DMT optimality of LR-aided linear decoders for a general class of channels, lattice designs, and system models

IEEE Transactions on Information Theory

Volumn 56, Issue 10, 2010, Pages 4765-4780

  Jaldén, Joakim ^a   Elia, Petros ^b  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b EURECOM   (France)

Author keywords

Diversity multiplexing tradeoff; lattice decoding; lattice reduction; linear decoding; multiple input multiple output (MIMO); regularization; space time coders decoders

Indexed keywords

DIVERSITY-MULTIPLEXING TRADE-OFF; LATTICE DECODING; LATTICE REDUCTION; LINEAR DECODING; MULTIPLE-INPUT-MULTIPLE-OUTPUT; REGULARIZATION; SPACE-TIME CODERS-DECODERS;

COMMUNICATION CHANNELS (INFORMATION THEORY); MAXIMUM LIKELIHOOD; MIMO SYSTEMS; MULTIPLEXING; OPTIMAL SYSTEMS; ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING;

DECODING;

EID: 77956706410     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2059493     Document Type: Article

References (69)

1. S. M. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE J. Sel. Areas Commun., vol.16, pp. 1451-1458, Oct. 1998.
2. V. Tarokh, H. Jafarkhani, and A. R. Calderbank, "Space-time block codes from orthogonal designs," IEEE Trans. Inf. Theory, vol.45, pp. 1456-1467, Jul. 1999.
3. 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., Pisa, Italy, 1998.
4. B. Hassibi and B. M. Hochwald, "High-rate codes that are linear in space and time," IEEE Trans. Inf. Theory, vol.48, pp. 1804-1824, Jul. 2002.
5. L. Zheng and D. N. C. Tse, "Diversity and multiplexing:A fundamental tradeoff in multiple-antenna channels," IEEE Trans. Inf. Theory, vol.49, pp. 1073-1096, May 2003.
6. H. E. 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, pp. 968-985, Jun. 2004.
7. P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H.-F. Lu, "Explicit space-time codes that achieve the diversity-multiplexing gain tradeoff," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Adelaide, Australia, 2005.
8. P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H.-F. Lu, "Explicit space-time codes achieving the diversity-multiplexing gain tradeoff," IEEE Trans. Inf. Theory, vol.52, pp. 3869-3884, Sep. 2006.
9. B. A. Sethuraman, B. S. Rajan, and V. Shashidhar, "Full-diversity, high-rate, space-time block codes from division algebras," IEEE Trans. Inf. Theory, vol.49, pp. 2596-2616, Oct. 2003.
10. J.-C. Belfiore and G. Rekaya, "Quaternionic lattices for space-time coding," in Proc. IEEE Inf. TheoryWorshop (ITW), Paris, France, Mar. 2003.
11. T. Kiran and B. S. Rajan, "STBC-schemes with non-vanishing determinant for certain number of transmit antennas," IEEE Trans. Inf. Theory, vol.51, pp. 2984-2992, Aug. 2005. (Pubitemid 41158622)
12. S. Tavildar and P. Viswanath, "Approximately universal codes over slow-fading channels," IEEE Trans. Inf. Theory, vol.52, pp. 3233-3258, Jul. 2006.
13. F. Oggier, G. Rekaya, J.-C. Belfiore, and E. Viterbo, "Perfect spacetime block codes," IEEE Trans. Inf. Theory, vol.52, pp. 3885-3902, Sep. 2006.
14. P. Elia, B. A. Sethuraman, and P. V. Kumar, "Perfect space-time codes for any number of transmit antennas," IEEE Trans. Inf. Theory, vol.53, pp. 3853-3868, Nov. 2007.
15. K. R. Kumar and G. Caire, "Space-time codes from structured lattices," IEEE Trans. Inf. Theory, vol.55, pp. 547-556, Feb. 2009.
16. C. Hollanti, J. Lahtonen, K. Ranto, and R. Vehkalahti, "On the densest MIMO lattices from cyclic division algebras," IEEE Trans. Inf. Theory, vol.55, no.8, pp. 3751-3780, Aug. 2009.
17. M. O. Damen, A. Tewfik, and J.-C. Belfiore, "A construction of a spacetime code based on number theory," IEEE Trans. Inf. Theory, vol.48, pp. 753-760, Mar. 2002.
18. S. Yang and J.-C. Belfiore, "Optimal space-time codes for the MIMO amplify-and-forward cooperative channel," IEEE Trans. Inf. Theory, vol.53, pp. 647-663, Feb. 2007.
19. H.-F. Lu, "Constructions of multiblock space-time coding schemes that achieve the diversity multiplexing tradeoff," IEEE Trans. Inf. Theory, vol.54, pp. 3790-3796, Aug. 2008.
20. P. Elia, K. Vinodh, M. Anand, and P. V. Kumar, "D-MG tradeoff and optimal codes for a class of AF and DF cooperative communication protocols," IEEE Trans. Inf. Theory, vol.55, Jul. 2009.
