Optimal strategies for communicator-jammer problems.

Abstract

We consider a binary communication system where the transmitted signal amplitude varies according to a pseudorandom pattern known at the receiver. Additive noise is introduced by a hostile jammer. The system may be viewed as a game between the communicator, who can pick the amplitude distribution, and the jammer, who can choose the noise distribution. A general framework is used which allows for measuring the channel performance by different criteria such as error probability and rate of reliable communication. The basic model assumes that the receiver knows the noise distribution. It is determined that a saddle value always exists for this game, and conditions are determined under which there exists a saddle point (simultaneously optimal communicator and jammer strategies). Results are obtained for several cases in which the amplitude distribution or the noise distribution is discrete. We describe the optimal noise distributions for the case where the channel performance is based on probability of error and the amplitude random variable takes on at most two different values. Finally, we obtain tight upper and lower bounds on the value of the game when the channel performance is based on error probability.