The MIMO Wiretap Channel Decomposed

DOI10.1109/TIT.2017.2710058zbMATH Open1390.94863arXiv1509.01822OpenAlexW2964352372MaRDI QIDQ4566685

Anatoly Khina, Ashish Khisti, Yuval Kochman

Publication date: 27 June 2018

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1509.01822

Mathematics Subject Classification ID

Authentication, digital signatures and secret sharing (94A62)