Wiretap channels with causal and non-causal state information: revisited

TL;DR

This paper revisits wiretap channels with causal and non-causal state information, extending achievable secret-message and secret-key rates, and providing a unifying theorem that simplifies previous encoding schemes.

Contribution

It introduces a unifying theorem for wiretap channels with causal CSI, removing the need for block-Markov encoding, and characterizes the exact secret-message key capacity region.

Findings

Extended all previous achievable rate results.

Derived a unifying theorem for causal CSI scenarios.

Provided the exact capacity region for non-causal CSI at both parties.

Abstract

The coding problem for wiretap channels with causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied. We are concerned here particularily with the problem of achievable secret-message secret-key rate pairs under the semantic security criterion. Our main result extends all the previous results on achievable rates as given by Chia and El Gamal [10], Fujita [11], and Han and Sasaki [23]. In order to do this, we first derive a unifying theorem (Theorem 2) with causal CSI at Alice, which follows immediately by leveraging the unifying seminal theorem for wiretap channels with non-causal CSI at Alice as recently established by Bunin et al. [22]. The only thing to do here is just to re-interpret the latter non-causal one in a causal manner. A prominent feature of this approach is that we are able to dispense with the block-Markov encoding scheme as used in the previous works. Also, the exact secret-message key capacity region for wiretap channels with non-causal CSI at both Alice and Bob is given.