A Note on the Secrecy Capacity of the Multiple-Antenna Wiretap Channel

The secrecy capacity of the multiple-antenna wiretap channel under the average total power constraint was recently characterized, independently, by Khisti and Wornell and Oggier and Hassibi using a Sato-like argument and matrix analysis tools. This paper presents an alternative characterization of the secrecy capacity of the multiple-antenna wiretap channel under a more general matrix constraint on the channel input using a channel-enhancement argument. This characterization is by nature information-theoretic and is directly built on the intuition regarding to the optimal transmission strategy in this communication scenario.

[1]  David Tse,et al.  DIMACS Series in Discrete Mathematics and Theoretical Computer Science On the Capacity of the Multiple Antenna Broadcast Channel , 2002 .

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

[3]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[4]  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.

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

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

[7]  Shlomo Shamai,et al.  The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel , 2006, IEEE Transactions on Information Theory.

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

[9]  Shlomo Shamai,et al.  The Capacity Region of the Degraded Multiple-Input Multiple-Output Compound Broadcast Channel , 2009, IEEE Transactions on Information Theory.

[10]  G. Wornell,et al.  Secure Transmission with Multiple Antennas: The MIMOME Channel , 2008 .

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

[12]  Shlomo Shamai,et al.  Capacity bounds for Gaussian vector broadcast channels , 2003, Multiantenna Channels: Capacity, Coding and Signal Processing.

[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]  Suhas N. Diggavi,et al.  The worst additive noise under a covariance constraint , 2001, IEEE Trans. Inf. Theory.

[16]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

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

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

[19]  Frédérique E. Oggier,et al.  The secrecy capacity of the MIMO wiretap channel , 2007, 2008 IEEE International Symposium on Information Theory.

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

[21]  Hiroshi Sato,et al.  An outer bound to the capacity region of broadcast channels (Corresp.) , 1978, IEEE Trans. Inf. Theory.