Communication in the Presence of Jamming-An Information-Theoretic Approach

In traditional information theoretic studies, the channel is entirely passive, though possibly quite complex probabilistically. However, it sometimes happens in practice that the channel is partially controlled by an adversary (the Jammer) whose goal is to do everything in his power to make communication difficult. This possibility leads to a whole host of interesting mathematical and-engineering problems, and in this paper we will study a few of these. In the next section, we will introduce a two-person zero-sum game with mutual information as the payoff function. The first player (the Communicator) wants to maximize this function, and the second player (the Jammer) wants to minimize it. Since mutual information is convex-concave in just the right way, a generalization of Von Neumann’s minimax theorem turns out to guarantee the existence of jointly optimal saddlepoint strategies for the players. We show that these strategies are memory-less for both players.