The MIMO wiretap channel decomposed

IEEE Transactions on Information Theory

Volumn 64, Issue 2, 2018, Pages 1046-1063

  Khina, Anatoly ^a,b   Kochman, Yuval ^c   Khisti, Ashish ^d  

^a TEL AVIV UNIVERSITY   (Israel)

^b California Institute of Technology   (United States)

^c HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^d UNIVERSITY OF TORONTO   (Canada)

Author keywords

Confidential broadcast; Dirty paper coding; Matrix decomposition; MIMO channel; Successive interference cancellation; Wiretap channel

Indexed keywords

COMMUNICATION CHANNELS (INFORMATION THEORY); FADING CHANNELS; GAUSSIAN DISTRIBUTION; MIMO SYSTEMS; TRANSMISSIONS; TRELLIS CODES;

DIRTY PAPER CODING; MATRIX DECOMPOSITION; MIMO CHANNEL; SUCCESSIVE INTERFERENCE CANCELLATIONS; WIRE-TAP CHANNELS;

CHANNEL CODING;

EID: 85040937077     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2017.2710058     Document Type: Article

References (56)

1. A. D. Wyner, "The wire-tap channel," Bell Syst. Tech. J., vol. 54, no. 8, pp. 1355-1387, Oct. 1975.
2. I. Csiszár and J. Körner, "Broadcast channels with confidential messages," IEEE Trans. Inf. Theory, vol. 24, no. 3, pp. 339-348, May 1978.
3. S. K. Leung-Yan-Cheong and M. E. Hellman, "The Gaussian wire-tap channel," IEEE Trans. Inf. Theory, vol. 24, no. 4, pp. 451-456, Jul. 1978.
4. A. Khisti and G. W. Wornell, "Secure transmission with multiple antennas-Part II: The MIMOME wiretap channel," IEEE Trans. Inf. Theory, vol. 56, no. 11, pp. 5515-5532, Nov. 2010.
5. F. Oggier and B. Hassibi, "The secrecy capacity of the MIMO wiretap channel," IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 4961-4972, Aug. 2011.
6. T. Liu and S. Shamai (Shitz), "A note on the secrecy capacity of the multiple-antenna wiretap channel," IEEE Trans. Inf. Theory, vol. 55, no. 6, pp. 2547-2553, Jun. 2009.
7. R. Bustin, R. Liu, H. V. Poor, and S. Shamai (Shitz), "An MMSE approach to the secrecy capacity of the MIMO Gaussian wiretap channel," EURASIP J. Wireless Commun. Netw. Special Issue Wireless Phys. Secur., vol. 2009, no. 1, p. 370970, Jul. 2009.
8. S. Loyka and C. D. Charalambous, "An algorithm for global maximization of secrecy rates in Gaussian MIMO wiretap channels," IEEE Trans. Commun., vol. 63, no. 6, pp. 2288-2299, Jun. 2015.
9. S. Loyka and C. D. Charalambous, "Optimal signaling for secure communications over Gaussian mimo wiretap channels," IEEE Trans. Inf. Theory, vol. 62, no. 12, pp. 7207-7215, Dec. 2016.
10. 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.
11. R. Liu and H. V. Poor, "Secrecy capacity region of a multiple-antenna Gaussian broadcast channel with confidential messages," IEEE Trans. Inf. Theory, vol. 55, no. 3, pp. 1235-1249, Mar. 2009.
12. R. Liu, T. Liu, H. V. Poor, and S. Shamai (Shitz), "Multiple-input multiple-output Gaussian broadcast channels with confidential messages," IEEE Trans. Inf. Theory, vol. 56, no. 9, pp. 4215-4227, Sep. 2010.
13. H. Tyagi and A. Vardy, "Explicit capacity-achieving coding scheme for the Gaussian wiretap channel," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Honolulu, HI, USA, Jun./Jul. 2014, pp. 956-960.
14. A. Thangaraj, S. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J.-M. Merolla, "Applications of LDPC codes to the wiretap channel," IEEE Trans. Inf. Theory, vol. 53, no. 8, pp. 2933-2945, Aug. 2007.
