The secrecy capacity of the MIMO wiretap channel

We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers. Our technique involves a careful study of a Sato-like upper bound via the solution of a certain algebraic Riccati equation.

[1]  Shlomo Shamai,et al.  An MMSE Approach to the Secrecy Capacity of the MIMO Gaussian Wiretap Channel , 2009, 2009 IEEE International Symposium on Information Theory.

[2]  H. Vincent Poor,et al.  Secrecy Capacity Region of a Multiple-Antenna Gaussian Broadcast Channel With Confidential Messages , 2007, IEEE Transactions on Information Theory.

[3]  Roy D. Yates,et al.  Secret Communication via Multi-antenna Transmission , 2007, 2007 41st Annual Conference on Information Sciences and Systems.

[4]  Tie Liu,et al.  An Extremal Inequality Motivated by Multiterminal Information Theoretic Problems , 2006, ISIT.

[5]  Matthieu R. Bloch,et al.  Wireless Information-Theoretic Security - Part I: Theoretical Aspects , 2006, ArXiv.

[6]  Martin E. Hellman,et al.  The Gaussian wire-tap channel , 1978, IEEE Trans. Inf. Theory.

[7]  Tie Liu,et al.  An Extremal Inequality Motivated by Multiterminal Information-Theoretic Problems , 2006, IEEE Transactions on Information Theory.

[8]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[9]  Roy D. Yates,et al.  Secrecy capacity of independent parallel channels , 2009 .

[10]  Nan Liu,et al.  Towards the Secrecy Capacity of the Gaussian MIMO Wire-Tap Channel: The 2-2-1 Channel , 2007, IEEE Transactions on Information Theory.

[11]  Shlomo Shamai,et al.  Secure Communication Over Fading Channels , 2007, IEEE Transactions on Information Theory.

[12]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[13]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[14]  Joy A. Thomas,et al.  Feedback can at most double Gaussian multiple access channel capacity , 1987, IEEE Trans. Inf. Theory.

[15]  Hesham El Gamal,et al.  On the Secrecy Capacity of Fading Channels , 2006, 2007 IEEE International Symposium on Information Theory.

[16]  Gregory W. Wornell,et al.  Secure Transmission With Multiple Antennas I: The MISOME Wiretap Channel , 2010, IEEE Transactions on Information Theory.

[17]  Ami Wiesel,et al.  On the Gaussian MIMO Wiretap Channel , 2007, 2007 IEEE International Symposium on Information Theory.

[18]  Shlomo Shamai,et al.  A Note on the Secrecy Capacity of the Multiple-Antenna Wiretap Channel , 2007, IEEE Transactions on Information Theory.

[19]  Gregory W. Wornell,et al.  The MIMOME Channel , 2007, ArXiv.

[20]  Frédérique E. Oggier,et al.  The secrecy capacity of the MIMO wiretap channel , 2008, ISIT.

[21]  Alfred O. Hero,et al.  Secure space-time communication , 2003, IEEE Trans. Inf. Theory.

[22]  Imre Csiszár,et al.  Broadcast channels with confidential messages , 1978, IEEE Trans. Inf. Theory.

[23]  Gerhard Freiling,et al.  A survey of nonsymmetric Riccati equations , 2002 .

[24]  Richard E. Blahut,et al.  Secrecy capacity of SIMO and slow fading channels , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[25]  H. Vincent Poor,et al.  Multiple Antenna Secure Broadcast over Wireless Networks , 2007, ArXiv.

[26]  Matthieu R. Bloch,et al.  Wireless Information-Theoretic Security , 2008, IEEE Transactions on Information Theory.

[27]  Babak Hassibi,et al.  The Secrecy Capacity of the 2 × 2 MIMO Wiretap Channel , 2007 .

[28]  Miguel R. D. Rodrigues,et al.  Secrecy Capacity of Wireless Channels , 2006, 2006 IEEE International Symposium on Information Theory.

[29]  Sennur Ulukus,et al.  Achievable Rates in Gaussian MISO Channels with Secrecy Constraints , 2007, 2007 IEEE International Symposium on Information Theory.