Capacity of the State-Dependent Wiretap Channel: Secure Writing on Dirty Paper

TL;DR

This paper models the state-dependent wiretap channel as a cognitive interference channel, applying coding techniques to determine its capacity, and extends the results to Gaussian and binary cases, revealing capacity equivalences.

Contribution

It introduces a novel modeling of the SD-WC as a CIC and applies coding strategies to derive new capacity results, including for Gaussian and binary scenarios.

Findings

Capacity of Gaussian SD-WC equals that of the wiretap channel without state.

Capacity of Binary SD-WC equals that of the binary wiretap channel.

Achievability approaches meet capacity under certain rate constraints.

Abstract

In this paper we consider the State-Dependent Wiretap Channel (SD-WC). As the main idea, we model the SD-WC as a Cognitive Interference Channel (CIC), in which the primary receiver acts as an eavesdropper for the cognitive transmitter's message. By this point of view, the Channel State Information (CSI) in SD-WC plays the role of the primary user's message in CIC which can be decoded at the eavesdropper. This idea enables us to use the main achievability approaches of CIC, i.~e., Gel'fand-Pinsker Coding (GPC) and Superposition Coding (SPC), to find new achievable equivocation-rates for the SD-WC. We show that these approaches meet the capacity under some constraints on the rate of the channel state. Similar to the dirty paper channel, extending the results to the Gaussian case shows that the GPC lead to the capacity of the Gaussian SD-WC which is equal to the capacity of the wiretap channel without channel state. Hence, we achieve the capacity of the Gaussian SD-WC using the dirty paper technique. Moreover, our proposed approaches provide the capacity of the Binary SD-WC. It is shown that the capacity of the Binary SD-WC is equal to the capacity of the Binary wiretap channel without channel state.