메뉴 건너뛰기




Volumn 57, Issue 4, 2011, Pages 2083-2114

The secrecy capacity region of the Gaussian MIMO multi-receiver wiretap channel

Author keywords

Gaussian MIMO broadcast channel; information theoretic security; secrecy capacity region

Indexed keywords

ARBITRARY NUMBER; BROADCAST CHANNELS; CODING SCHEME; DIFFERENTIAL ENTROPY; DIRTY-PAPER CODING; ENHANCEMENT TECHNIQUES; FISHER INFORMATION; GAUSSIAN SIGNALS; GAUSSIANS; INFORMATION THEORETIC SECURITY; MIMO BROADCAST CHANNELS; MIMO CHANNEL; MINIMUM MEAN SQUARE ERRORS; MULTI-RECEIVER; MULTIPLE-INPUT-MULTIPLE-OUTPUT; MUTUAL INFORMATIONS; NOISE COVARIANCE; SECRECY CAPACITY; SECRECY CAPACITY REGION; SINGLE INPUT SINGLE OUTPUT CASE; SISO CHANNELS; WIRETAP CHANNEL;

EID: 79952846257     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2111750     Document Type: Article
Times cited : (195)

References (46)
  • 1
    • 0016562514 scopus 로고
    • The wire-tap channel
    • Jan.
    • A. Wyner, "The wire-tap channel," Bell Syst. Tech. J., vol. 54, no. 8, pp. 1355-1387, Jan. 1975.
    • (1975) Bell Syst. Tech. J. , vol.54 , Issue.8 , pp. 1355-1387
    • Wyner, A.1
  • 2
    • 0017973511 scopus 로고
    • Broadcast channels with confidential messages
    • May
    • I. Csiszar and J. Korner, "Broadcast channels with confidential messages," IEEE Trans. Inf. Theory, vol. IT-24, no. 3, pp. 339-348, May 1978.
    • (1978) IEEE Trans. Inf. Theory , vol.IT-24 , Issue.3 , pp. 339-348
    • Csiszar, I.1    Korner, J.2
  • 3
    • 57349093480 scopus 로고    scopus 로고
    • The Gaussian multiple access wire-tap channel
    • Dec.
    • E. Tekin and A. Yener, "The Gaussian multiple access wire-tap channel," IEEE Trans. Inf. Theory, vol. 54, no. 12, pp. 5747-5755, Dec. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.12 , pp. 5747-5755
    • Tekin, E.1    Yener, A.2
  • 4
    • 45249101530 scopus 로고    scopus 로고
    • The general Gaussian multiple access and two-way wire-tap channels: Achievable rates and cooperative jamming
    • Jun.
    • E. Tekin and A. Yener, "The general Gaussian multiple access and two-way wire-tap channels: Achievable rates and cooperative jamming," IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 2735-2751, Jun. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.6 , pp. 2735-2751
    • Tekin, E.1    Yener, A.2
  • 6
    • 45249090083 scopus 로고    scopus 로고
    • Discrete memoryless interference and broadcast channels with confidential messages: Secrecy rate regions
    • Jun.
    • R. Liu, I. Maric, P. Spasojevic, and R. D. Yates, "Discrete memoryless interference and broadcast channels with confidential messages: Secrecy rate regions," IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 2493-2507, Jun. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.6 , pp. 2493-2507
    • Liu, R.1    Maric, I.2    Spasojevic, P.3    Yates, R.D.4
  • 7
    • 62749109096 scopus 로고    scopus 로고
    • Secrecy capacity region of a multi-antenna Gaussian broadcast channel with confidential messages
    • Mar.
    • R. Liu and H. V. Poor, "Secrecy capacity region of a multi-antenna Gaussian broadcast channel with confidential messages," IEEE Trans. Inf. Theory, vol. 55, no. 3, pp. 1235-1249, Mar. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.3 , pp. 1235-1249
    • Liu, R.1    Poor, H.V.2
  • 8
    • 45249092485 scopus 로고    scopus 로고
    • Secure broadcasting over fading channels
    • Jun.
    • A. Khisti, A. Tchamkerten, and G. W. Wornell, "Secure broadcasting over fading channels," IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 2453-2469, Jun. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.6 , pp. 2453-2469
    • Khisti, A.1    Tchamkerten, A.2    Wornell, G.W.3
  • 12
    • 51349098469 scopus 로고    scopus 로고
    • Relay channels with confidential messages
    • also available at [arXiv:0611125], to be published
