TY - JOUR
T1 - Secure communications with insecure feedback
T2 - Breaking the high-SNR ceiling
AU - Kim, Tùng T.
AU - Poor, H. Vincent
N1 - Funding Information:
Manuscript received June 12, 2009; revised November 21, 2009. Date of current version July 14, 2010. This work was supported in part by the Office of Naval Research under Grant N00014-09-1-0342. The material in this paper was presented in part at the Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 2009. The authors are with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: [email protected]; [email protected]). Communicated by Elza Erkip, Associate Editor for Shannon Theory. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2010.2050798
PY - 2010/8
Y1 - 2010/8
N2 - A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not greater than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively transfer random keys in the form of known interference is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with log SNR. The pre-log factor of the secrecy rate, i.e., the number of secure degrees of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes. The relationship of the achievable secure degrees of freedom to those obtained in the case without feedback is finally discussed.
AB - A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not greater than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively transfer random keys in the form of known interference is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with log SNR. The pre-log factor of the secrecy rate, i.e., the number of secure degrees of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes. The relationship of the achievable secure degrees of freedom to those obtained in the case without feedback is finally discussed.
KW - Feedback
KW - information-theoretic security
KW - multiple-input multiple-output (MIMO) systems
KW - public channels
KW - wiretap channels
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U2 - 10.1109/TIT.2010.2050798
DO - 10.1109/TIT.2010.2050798
M3 - Article
AN - SCOPUS:77954592247
SN - 0018-9448
VL - 56
SP - 3700
EP - 3711
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 8
M1 - 5508616
ER -