A Degraded Practical MIMOME Channel: Issues Insecret Data Communications
In this paper, a Gaussian multiple input multiple output multiple eavesdropper (MIMOME) channel is considered where a transmitter communicates to a receiver in the presence of an eavesdropper. We present a technique for determining the secrecy capacity of the multiple input multiple output (MIMO) channel under Gaussian noise. We transform the degraded MIMOME channel into multiple single input multiple output (SIMO) Gaussian wire-tap channels and then use scalar approach to convert it into two equivalent multiple input single output (MISO) channels. The secrecy capacity model is then developed for the condition where the channel state information (CSI) for main channel only is known to the transmitter. The results show that the secret communication is possible when the eavesdropper channel noise is greater than a cutoff noise level. The outage probability is also analyzed of secrecy capacity is also analyzed. The effect of fading and outage probability is also analyzed.
[1] A. D. Wyner,"The wire-tap channel," Bell Syst. Tech. J., 54(8):210,
October 1975.
[2] S. K. Leung Yan Cheong and M. E. Hellman,"The Gaussian wire-tap
channel," IEEE Trans. on Information Theory, 24(4):451-456, July 1978.
[3] U. M. Maurer,"Secret key agreement by public discussion from common
information," IEEE Trans. on Information Theory, vol. 39, pp. 733742,
May 1993.
[4] R. Ahlswede and I. Csiszar,"Common randomness in information theory
and cryptography, part I: Secret sharing," IEEE Trans. on Information
Theory, vol. 39, pp. 11211132, July 1993.
[5] I. Csiszar and J. Korner,"Broadcast channels with confidential messages,"
IEEE Trans. on Information Theory, 24(3):339-348, May 1978.
[6] I. E. Telatar,"Capacity of multi-antenna Gaussian channels," European
Trans. Telecommunications, 10:585-595, November 1999.
[7] R. Negi and S. Goel,"Secret communication using artificial noise,"IEEE
Vehicular Technology Conference, Toulouse, France, May 2006.
[8] P. Parada and R. Blahut,"Secrecy capacity of SIMO and slow fading channels,"
IEEE International Symposium on Information Theory, Adelaide,
Australia, September 2005.
[9] J. Barros and M. Rodrigues,"Secrecy capacity of wireless channels," IEEE
International Symposium on Information Theory, USA, 2006
[10] M. Bloch, J. Barros, M. Rodrigues and S. Mclaughlin,"Wireless information
theoretic security," IEEE Transactions on Information Theory, vol.
54, no. 6, pp. 2515-2534, June 2008.
[11] S. Shafiee and S. Ulukus,"Achievable rates in Gaussian MISO channels
with secrecy constraints," In IEEE International Symposium on Information
Theory, Nice, France, June 2007.
[12] Z. Li, W. Trappe, and R. D. Yates,"Secret communication via multi
antenna transmission," 41st Conference on Information Sciences and
Systems, Baltimore, MD, March 2007.
[13] A. Khisti, G. Wornell, A. Wiesel, and Y. Eldar,"On the Gaussian MIMO
wiretap channel," IEEE International Symposium on Information Theory,
Nice, France, June 2007.
[14] A. Khisti and G. Wornell,"Secure transmission with multiple antennas:
The MISOME wiretap channel," Submitted to IEEE Trans. on Information
Theory
[15] T. Cover and J. Thomas, Elements of Information Theory Wiley, 1991.
[16] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University
Press, 1987.
[17] X. Li and E. P. Ratazzi,"MIMO transmissions with information theoretic
secrecy for secret key agreement in wireless networks," IEEE Military
Communications Conference (MILCOM2005), 2005. Atlantic City, NJ.
[18] X. Li, M. Chen, and E. P. Ratazzi,"Space time transmissions for
wireless secret key agreement with information-theoretic secrecy," IEEE
International Workshop on Signal Processing Advances in Wireless
Communications (SPAWC05), 2005. The Italian Academy at Columbia
University, New York.
[19] P. Viswanath and D. Tse,"Fundamentals of wireless communications,"
class notes for ECE 459, Department of Electrical and Computer Engineering,
University of Illinois at Urbana Champaign, Fall 2003.
[20] S. Shafiee, N. Liu and S. Ulukus,"Secrecy Capacity of the 2-2-1
Gaussian MIMO Wire-tap Channel," ISCCSP, 2008
[21] A. Paulraj, R. Nabar, and D. Gore (2003) Introduction to Space-Time
Wireless Communications, Cambridge, U.K.: Cambridge Univ. Press
[1] A. D. Wyner,"The wire-tap channel," Bell Syst. Tech. J., 54(8):210,
October 1975.