    • Y. Oohama, "Relay channels with confidential messages," IEEE Trans. Inf. Theory, also available at [arXiv:0611125], to be published.
    • IEEE Trans. Inf. Theory
    • Oohama, Y.1
  • 13
    • 51349109773 scopus 로고    scopus 로고
    • The relay-eavesdropper channel: Cooperation for secrecy
    • Sep.
    • L. Lai and H. El Gamal, "The relay-eavesdropper channel: Cooperation for secrecy," IEEE Trans. Inf. Theory, vol. 54, no. 9, pp. 4005-4019, Sep. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.9 , pp. 4005-4019
    • Lai, L.1    El Gamal, H.2
  • 15
    • 77954584734 scopus 로고    scopus 로고
    • Cooperation with an untrusted relay: A secrecy perspective
    • Aug.
    • X. He and A. Yener, "Cooperation with an untrusted relay: A secrecy perspective," IEEE Trans. Inf. Theory, vol. 56, no. 8, pp. 3801-3827, Aug. 2010.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.8 , pp. 3801-3827
    • He, X.1    Yener, A.2
  • 16
    • 51849115215 scopus 로고    scopus 로고
    • Effects of cooperation on the secrecy of multiple access channels with generalized feedback
    • presented at the, Mar.
    • E. Ekrem and S. Ulukus, "Effects of cooperation on the secrecy of multiple access channels with generalized feedback," presented at the Conf. Information Sciences and Systems, Mar. 2008.
    • (2008) Conf. Information Sciences and Systems
    • Ekrem, E.1    Ulukus, S.2
  • 17
    • 78650894311 scopus 로고    scopus 로고
    • Secrecy in cooperative relay channels
    • Jan.
    • E. Ekrem and S. Ulukus, "Secrecy in cooperative relay channels," IEEE Trans. Inf. Theory, vol. 57, no. 1, pp. 137-155, Jan. 2011.
    • (2011) IEEE Trans. Inf. Theory , vol.57 , Issue.1 , pp. 137-155
    • Ekrem, E.1    Ulukus, S.2
  • 18
    • 51849134999 scopus 로고    scopus 로고
    • Confidential messages to a cooperative relay
    • presented at the, May
    • M. Bloch and A. Thangaraj, "Confidential messages to a cooperative relay," presented at the IEEE Information Theory Workshop, May 2008.
    • (2008) IEEE Information Theory Workshop
    • Bloch, M.1    Thangaraj, A.2
  • 19
    • 40949147785 scopus 로고    scopus 로고
    • Multiple-access channels with confidential messages
    • DOI 10.1109/TIT.2007.915978
    • Y. Liang and H. V. Poor, "Multiple access channels with confidential messages," IEEE Trans. Inf. Theory, vol. 54, no. 3, pp. 976-1002, Mar. 2008. (Pubitemid 351410914)
    • (2008) IEEE Transactions on Information Theory , vol.54 , Issue.3 , pp. 976-1002
    • Liang, Y.1    Poor, H.V.2
  • 20
    • 39049089566 scopus 로고    scopus 로고
    • The discrete memoryless multiple access channel with confidential messages
    • presented at the, Jul.
    • R. Liu, I. Maric, R. D. Yates, and P. Spasojevic, "The discrete memoryless multiple access channel with confidential messages," presented at the IEEE Int. Symp. Inf. Theory, Jul. 2006.
    • (2006) IEEE Int. Symp. Inf. Theory
    • Liu, R.1    Maric, I.2    Yates, R.D.3    Spasojevic, P.4
  • 22
    • 0016037985 scopus 로고
    • A simple converse for broadcast channels with additive white Gaussian noise
    • Mar.
    • P. Bergmans, "A simple converse for broadcast channels with additive white Gaussian noise," IEEE Trans. Inf. Theory, vol. 20, no. 3, pp. 279-280, Mar. 1974.
    • (1974) IEEE Trans. Inf. Theory , vol.20 , Issue.3 , pp. 279-280
    • Bergmans, P.1
  • 24
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • Oct.
    • C. E. Shannon, "A mathematical theory of communication," Bell Sys. Tech. J., vol. 27, pp. 623-656, Oct. 1948.
    • (1948) Bell Sys. Tech. J. , vol.27 , pp. 623-656
    • Shannon, C.E.1
  • 25
    • 12944295719 scopus 로고
    • Some inequalities satisfied by the quantities of information of Fisher and Shannon
    • June
    • A. J. Stam, "Some inequalities satisfied by the quantities of information of Fisher and Shannon," Inf. Control, vol. 2, pp. 101-112, June 1959.
