Noise. I. Finite-Dimensional Channels

Information capacity is considered for a finite-dimensional communication channel in which the noise is the sum of a known Gaussian noise and an independent component with unknown statistical properties. The problem is modeled as a zero-sum two-person game between the coder and a jammer, with mutual information as the payoff function. The jammer does not control the ambient Gaussian noise. The constraints employed are appropriate for extension to infinite-dimensional channels and for consideration of coding capacity. The original problem is reformulated to prove existence of both a saddle value and a saddle point. The saddle value and a saddle point are determined, along with the jammer’s minimax strategy.