SOLUTIONS TO A CLASS OF MINIMAX DECISION PROBLEMS ARISING IN COMMUNICATION SYSTEMS.

A class of minimax decision problems is considered which arise in the transmission of a Gaussian vector message over a vector channel with partially unknown statistical description. The statistically unknown part of the channel is modeled as one which is controlled by a jammer who can corrupt the transmitted message by sending noise which may be correlated with the original message under a given power constraint. Under two types of structural assumptions on the transmitter (encoder), the problem is posed as one in which the optimum decision rules at the encoder and the decoder jointly minimize a square distortion measure at the output, under the worst possible choices for the jamming noise. It is shown that a saddle-point solution exists when the linear encoder structure is of the mixed type, whereas it does not exist when it is restricted to be deterministic.