Information Capacity of the Matched Gaussian Channel with Jamming. 2. Infinite-Dimensional Channels

摘要

The additive infinite-dimensional Gaussian channel subject to jamming is modeledas a two-person zero-sum game with mutual information as the payoff function. The jammer's noise is added to the ambient Gaussian noise. The coder's signal energy is subject to a constraint is necessary in order that the capacity without feedback be finite. It is shown that use of this same RKHS constraint on the jammer's process is too strong; the jammer would then not be able to reduce capacity, regardless of the amount of jamming energy available. The constraint on the jammer is thus on the total jamming energy, without regard to its distribution relative to that of the ambient noise energy. The existence of a saddle value for the problem does not follow from the von Neuman minimax theorem in the original problem formulation. However, a solution is shown to exist. A saddle point, saddle value, and the jammer's minimax strategy are determined. The solution is a function of the problem parameters: the constraint on the coder, the constraint on the jammer, and the covariance of the ambient Gaussian noise.