Feedback enhances the security of wiretap channel with states

Wyner, in his well-known paper on the wiretap channel, studied the problem on how to transmit the confidential messages to the legitimate receiver via a degraded broadcast channel, while keeping the wiretapper as ignorant of the messages as possible. In this paper, the model of wiretap channel has been reconsidered for the case that the main channel is controlled by channel state information (CSI), and it is available at the transmitter in a noncausal manner (termed here noncausal channel state information) or causal manner (termed here causal channel state information). Moreover, there is a noiseless feedback from the legitimate receiver to the transmitter. Measuring the uncertainty of the wiretapper by equivocation, the capacity-equivocation regions for both manners (causal and noncausal) are determined. Furthermore, the secrecy capacities are formulated, which provide the best transmission rate with perfect secrecy. The results of this paper are further explained via binary and Gaussian examples, and we find that the noiseless feedback helps to enhance the security of wiretap channel with noncausal or causal CSI at the transmitter.