The finite state multiple-access wiretap channel in the presence of delayed feedback

Recently, the finite state Markov channel (FSMC) with an additional eavesdropper and delayed feedback from the legitimate receiver to the transmitter has been shown to be a useful model for the physical layer security of the practical mobile wireless communication systems. In this paper, we extend this model to a multiple-access situation (up-link of the wireless communication systems), which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. To be specific, the FS-MAC-WT is a channel with two inputs (transmitters) and two outputs (a legitimate receiver and an eavesdropper). The channel depends on a state which undergoes a Markov process, and the state is entirely known by the legitimate receiver and the eavesdropper. The legitimate receiver intends to send his channel output and the perfectly known state back to the transmitters through noiseless feedback channels after some time delay. The main contribution of this paper is to provide inner and outer bounds on the secrecy capacity region of this new model. The capacity results are further explained via a degraded Gaussian fading example, and from this example we see that sending the legitimate receiver's channel output back to the transmitters helps to enhance the security of the FS-MAC-WT with only delayed state feedback.