INFORMATION CAPACITY OF CHANNELS WITH PARTIALLY UNKNOWN NOISE .2. INFINITE-DIMENSIONAL CHANNELS

Information capacity is considered for a communication channel in whic h the noise is the sum of a known Gaussian component and an independen t component with unknown statistical distributions. A lower bound on c apacity is sought; the unknown noise component is thus assumed to be u nder the control of an adversary-a jammer. The problem is modeled as a zero-sum two-person game with mutual information as the payoff functi on. Appropriate constraints are determined on the transmitted signal a nd the unknown noise component. Although the usual conditions sufficie nt for application of the general form of the von Neumann minimax theo rem are shown not to hold, a solution is obtained for the game: a sadd le value, saddle point, and minimax strategy for the jammer are obtain ed. The essential effect of jamming is to convert the infinite-dimensi onal channel into a finite-dimensional channel having the same constra ints, with the dimensionality depending upon the problem parameters: t he covariance of the known Gaussian noise component and the constraint s on the transmitted signal and the unknown noise component.