Towards the Secrecy Capacity of the Gaussian MIMO Wire-tap Channel: The 2-2-1 Channel

TL;DR

This paper determines the secrecy capacity of a specific 2-2-1 Gaussian MIMO wire-tap channel, showing that Gaussian beam-forming is optimal and no pre-processing is needed, by matching an achievable scheme with a tight upper bound.

Contribution

It provides the first exact secrecy capacity characterization for the 2-2-1 Gaussian MIMO wire-tap channel using a novel matching upper bound and achievable scheme.

Findings

Gaussian beam-forming achieves secrecy capacity

Achievable scheme matches the tight upper bound

Pre-processing of information is unnecessary

Abstract

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wire-tap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.