[2] S. K. Leung Yan Cheong and M. E. Hellman,"The Gaussian wire-tap
channel," IEEE Trans. on Information Theory, 24(4):451-456, July 1978.
[3] U. M. Maurer,"Secret key agreement by public discussion from common
information," IEEE Trans. on Information Theory, vol. 39, pp. 733742,
May 1993.
[4] R. Ahlswede and I. Csiszar,"Common randomness in information theory
and cryptography, part I: Secret sharing," IEEE Trans. on Information
Theory, vol. 39, pp. 11211132, July 1993.
[5] I. Csiszar and J. Korner,"Broadcast channels with confidential messages,"
IEEE Trans. on Information Theory, 24(3):339-348, May 1978.
[6] I. E. Telatar,"Capacity of multi-antenna Gaussian channels," European
Trans. Telecommunications, 10:585-595, November 1999.
[7] R. Negi and S. Goel,"Secret communication using artificial noise,"IEEE
Vehicular Technology Conference, Toulouse, France, May 2006.
[8] P. Parada and R. Blahut,"Secrecy capacity of SIMO and slow fading channels,"
IEEE International Symposium on Information Theory, Adelaide,
Australia, September 2005.
[9] J. Barros and M. Rodrigues,"Secrecy capacity of wireless channels," IEEE
International Symposium on Information Theory, USA, 2006
[10] M. Bloch, J. Barros, M. Rodrigues and S. Mclaughlin,"Wireless information
theoretic security," IEEE Transactions on Information Theory, vol.
54, no. 6, pp. 2515-2534, June 2008.
[11] S. Shafiee and S. Ulukus,"Achievable rates in Gaussian MISO channels
with secrecy constraints," In IEEE International Symposium on Information
Theory, Nice, France, June 2007.
[12] Z. Li, W. Trappe, and R. D. Yates,"Secret communication via multi
antenna transmission," 41st Conference on Information Sciences and
Systems, Baltimore, MD, March 2007.
[13] A. Khisti, G. Wornell, A. Wiesel, and Y. Eldar,"On the Gaussian MIMO
wiretap channel," IEEE International Symposium on Information Theory,
Nice, France, June 2007.
[14] A. Khisti and G. Wornell,"Secure transmission with multiple antennas:
The MISOME wiretap channel," Submitted to IEEE Trans. on Information
Theory
[15] T. Cover and J. Thomas, Elements of Information Theory Wiley, 1991.
[16] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University
Press, 1987.
[17] X. Li and E. P. Ratazzi,"MIMO transmissions with information theoretic
secrecy for secret key agreement in wireless networks," IEEE Military
Communications Conference (MILCOM2005), 2005. Atlantic City, NJ.
[18] X. Li, M. Chen, and E. P. Ratazzi,"Space time transmissions for
wireless secret key agreement with information-theoretic secrecy," IEEE
International Workshop on Signal Processing Advances in Wireless
Communications (SPAWC05), 2005. The Italian Academy at Columbia
University, New York.
[19] P. Viswanath and D. Tse,"Fundamentals of wireless communications,"
class notes for ECE 459, Department of Electrical and Computer Engineering,
University of Illinois at Urbana Champaign, Fall 2003.
[20] S. Shafiee, N. Liu and S. Ulukus,"Secrecy Capacity of the 2-2-1
Gaussian MIMO Wire-tap Channel," ISCCSP, 2008
[21] A. Paulraj, R. Nabar, and D. Gore (2003) Introduction to Space-Time
Wireless Communications, Cambridge, U.K.: Cambridge Univ. Press
@article{"International Journal of Electrical, Electronic and Communication Sciences:60070", author = "Mohammad Rakibul Islam", title = "A Degraded Practical MIMOME Channel: Issues Insecret Data Communications", abstract = "In this paper, a Gaussian multiple input multiple output multiple eavesdropper (MIMOME) channel is considered where a transmitter communicates to a receiver in the presence of an eavesdropper. We present a technique for determining the secrecy capacity of the multiple input multiple output (MIMO) channel under Gaussian noise. We transform the degraded MIMOME channel into multiple single input multiple output (SIMO) Gaussian wire-tap channels and then use scalar approach to convert it into two equivalent multiple input single output (MISO) channels. The secrecy capacity model is then developed for the condition where the channel state information (CSI) for main channel only is known to the transmitter. The results show that the secret communication is possible when the eavesdropper channel noise is greater than a cutoff noise level. The outage probability is also analyzed of secrecy capacity is also analyzed. The effect of fading and outage probability is also analyzed.
", keywords = "Secrecy capacity, MIMO, wiretap channel, covariance matrix, fading.", volume = "4", number = "1", pages = "159-7", }
