Wiretap channel with causal state information and secure rate-limited feedback

In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate R_f. We shown that the secrecy capacity is bounded by Cs ≥ max {_{p(u|v) p(x|u,v)} max min{I(U;Y|v) - I(U;Z|V) + H(V|Z) + R_f, I(U;Y|V)}, _p(u)p(x|u,v) max min{H(V|Z,U) + Rf, I(U;Y|V)}}. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.