    • (1959) Inf. Control , vol.2 , pp. 101-112
    • Stam, A.J.1
  • 26
    • 84938171492 scopus 로고
    • The convolution inequality for entropy powers
    • Apr.
    • N. M. Blachman, "The convolution inequality for entropy powers," IEEE Trans. Inf. Theory, vol. IT-11, no. 2, pp. 267-271, Apr. 1965.
    • (1965) IEEE Trans. Inf. Theory , vol.IT-11 , Issue.2 , pp. 267-271
    • Blachman, N.M.1
  • 27
    • 0022148899 scopus 로고
    • A new entropy power inequality
    • Nov.
    • M. H. M. Costa, "A new entropy power inequality," IEEE Trans. Inf. Theory, vol. 31, no. 6, pp. 751-760, Nov. 1985.
    • (1985) IEEE Trans. Inf. Theory , vol.31 , Issue.6 , pp. 751-760
    • Costa, M.H.M.1
  • 28
    • 77950269477 scopus 로고    scopus 로고
    • A vector generalization of Costa's entropy-power inequality with applications
    • Apr.
    • R. Liu, T. Liu, H. V. Poor, and S. Shamai (Shitz), "A vector generalization of Costa's entropy-power inequality with applications," IEEE Trans. Inf. Theory, vol. 56, no. 4, pp. 1865-1879, Apr. 2010.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.4 , pp. 1865-1879
    • Liu, R.1    Liu, T.2    Poor, H.V.3    Shamai, S.4
  • 29
    • 17644366813 scopus 로고    scopus 로고
    • Mutual information and minimum mean-square error in Gaussian channels
    • Apr.
    • D. Guo, S. Shamai (Shitz), and S. Verdu, "Mutual information and minimum mean-square error in Gaussian channels," IEEE Trans. Inf. Theory, vol. 51, no. 4, pp. 1261-1283, Apr. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.4 , pp. 1261-1283
    • Guo, D.1    Shamai, S.2    Verdu, S.3
  • 30
    • 79952847524 scopus 로고    scopus 로고
    • Estimation of non-Gaussian random variables in Gaussian noise: Properties of the MMSE
    • to be published
    • D. Guo, S. Shamai (Shitz), and S. Verdu, "Estimation of non-Gaussian random variables in Gaussian noise: Properties of the MMSE," IEEE Trans. Inf. Theory, to be published.
    • IEEE Trans. Inf. Theory
    • Guo, D.1    Shamai, S.2    Verdu, S.3
  • 31
    • 78650907825 scopus 로고    scopus 로고
    • Information theoretic proofs of entropy power inequalities
    • Jan.
    • O. Rioul, "Information theoretic proofs of entropy power inequalities," IEEE Trans. Inf. Theory, vol. 57, no. 1, pp. 33-55, Jan. 2011.
    • (2011) IEEE Trans. Inf. Theory , vol.57 , Issue.1 , pp. 33-55
    • Rioul, O.1
  • 32
    • 33748578624 scopus 로고    scopus 로고
    • The capacity region of the Gaussian multiple-input multiple-output broadcast channel
    • DOI 10.1109/TIT.2006.880064
    • H. Weingarten, Y. Steinberg, and S. Shamai (Shitz), "The capacity region of the Gaussian multiple-input multiple-output broadcast channel," IEEE Trans. Inf. Theory, vol. 52, no. 9, pp. 3936-3964, Sep. 2006. (Pubitemid 44363826)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.9 , pp. 3936-3964
    • Weingarten, H.1    Steinberg, Y.2    Shamai, S.3
  • 33
    • 66949180834 scopus 로고    scopus 로고
    • A note on the secrecy capacity of the multi-antenna wiretap channel
    • Jun.
    • T. Liu and S. Shamai (Shitz), "A note on the secrecy capacity of the multi-antenna wiretap channel," IEEE Trans. Inf. Theory, vol. 55, no. 6, pp. 2547-2553, Jun. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.6 , pp. 2547-2553
    • Liu, T.1    Shamai, S.2
  • 34
    • 33144485285 scopus 로고    scopus 로고
    • Gradient of mutual information in linear vector Gaussian channels
    • DOI 10.1109/TIT.2005.860424
    • D. P. Palomar and S. Verdu, "Gradient of mutual information in linear vector Gaussian channels," IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 141-154, Jan. 2006. (Pubitemid 43263124)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.1 , pp. 141-154
    • Palomar, D.P.1    Verdu, S.2
  • 35
    • 77958560746 scopus 로고    scopus 로고
