Wiretap Channels With Causal and Non-Causal State Information: Revisited

Abstract

The coding problem for wiretap channels (WTCs) with causal and/or non-causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied, particularly focusing on achievable secret-message secret-key (SM-SK) rate pairs under the semantic security criterion. One of our main results is summarized as Theorem 3 on causal inner bounds for SM-SK rate pairs, which follows immediately by leveraging the unified seminal theorem for WTCs with non-causal CSI at Alice that has been recently established by Bunin et al.. The only thing to do here is just to re-interpret the latter non-causal scheme in a causal manner by restricting the range of auxiliary random variables appearing in non-causal encoding to a subclass of auxiliary random variables for the causal encoder. This technique is referred to as “plugging.” Then, we are able to dispense with the block-Markov encoding scheme used in the previous works by Chia and El Gamal, Fujita, and Han and Sasaki and then extend all the known results on achievable rates. The other main results include the exact SM-SK capacity region for WTCs with non-causal CSI at “both” Alice and Bob (Theorem 2), a “tighter” causal SM-SK outer bound for state-reproducing coding schemes with CSI at Alice (Proposition 4), and the exact SM-SK capacity region for degraded WTCs with causal/non-causal CSI at both Alice and Bob (Theorem 4).