Wiretap and Gelfand-Pinsker Channels Analogy and its Applications

TL;DR

This paper introduces an analogy framework linking wiretap channels and Gelfand-Pinsker channels, enabling the transfer of capacity results and converse proofs between them, with applications to multiuser broadcast scenarios and secrecy capacity characterization.

Contribution

The paper develops a novel analogy framework between wiretap and Gelfand-Pinsker channels, facilitating new converse proofs and capacity characterizations for complex multiuser secrecy scenarios.

Findings

Established an analogy between wiretap and Gelfand-Pinsker channels.

Derived secrecy capacity regions for semi-deterministic and degraded wiretap broadcast channels.

Enabled transfer of known capacity results through the analogy framework.

Abstract

An analogy framework between wiretap channels (WTCs) and state-dependent point-to-point channels with non-causal encoder channel state information (referred to as Gelfand-Pinker channels (GPCs)) is proposed. A good sequence of stealth-wiretap codes is shown to induce a good sequence of codes for a corresponding GPC. Consequently, the framework enables exploiting existing results for GPCs to produce converse proofs for their wiretap analogs. The analogy readily extends to multiuser broadcasting scenarios, encompassing broadcast channels (BCs) with deterministic components, degradation ordering between users, and BCs with cooperative receivers. Given a wiretap BC (WTBC) with two receivers and one eavesdropper, an analogous Gelfand-Pinsker BC (GPBC) is constructed by converting the eavesdropper's observation sequence into a state sequence with an appropriate product distribution (induced by the stealth-wiretap code for the WTBC), and non-causally revealing the states to the encoder. The transition matrix of the state-dependent GPBC is extracted from WTBC's transition law, with the eavesdropper's output playing the role of the channel state. Past capacity results for the semi-deterministic (SD) GPBC and the physically-degraded (PD) GPBC with an informed receiver are leveraged to furnish analogy-based converse proofs for the analogous WTBC setups. This characterizes the secrecy-capacity regions of the SD-WTBC and the PD-WTBC, in which the stronger receiver also observes the eavesdropper's channel output. These derivations exemplify how the wiretap-GP analogy enables translating results on one problem into advances in the study of the other.