21. S. A. Pawar, K. R. Kumar, P. Elia, P. V. Kumar, and B. A. Sethuraman, "Space-time codes achieving the DMD tradeoff of the MIMO-ARQ channel," IEEE Trans. Inf. Theory, vol.55, Jul. 2009.
22. P. Elia and P. V. Kumar, "Space-time codes that are approximately universal for the parallel, multiblock and cooperative DDF channels," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Seoul, Korea, 2009.
23. E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, "Closest point search in lattices," IEEE Trans. Inf. Theory, vol.48, pp. 2201-2214, Aug. 2002.
24. M. O. Damen, H. E. Gamal, and G. Caire, "On maximum-likelihood detection and the search for the closest lattice point," IEEE Trans. Inf. Theory, vol.49, pp. 2389-2401, Oct. 2003.
25. A. D. Murugan, H. E. Gamal, M. O. Damen, and G. Caire, "A unified framework for tree search decoding: Rediscovering the sequential decoder," IEEE Trans. Inf. Theory, vol.52, pp. 933-953, Mar. 2006.
26. A. Burg, M. Borgmann, M. Wenk, M. Zellweger, W. Fichtner, and H. Bölcskei, "VLSI implementation of MIMO detection using the sphere decoding algorithm," IEEE J. Solid-State Circuits, vol.40, pp. 1566-1577, Jul. 2005.
27. J. Jaldén and B. Ottersten, "On the complexity of sphere decoding in digital communications," IEEE Trans. Signal Process., vol.53, pp. 1474-1484, Apr. 2005.
28. J. Jaldén and B. Ottersten, "On the limits of sphere decoding," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Adelaide, Australia, Sep. 2005.
29. D. Tse and P.Viswanath, Fundamentals ofWireless Communication. Cambridge , U.K.: Cambridge Univ. Press, 2005.
30. K. K. Raj, G. Caire, and A. L. Moustakas, "The diversity- multiplexing tradeoff of linear MIMO receivers," in Proc. IEEE Inf. TheoryWorshop (ITW), Lake Tahoe, NV, Sep. 2007, pp. 487-492.
31. H. Yao and G. W. Wornell, "Lattice-reduction-aided detectors for MIMO communication systems," in Proc. IEEE Global Conf. Commun. (GLOBECOM), Taipei, Taiwan, Nov. 2002.
32. C. Windpassinger and R. F. H. Fischer, "Low-complexity near-maximum- likelihood detection and precoding for MIMO systems using lattice reduction," in Proc. IEEE Inf. Theory Worshop (ITW), Paris, France, Mar. 2003.
33. M. Taherzadeh, A. Mobasher, and A. K. Khandani, "LLL reduction achieves the receive diversity in MIMO decoding," IEEE Trans. Inf. Theory, vol.53, pp. 4801-4805, Dec. 2007.
34. M. Taherzadeh and A. K. Khandani, "On the limitations of the naive lattice decoding," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Nice, France, Jun. 2007.
35. M. O. Damen, H. E. Gamal, and G. Caire, "MMSE-GDFE lattice decoding for underdetermined linear channels," in Proc. Conf. Inf. Sci. Syst., Princeton, NJ, 2004.
36. D. Wübben, R. Bohnke, V. Kuhn, and K.-D. Kammeyer, "Near-maximum- likelihood detection of MIMO systems using MMSE-based lattice reduction," in Proc. IEEE Int. Conf. Commun. (ICC), Paris, France, Jun. 2004.
37. S. Karmakar and B. S. Rajan, "Multigroup-decodable STBCs from Clifford algebra," IEEE Trans. Inf. Theory, vol.55, pp. 223-231, Jan. 2009.
38. C. Hollanti and K. Ranto, "Asymmetric space-time block codes for MIMO systems," in Proc. IEEE Inf. Theory Workshop on Inf. Theory for Wireless Netw., Bergen, Norway, Jul. 2007.
39. E. Biglieri, Y. Hong, and E. Viterbo, "On fast-decodable space-time block codes," IEEE Trans. Inf. Theory, vol.55, pp. 524-530, Feb. 2009.
40. O. Tirkkonen and R. Kashaev, "Combined information and performance optimization of linear MIMO modulations," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Lausanne, Switzerland, Jun. 2002.
41. J. Paredes, A. B. Gershman, and M. Gharavi-Alkhansari, "A 2 × 2 space-time code with non-vanishing determinant and fast maximum likelihood decoding," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Honolulu, HI, Apr. 2007.
42. M. Samuel and M. P. Fitz, "Reducing the detection complexity by using 2 × 2 multi-strata space-time codes," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Nice, France, Jun. 2007.
43. A. Medles and D. T. M. Slock, "Achieving the optimal diversity vs multiplexing tradeoff for MIMO flat channels with QAM space-time spreading and DFE equalization," IEEE Trans. Inf. Theory, vol.52, Dec. 2006.
44. D. Micciancio, "The hardness of the closest vector problem with preprocessing," IEEE Trans. Inf. Theory, vol.47, pp. 1212-1215, Mar. 2001.
