The Secrecy Capacity Region of the Gaussian MIMO Broadcast Channel

• Published in: IEEE transactions on information theory Vol. 59; no. 5; pp. 2673 - 2682
• Main Authors: Bagherikaram, G., Motahari, A. Seyed, Khandani, A. Keyvan
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Broadcasting. Videocommunications. Audiovisual; Coding theory; Coding, codes; Communication channels; Covariance matrix; Dirty paper coding; Electronic eavesdropping; Encoding; Entropy; entropy power inequality (EPI); Exact sciences and technology; Information theory; Information, signal and communications theory; Input output; MIMO; Miscellaneous; multiple-input multiple-output (MIMO) broadcast channel (BC); Noise; Receivers; Receivers & amplifiers; secrecy capacity region; Secret; Signal and communications theory; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmitters; Vectors; wiretap channel; MIMO system; Discrete channel; Gaussian channel; Dirty paper coding; Entropy; Eavesdropping; multiple-input multiple-output (MIMO) broadcast channel (BC); entropy power inequality (EPI); Memoryless channel; Coding; secrecy capacity region; Broadcast channels; wiretap channel; Secrecy; Telecommunication security
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2012.2236972

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian multiple-input multiple-output (MIMO) broadcast channel. An eavesdropper also receives the transmitted signal via another MIMO channel. We first consider the discrete memoryless channel and obtain the capacity region of the degraded channel. The secret dirty paper coding (SDPC) region as an achievable rate region for the general discrete channel is introduced. Relying on the results for the discrete channel, we fully characterize the secrecy capacity region of MIMO broadcast channel. It is shown that the SDPC scheme is optimal. The converse part of the proof relies on the generalized Costa's entropy power inequality and a new channel enhancement strategy in which we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged.