Capacity results on the finite state Markov wiretap channel with delayed state feedback

Abstract

The finite state Markov channel (FSMC) has been shown to be a useful model for the time-varying fading channels. In this paper, we study the security issue in the wireless communication systems by considering the FSMC with an eavesdropper, which we call the finite state Markov wiretap channel (FSM-WC). More specifically, the FSM-WC is a channel with one input (the transmitter) and two outputs (the legitimate receiver and the eavesdropper). The transition probability of the FSM-WC is controlled by a channel state which takes values in a finite set, and it undergoes a Markov process. We assume that the state is perfectly known by the legitimate receiver and the eavesdropper, and through a noiseless feedback channel, the legitimate receiver sends the state back to the transmitter after some time delay. Measuring the eavesdropper's uncertainty about the transmitted message by equivocation, we provide inner and outer bounds on the capacity-equivocation region of this novel model, and show that these bounds meet (the capacity-equivocation region is determined) if the channel output for the eavesdropper is a degraded version of that for the legitimate receiver. The capacity results of this paper are further explained via degraded Gaussian and Gaussian fading examples.