COMPLETE CLASS OF MINIMAX AND MAXIMIN ENCODER-DECODER POLICIES FOR COMMUNICATION CHANNELS WITH INCOMPLETE STATISTICAL DESCRIPTION.

We consider the problem of transmission of a sequence of i. i. d. Gaussian random variables over a channel whose statistical description is incomplete. The channel is modeled as one which is conditionally Gaussian, with the unknown part being controlled by a so-called 'jammer' who may have access to the input to the encoder and operates under a given power constraint. By adopting a game-theoretic approach we obtain a complete set of solutions for this statistical decision problem, under two different sets of conditions, depending on whether the encoder mapping is deterministic or stochastic. In the latter case, existence of a mixed saddle-point solution can be verified when a side channel of a specific nature is available between the transmitter and the receiver. In the former case, however, only minimax and maximin solutions can be derived.