Interference Alignment for the Multi-Antenna Compound Wiretap Channel

TL;DR

This paper investigates interference alignment techniques in multi-antenna wiretap channels, deriving bounds on secure degrees of freedom for scenarios involving legitimate and eavesdropper groups, highlighting the limitations of previous bounds.

Contribution

It introduces new bounds on secure degrees of freedom for compound wiretap and private broadcast channels, utilizing real interference alignment and challenging existing pairwise bounds.

Findings

Lower bounds on secure degrees of freedom established

Upper bounds show limitations of previous pairwise bounds

Extension of results to private broadcast channels

Abstract

We study a wiretap channel model where the sender has $M$ transmit antennas and there are two groups consisting of $J_1$ and $J_2$ receivers respectively. Each receiver has a single antenna. We consider two scenarios. First we consider the compound wiretap model -- group 1 constitutes the set of legitimate receivers, all interested in a common message, whereas group 2 is the set of eavesdroppers. We establish new lower and upper bounds on the secure degrees of freedom. Our lower bound is based on the recently proposed \emph{real interference alignment} scheme. The upper bound provides the first known example which illustrates that the \emph{pairwise upper bound} used in earlier works is not tight. The second scenario we study is the compound private broadcast channel. Each group is interested in a message that must be protected from the other group. Upper and lower bounds on the degrees of freedom are developed by extending the results on the compound wiretap channel.