45. J. Jaldén, D. Seethaler, and G. Matz, "Worst- and average-case complexity of LLL lattice reduction in MIMO wireless systems," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Las Vegas, NV, Apr. 2008.
46. L. Zhao, W. Mo, Y. Ma, and Z. Wang, "Diversity and multiplexing tradeoff in general fading channels," IEEE Trans. Inf. Theory, vol.53, pp. 1547-1557, Apr. 2007.
47. U. Betke and K. Böröczky, Jr, "Asymptotic formulae for the lattice point enumerator," Canad. J. Math., vol.51, no.2, pp. 225-249, 1999.
48. G. D. Forney, Jr, R. G. Gallager, G. R. Lang, F. M. Longstaff, and S. U. Qureshi, "Efficient modulation for band-limited channels," IEEE J. Sel. Areas Commun., vol.2, pp. 632-647, Sep. 1984.
49. C. Studer, D. Seethaler, and H. Bölcskei, "Finite lattice-size effects in MIMO detection," in Proc. Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, Oct. 2008.
50. A. N. Tikhonov, A. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-posed Problems, 1st ed. New York: Springer, 1995.
51. J. Hromkovič, Algorithms for Hard Problems: Introduction to Combinatorial Optimization, Randomization, Approximation and Heuristics, 2nd ed. New York: Springer, 2002.
52. L. Babai, "On lovász' lattice reduction and the nearest lattice point problem," Combinatorica, vol.6, no.1, pp. 1-13, Mar. 1986.
53. A. K. Lenstra, H. W. Lenstra, and L. Lovász, "Factoring polynomials with rational coefficients," Matematische Annalen, vol.261, no.4, pp. 1432-1807, Dec. 1982.
54. C. P. Schnorr and M. Euchner, "Lattice basis reduction: Improved practical algorithms and solving subset sum problems," Math. Program., vol.66, pp. 181-191, 1994.
55. H. Daudée and B. Vallée, "An upper bound on the average number of iterations of the LLL algorithm," Theoret. Comput. Sci., vol.123, no.1, Jan. 1994.
56. C. Ling and H. Howgrave-Graham, "Effective LLL reduction for lattice decoding," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Nice, France, Jun. 2007.
57. L. Luzzi, G. R.-B. Othman, and J.-C. Belfiore, "Algebraic reduction for space-time codes based on quaternion algebras," in IEEE Trans. Inf. Theory, 2008, available on arXiv:0809.3365v2 (cs.IT).
58. J.-C. Belfiore, G. Rekaya, and E. Viterbo, "The golden code: A 2 × 2 full-rate space-time code with non-vanishing determinants," IEEE Trans. Inf. Theory, vol.51, Apr. 2005.
59. U. Erez and R. Zamir, "Achieving 1/2 log (1 + SNR) on the AWGN channel with lattice encoding and decoding," IEEE Trans. Inf. Theory, vol.50, Oct. 2004.
60. A. Medles and D. T. M. Slock, "Optimal diversity vs. multiplexing treadeoff for frequency selective MIMO channels," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Adelaide, Australia, Sep. 2005.
61. S. Yang, J.-C. Belfiore, and G. R.-B. Othman, "Perfect space-time block codes for parallel MIMO channels," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Seattle, WA, Jul. 2006.
62. P. Elia and P. K. Vijay, "Approximately-universal space-time codes for the parallel, multi-block and cooperative-dynamic-decode-and-forward channels," 2007 [Online]. Available: arXiv:0706.3502v2 [cs.IT]
63. P. Coronel and H. Bölcskei, "Diversity-multiplexing tradeoff in selective- fading MIMO channels," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Nice, France, Jun. 2007.
64. J. N. Laneman and G. W.Wornell, "Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks," IEEE Trans. Inf. Theory, vol.49, pp. 2415-2425, Oct. 2003.
65. R. U. Nabar, H. Bölcskei, and F. W. Kneubuhler, "Fading relay channels: Performance limits and space-time signal design," IEEE J. Sel. Areas Commun., vol.22, pp. 1099-1109, Aug. 2004.
66. K. Azarian, H. E. Gamal, and P. Schniter, "On the achievable diversity- multiplexing tradeoff in half-duplex cooperative channels," IEEE Trans. Inf. Theory, vol.51, pp. 4152-4172, Dec. 2005.
67. S. Yang and J.-C. Belfiore, "Towards the optimal amplify-and-forward cooperative diversity scheme," IEEE Trans. Inf. Theory, vol.53, pp. 3114-3126, Sep. 2007.
68. H. E. Gamal, G. Caire, and M. O. Damen, "The MIMO ARQ channel: Diversity-multiplexing-delay tradeoff," IEEE Trans. Inf. Theory, vol.52, pp. 3601-3621, Aug. 2006.
69. T. T. Kim and M. Skoglund, "Diversity-multiplexing tradeoff in MIMO channels with partial CSIT," IEEE Trans. Inf. Theory, vol.53, pp. 2743-2759, Aug. 2007.