15. D. Klinc, J. Ha, S. W. McLaughlin, J. Barros, and B.-J. Kwak, "LDPC codes for the Gaussian wiretap channel," IEEE Trans. Inf. Forensics Security, vol. 6, no. 3, pp. 532-540, Sep. 2011.
16. F. Oggier, P. Solë, and J.-C. Belfiore, "Lattice codes for the wiretap Gaussian channel: Construction and analysis," IEEE Trans. Inf. Theory, vol. 62, no. 10, pp. 5690-5708, Oct. 2016.
17. H. Mahdavifar and A. Vardy, "Achieving the secrecy capacity of wiretap channels using polar codes," IEEE Trans. Inf. Theory, vol. 57, no. 10, pp. 6428-6443, Oct. 2011.
18. M. Andersson, "Coding for the wiretap channel," Ph.D. dissertation, School Elect. Eng. (EES), Royal Inst. Technol. (KTH), Stockholm, Sweden, 2011.
19. Y. Yan, L. Liu, and C. Ling, "Polar lattices for strong secrecy over the mod-? Gaussian wiretap channel," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Honolulu, HI, USA, Jun./Jul. 2014, pp. 961-965.
20. A. Khina, Y. Kochman, and U. Erez, "Joint unitary triangularization for MIMO networks," IEEE Trans. Signal Process., vol. 60, no. 1, pp. 326-336, Jan. 2012.
21. I. E. Telatar, "Capacity of multi-antenna Gaussian channels," Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585-595, Nov. 1999.
22. G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Tech. J., vol. 1, no. 2, pp. 41-59, 1996.
23. P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela, "V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel," in Proc. URSI Int. Symp. Sig., Syst., Elect. (ISSSE), Sep./Oct. 1998, pp. 295-300.
24. J. M. Cioffi and G. D. Forney, Jr., "Generalized decision-feedback equalization for packet transmission with ISI and Gaussian noise," in Communications, Computation, Control, and Signal Processing. Springer, 1997, pp. 79-127.
25. B. Hassibi, "An efficient square-root algorithm for BLAST," in Proc. IEEE Int. Conf. Acoust. Speech Sig. Proc. (ICASSP), vol. 2. Istanbul, Turkey, Jun. 2000, pp. 737-740.
26. M. H. M. Costa, "Writing on dirty paper," IEEE Trans. Inf. Theory, vol. 29, no. 3, pp. 439-441, May 1983.
27. A. Khina, I. Livni, A. Hitron, and U. Erez, "Joint unitary triangularization for Gaussian multi-user MIMO networks," IEEE Trans. Inf. Theory, vol. 61, no. 5, pp. 2662-2692, May 2015.
28. D. P. Palomar and Y. Jiang, "MIMO transceiver design via majorization theory," Found. Trends Commun. Inf. Theory, vol. 3, nos. 4-5, pp. 331-551, Nov. 2006.
29. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD, USA: The Johns Hopkins Univ. Press, 1996.
30. H. Weyl, "Inequalities between two kinds of eigenvalues of a linear transformation," Proc. Nat. Acad. Sci. USA, vol. 35, no. 7, pp. 408-411, May 1949.
31. P. Kosowski and A. Smoktunowicz, "On constructing unit triangular matrices with prescribed singular values," Computing, vol. 64, no. 3, pp. 279-285, May 2000.
32. Y. Jiang, W. W. Hager, and J. Li, "The generalized triangular decompostion," Math. Comput., vol. 77, no. 262, pp. 1037-1056, Oct. 2008.
33. J.-K. Zhang and K. M. Wong, "Fast QRS decomposition of matrix and its applications to numerical optimization," Dept. Elect. Comp. Eng., McMaster Univ., Hamilton, ON, Canada, Tech. Rep. [Online]. Available: http://www.ece.mcmaster.ca/~jkzhang/papers/sam-qrs.pdf
34. A. Horn, "On the eigenvalues of a matrix with prescribed singular values," in Proc. Amer. Math. Soc., vol. 5, no. 1, pp. 4-7, Feb. 1954.
35. J.-K. Zhang, A. Kavcíc, and K. M. Wong, "Equal-diagonal QR decomposition and its application to precoder design for successivecancellation detection," IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 154-172, Jan. 2005.
