NDLI: Secure Transmission With Multiple Antennas—Part II: The MIMOME Wiretap Channel

Content Provider	IEEE Xplore Digital Library
Author	Khisti, A. Wornell, G.W.
Copyright Year	1963
Abstract	The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks. At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semi-blind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime. Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs three times as many antennas as the sender and intended receiver have jointly, and that the optimum division of antennas between sender and intended receiver is in the ratio of 2:1.
Sponsorship	IEEE Information Theory Society
Starting Page	5515
Ending Page	5532
Page Count	18
File Size	510181
File Format	PDF
ISSN	00189448
Volume Number	56
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Receiving antennas Transmitting antennas Noise Upper bound MIMO secrecy capacity Broadcast channel cryptography MIMO wiretap channel multiple antennas
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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