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The MIMO Wiretap Channel Decomposed

Khina, Anatoly and Kochman, Yuval and Khisti, Ashish (2018) The MIMO Wiretap Channel Decomposed. IEEE Transactions on Information Theory, 64 (2). pp. 1046-1063. ISSN 0018-9448.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Khina, Anatoly0000-0003-2359-1678
Khisti, Ashish0000-0002-2331-8965
Additional Information:© 2017 IEEE. Manuscript received August 18, 2015; revised October 25, 2016; accepted February 17, 2017. Date of publication June 1, 2017; date of current version January 18, 2018. A. Khina was supported in part by the Feder Family Award, in part by the Yitzhak and Chaya Weinstein Research Institute for Signal Processing, and in part by the Clore Israel Foundation. Y. Kochman was supported in part by the Israeli Science Foundation under Grant 956/12, in part by the German–Israeli Foundation for Scientific Research and Development, and in part by the HUJI Cyber Security Research Center in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. A. Khisti was supported by QNRF, a member of Qatar Foundation, through the NPRP Project under Grant 5-603-2-243. This paper was presented in part at the 2014 IEEE International Symposium of Information Theory (ISIT) and at the 2015 IEEE ISIT.
Funding AgencyGrant Number
Feder Family AwardUNSPECIFIED
Yitzhak and Chaya Weinstein Research Institute for Signal ProcessingUNSPECIFIED
Clore Israel FoundationUNSPECIFIED
Israel Science Foundation956/12
German-Israeli Foundation for Research and DevelopmentUNSPECIFIED
HUJI Cyber Security Research CenterUNSPECIFIED
Israel National Cyber BureauUNSPECIFIED
Qatar National Research Fund5-603-2-243
Subject Keywords:Wiretap channel, MIMO channel, confidential broadcast, successive interference cancellation, dirty-paper coding, matrix decomposition
Issue or Number:2
Record Number:CaltechAUTHORS:20170613-163206628
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Official Citation:A. Khina, Y. Kochman and A. Khisti, "The MIMO Wiretap Channel Decomposed," in IEEE Transactions on Information Theory, vol. 64, no. 2, pp. 1046-1063, Feb. 2018. doi: 10.1109/TIT.2017.2710058. URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78178
Deposited By: Kristin Buxton
Deposited On:14 Jun 2017 02:26
Last Modified:03 Oct 2019 18:06

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