36. Y. Jiang, W. W. Hager, and J. Li, "The geometric mean decomposition," Lin. Algebra Appl., vol. 396, pp. 373-384, Feb. 2005.
37. C. F. Van Loan, "Generalizing the singular value decomposition," SIAM J. Numer., vol. 13, no. 1, pp. 76-83, Mar. 1976.
38. Z. Bai, "The CSD, GSVD, their applications and computations," Univ. Minnesota, Minneapolis, MN, USA, Tech. Rep., Apr. 1992.
39. C. C. Paige and M. A. Saunders, "Towards a generalized singular value decomposition," SIAM J. Numer. Anal., vol. 18, no. 3, pp. 398-405, Jun. 1981.
40. J. M. Cioffi, G. P. Dudevoir, M. V. Eyuboglu, and G. D. Forney, Jr., "MMSE decision-feedback equalizers and coding. I. Equalization results," IEEE Trans. Commun., vol. 43, no. 10, pp. 2582-2594, Oct. 1995.
41. Y. Jiang, J. Li, and W. M. Hager, "Uniform channel decomposition for MIMO communications," IEEE Trans. Signals Process., vol. 53, no. 11, pp. 4283-4294, Nov. 2005.
42. H. El Gamal, G. Caire, and M. O. Damen, "Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 968-985, Jun. 2004.
43. M. R. Bloch and J. N. Laneman, "Strong secrecy from channel resolvability," IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 8077-8098, Dec. 2013.
44. A. El Gamal and Y.-H. Kim, Network Information Theory. Cambridge, U.K.: Cambridge Univ. Press, 2011.
45. J. M. Cioffi and G. Ginis, "A multi-user precoding scheme achieving crosstalk cancellation with application to DSL systems," in Proc. Asilomar Conf. Sig., Syst. Comput., vol. 2. Pacific Grove, CA, USA, Oct./Nov. 2000, pp. 1627-1631.
46. G. Caire and S. Shamai (Shitz), "On the achievable throughput of a multiantenna Gaussian broadcast channel," IEEE Trans. Inf. Theory, vol. 49, no. 7, pp. 1649-1706, Jul. 2003.
47. C. Mitrpant, A. J. H. Vinck, and Y. Luo, "An achievable region for the Gaussian wiretap channel with side information," IEEE Trans. Inf. Theory, vol. 52, no. 5, pp. 2181-2190, May 2006.
48. Y. Chen and A. J. H. Vinck, "Wiretap channel with side information," IEEE Trans. Inf. Theory, vol. 54, no. 1, pp. 395-402, Jan. 2008.
49. M. Bellare, S. Tessaro, and A. Vardy, "Semantic security for the wiretap channel," in Advances in Cryptology (Lecture Notes in Computer Science), R. Safavi-Naini and R. Canetti, Eds., vol. 7417. Berlin, Germany: Springer, 2012, pp. 294-311.
50. M. Hayashi and R. Matsumoto, "Construction of wiretap codes from ordinary channel codes," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Austin, TX, USA, Jun. 2010, pp. 2538-2542.
51. A. Khina, Y. Kochman, and A. Khisti, "From ordinary AWGN codes to optimal MIMO wiretap schemes," in Proc. IEEE Inf. Theory Workshop (ITW), Hobart, TAS, Australia, Oct./Nov. 2014, pp. 632-636.
52. F. Baccelli, A. El Gamal, and D. N. C. Tse, "Interference networks with point-to-point codes," IEEE Trans. Inf. Theory, vol. 57, no. 5, pp. 2582-2596, May 2011.
53. O. Ordentlich and U. Erez, "On the robustness of lattice interference alignment," IEEE Trans. Inf. Theory, vol. 59, no. 5, pp. 2735-2759, May 2013.
54. J. de Leeuw, "Derivatives of generalized eigen systems with applications," Dept. Statist., UCLA, Los Angeles, CA, USA, Tech. Rep., Dec. 2007.
55. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York, NY, USA: Wiley, 2006.
56. Y.-K. Chia and A. El Gamal, "Three-receiver broadcast channels with common and confidential messages," IEEE Trans. Inf. Theory, vol. 58, no. 5, pp. 2748-2765, May 2012.