On the performance of multi-layer superposition coding scheme under constrained jamming

In this paper we employ a game theoretic approach to formulate communication between two nodes over a packetized, wireless AWGN channel in the presence of an adversary. We define a constrained, two-player, zero-sum game between a transmitter/receiver pair and a jammer with maximum and average power constraints. We consider the case where the transmitter and the receiver use an adaptive m-layer (m ≥ 2) superposition coding scheme to communicate. We use capacity/rate as a performance measure and define the preference/utility function based on the capacity of the discrete AWGN channel. In our game model, transmitter's goal is to maximize the achievable expected performance of the communication link, defined by a utility function, while the jammer's goal is to minimize the same utility function. We provide analytical and numerical results for transmitter's and jammer's optimal strategies and prove the existence of a threshold such that when the jammer's average power exceeds this threshold, the expected payoff of the transmitter at the Nash equilibrium (NE) is the same as if the jammer uses his maximum power all the time.