The MIMO Wiretap Channel Decomposed

TL;DR

This paper introduces a novel linear algebra-based method to achieve the capacity of the MIMO wiretap channel using joint triangularization, enabling secure parallel channel coding and extending strong security proofs to MIMO systems.

Contribution

It presents a new scheme based on joint triangularization of channel matrices to achieve MIMO wiretap capacity with simple, effective coding strategies and extends security proofs to MIMO channels.

Findings

Achieves MIMO wiretap capacity with scalar Gaussian codes.

Provides a simple derivation of capacity expressions for MIMO wiretap channels.

Extends strong security results from scalar to MIMO channels.

Abstract

The problem of sending a secret message over the Gaussian multiple-input multiple-output (MIMO) wiretap channel is studied. While the capacity of this channel is known, it is not clear how to construct optimal coding schemes that achieve this capacity. In this work, we use linear operations along with successive interference cancellation to attain effective parallel single-antenna wiretap channels. By using independent scalar Gaussian wiretap codebooks over the resulting parallel channels, the capacity of the MIMO wiretap channel is achieved. The derivation of the schemes is based upon joint triangularization of the channel matrices. We find that the same technique can be used to re-derive capacity expressions for the MIMO wiretap channel in a way that is simple and closely connected to a transmission scheme. This technique allows to extend the previously proven strong security for scalar Gaussian channels to the MIMO case. We further consider the problem of transmitting confidential messages over a two-user broadcast MIMO channel. For that problem, we find that derivation of both the capacity and a transmission scheme is a direct corollary of the proposed analysis for the MIMO wiretap channel.