Jamming games against multi-rate superposition coding transmitters

In this paper, we study the problem of jamming between two communicating nodes in a game theoretic framework. The game is between the jammer and the transmitter. We formulate their interaction as a two-player, zero-sum game. The jammer is assumed to be a Gaussian pulse-noise jammer with a fixed average power. A Jammer´s strategy consists of choosing a duty factor such that transmitter´s payoff is minimized. We consider a transmitter that has two possible options to communicate with the receiver; the transmitter can use a “low-rate code” which can be recovered at the receiver regardless of the jammer´s activity, or he can use a “high-rate code” that will be lost if the jammer is active. We study two scenarios in which transmitter uses the codes in different manners; in the first scenario, the transmitter uses one code at a time with a duty factor (or probability) while in the second scenario, he superimposes the high-rate code over the low-rate code and transmits both codes simultaneously. We study these two scenarios against the jammer´s strategy and identify a mixed-strategy Nash equilibrium and the game value for both cases. We show that superposition coding can achieve a higher payoff to the transmitter than the first scenario.