Interference Alignment for Secrecy

TL;DR

This paper demonstrates how interference alignment combined with secrecy coding enables multiple users in a Gaussian interference channel to achieve positive secure degrees of freedom, enhancing wireless secrecy capacity.

Contribution

It introduces a novel interference alignment scheme that achieves non-zero secure DoF in both confidential and eavesdropper scenarios, with specific DoF formulas.

Findings

Achieves .5 secure DoF per user in confidential message model.

Achieves .5 secure DoF per user with an external eavesdropper.

Shows positive impact of interference on secrecy capacity.

Abstract

This paper studies the frequency/time selective $K$-user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the one with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) about the external eavesdropper. Using interference alignment along with secrecy pre-coding, it is shown that each user can achieve non-zero secure Degrees of Freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves $\frac{K-2}{2K-2}$ secure DoF {\em with probability one} per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve $\frac{K-2}{2K}$ secure DoF {\em in the ergodic setting}. Remarkably, these results establish the {\em positive impact} of interference on the secrecy capacity region of wireless networks.