Some Information Theoretic Saddlepoints
J. Martin Borden, David M. Mason, Robert J. McEliece · SIAM Journal on Control and Optimization · 1985
In order to study communication in the presence of jamming (or vice-versa), one can formulate a two person zero sum game with mutual information as the payoff function. Since mutual information is convex-concave in just the right way, one often finds saddlepoint strategies (which are simultaneously optimal for both players). In this paper we shall discuss these saddlepoints for four distinct cases: Additive noise, average power constraints, and any combination of “hard”/“soft” input/output quantization. One of these cases (soft/soft) has been previously studied (Shannon/Dobrushin/Blachman), but the other three appear to be new.