    • Secure transmission with multiple antennas II: The MIMOME channel
    • Nov.
    • A. Khisti and G.Wornell, "Secure transmission with multiple antennas II: The MIMOME channel," IEEE Trans. Inf. Theory vol. 56, no. 1, pp. 5515-5532, Nov. 2010.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.1 , pp. 5515-5532
    • Khisti, A.1    Wornell, G.2
  • 36
    • 79960996804 scopus 로고    scopus 로고
    • The secrecy capacity of the MIMO wiretap channel
    • also available at [arXiv:0710.1920], to be published
    • F. Oggier and B. Hassibi, "The secrecy capacity of the MIMO wiretap channel," IEEE Trans. Inf. Theory, also available at [arXiv:0710.1920], to be published.
    • IEEE Trans. Inf. Theory
    • Oggier, F.1    Hassibi, B.2
  • 37
    • 69449086815 scopus 로고    scopus 로고
    • Towards the secrecy capacity of the Gaussian MIMO wire-tap channel: The 2-2-1 channel
    • Sep.
    • S. Shafiee, N. Liu, and S. Ulukus, "Towards the secrecy capacity of the Gaussian MIMO wire-tap channel: The 2-2-1 channel," IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 4033-4039, Sep. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.9 , pp. 4033-4039
    • Shafiee, S.1    Liu, N.2    Ulukus, S.3
  • 40
    • 70350706020 scopus 로고    scopus 로고
    • The capacity region of the degraded multiple-input multiple- output compound broadcast channel
    • Nov.
    • H. Weingarten, T. Liu, S. Shamai (Shitz), Y. Steinberg, and P. Viswanath, "The capacity region of the degraded multiple-input multiple- output compound broadcast channel," IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 5011-5023, Nov. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.11 , pp. 5011-5023
    • Weingarten, H.1    Liu, T.2    Shamai, S.3    Steinberg, Y.4    Viswanath, P.5
  • 41
    • 0017960331 scopus 로고
    • On the capacity of channels with additive non-Gaussian noise
    • S. Ihara, "On the capacity of channels with additive non-Gaussian noise," Inf. Control, vol. 37, no. 1, pp. 34-39, Apr. 1978. (Pubitemid 8609487)
    • (1978) Information and Control , vol.37 , Issue.1 , pp. 34-39
    • Ihara Shunsuke1
  • 42
    • 0035504557 scopus 로고    scopus 로고
    • The worst additive noise under a covariance constraint
    • DOI 10.1109/18.959289, PII S0018944801089623
    • S. H. Diggavi and T. M. Cover, "The worst additive noise constraint under a covariance constraint," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 3072-3081, Nov. 2001. (Pubitemid 33053512)
    • (2001) IEEE Transactions on Information Theory , vol.47 , Issue.7 , pp. 3072-3081
    • Diggavi, S.N.1    Cover, T.M.2
  • 43
    • 34248373869 scopus 로고    scopus 로고
    • An extremal inequality motivated by multiterminal information-theoretic problems
    • DOI 10.1109/TIT.2007.894680
    • T. Liu and P. Viswanath, "An extremal inequality motivated by multiterminal information theoretic problems," IEEE Trans. Inf. Theory, vol. 53, no. 5, pp. 1839-1851, May 2007. (Pubitemid 46736820)
    • (2007) IEEE Transactions on Information Theory , vol.53 , Issue.5 , pp. 1839-1851
    • Liu, T.1    Viswanath, P.2
  • 45
    • 0018467629 scopus 로고
    • A coding theorem for the discrete memoryless channels
    • K. Marton, "A coding theorem for the discrete memoryless channels," IEEE Trans. Inf. Theory, vol. 25, no. 1, pp. 306-311, May 1979. (Pubitemid 9450752)
    • (1979) IEEE Trans Inf Theory , vol.IT-25 , Issue.3 , pp. 306-311
    • Marton Katalin1
  • 46
    • 4544346202 scopus 로고    scopus 로고
    • Sum capacity of Gaussian vector broadcast channels
    • Sep.
    • W. Yu and J. Cioffi, "Sum capacity of Gaussian vector broadcast channels," IEEE Trans. Inf. Theory, vol. 50, no. 9, pp. 1875-1892, Sep. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.9 , pp. 1875-1892
    • Yu, W.1    Cioffi, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.