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

Abstract

Abstract-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 the legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate R f .We derive upper and lower bounds on the secrecy capacity and show that, when the channel to the eavesdropper is degraded, the bounds are tight and the secrecy capacity is completely characterised.The capacity achieving scheme is based on Wyner, Csiszár and Körner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. The upper bound is more involved and requires a non-trivial recursive lemma extending previous results in the literature to include both state and feedback. We conclude the paper by showing that a few interesting known results can be seen as special cases of the above, especially the case where the state information is available only at the decoder, and the suggested scheme achieves the secrecy capacity without a source of randomness at the decoder.