A Useful Analogy between Wiretap and Gelfand - Pinsker Channels

A framework of analogy between wiretap channels (WTCs) and state-dependent point-to-point channels with noncausal encoder channel state information (referred to as Gelfand-Pinker channels (GPCs)) is proposed. A good (reliable and secure) sequence of wiretap codes is shown to induce a good (reliable) 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 fundamental limits of communication of two analogous wiretap and GP models are characterized by the same rate bounds; the optimization domains may differ. The analogy readily extends to multiuser broadcasting scenarios, encompassing broadcast channels (BCs) with deterministic components, degradation ordering between users, and BCs with cooperative receivers. The analogy is exploited to characterize the secrecy-capacity regions of the semideterministic WTBC (an open problem until this work) and a class of physically degraded WTBC. The derivations are based on known solutions for the corresponding GPBCs.