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.