Outer Bounds on the Secrecy Capacity Region of the 2-user Z Interference Channel With Unidirectional Transmitter Cooperation

TL;DR

This paper establishes outer bounds on the secrecy capacity region of the 2-user Z interference channel with unidirectional transmitter cooperation, using deterministic and Gaussian models, revealing conditions where secrecy constraints impact capacity.

Contribution

It introduces novel outer bounds for the secrecy capacity region of the Z-IC with transmitter cooperation, applicable to both deterministic and Gaussian models, and analyzes the impact of secrecy constraints.

Findings

Secrecy constraints do not reduce capacity in deterministic models under weak/moderate interference.

Outer bounds are tight and match achievable schemes in the deterministic setting.

Secrecy constraints can reduce capacity in Gaussian models under certain interference regimes.

Abstract

This paper derives outer bounds on the secrecy capacity region of the 2-user Z interference channel (Z-IC) with rate-limited unidirectional cooperation between the transmitters. First, the model is studied under the linear deterministic setting. The derivation of the outer bounds on the secrecy capacity region involves careful selection of the side information to be provided to the receivers and using the secrecy constraints at the receivers in a judicious manner. To this end, a novel partitioning of the encoded messages and outputs is proposed for the deterministic model based on the strength of interference and signal. The obtained outer bounds are shown to be tight using the achievable scheme derived by the authors in a previous work. Using the insight obtained from the deterministic model, outer bounds on the secrecy capacity region of the 2-user Gaussian Z-IC are obtained. The equivalence between the outer bounds for both the models is also established. It is also shown that secrecy constraint at the receiver does not hurt the capacity region of the 2-user Z-IC for the deterministic model in the weak/moderate interference regime. On the other hand, the outer bounds developed for the Gaussian case shows that secrecy constraint at the receiver can reduce the capacity region for the weak/moderate interference regime. The study of the relative performance of these bounds reveals insight into the fundamental limits of the 2-user Z-IC with limited rate transmitter cooperation.