Systematic and optimal cyclotomic lattices and diagonal space-time block code designs

IEEE Transactions on Information Theory

Volumn 50, Issue 12, 2004, Pages 3348-3360

  Wang, Genyuan ^a   Liao, Huiyong ^a   Wang, Haiquan ^a   Xia, Xiang Gen ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

Algebraic number theory; Cyclotomic fields; Cyclotomic lattices; Galois theory; Space time block codes

Indexed keywords

APPROXIMATION THEORY; COMMUNICATION CHANNELS (INFORMATION THEORY); COMPUTER SIMULATION; FOURIER TRANSFORMS; MATRIX ALGEBRA; NUMBER THEORY; RAYLEIGH FADING;

ALGEBRAIC NUMBER THEORY; CYCLOTOMIC FIELDS; CYCLOTOMIC LATTICES; GALOIS THEORY; SPACE TIME BLOCK CODES;

BLOCK CODES;

EID: 10644282291     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.838096     Document Type: Article

References (48)

1. K. Boulle and J.-C. Belfiore, "Modulation schemes designed for the Rayleigh fading channel," in Proc. CISS'92, Princeton, NJ, Mar. 1992.
2. X. Giraud, E. Boutillon, and J.-C. Belfiore, "Algebraic tools to build modulation schemes for fading channels," IEEE Trans. Inform. Theory vol. 43, pp. 938-952, May 1997.
3. J. Boutros and E. Viterbo, "Signal space diversity: A power- and bandwidth-efficient diversity technique for the Rayleigh fading channel," IEEE Trans. Inform. Theory, vol. 44, pp. 1453-1467, July 1998.
4. M. O. Damen, H. El Gamal, and N. C. Beaulieu, "A systematic construction of full diversity algebraic constellations," in Proc. Canadian Workshop on Information Theory (CWIT 2003), Waterloo, ON, Canada, May 2003.
5. M. O. Damen, K. A. Meraim, and J.-C. Belfiore, "Diagonal algebraic space-time block codes," IEEE Trans. Inform. Theory, vol. 48, pp. 628-636, Mar. 2002.
6. M. O. Damen, A. Tewfik, and J.-C. Belfiore, "A construction of a space-time code based on number theory," IEEE Trans. Inform. Theory vol. 48, pp. 753-760, Mar. 2002.
7. B. A. Sethuraman and B. S. Rajan, "Full-rank space-time block codes from division algebras," preprint, 2002. Presented in paart at the Int. Conf. Communications 2002 and the IEEE Int. Symp. Information Theory, 2002.
8. V. M. DaSilva and E. S. Sousa, "Fading-resistant modulation using several transmitter antennas," IEEE Trans. Commun., vol. 45, pp. 1236-1244, Oct. 1997.
9. N. Prasad and M. K. Varanasi, "D-BLAST lattice codes for MIMO block Rayleigh fading channels," in Proc. 40th Annu. Allerton Conf. Communications, Control, and Computing, Monticello, IL, Oct. 2002.
10. J.-C. Guey, M. P. Fitz, M. R. Bell, and W.-Y. Kuo, "Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels," in Proc. IEEE Vehicular Technology Conf. (VTC'96) pp. 136-140.
11. V. Tarokh, N. Seshadri, and A. R. Calderbank, "Space-time codes for high data rate wireless communication: Performance criterion and code construction," IEEE Trans. Inform. Theory, vol. 44, pp. 744-765, Mar. 1998.
12. S. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE J. Select. Areas Commun., vol. 16, pp. 1451-1458, Aug. 1998.
13. V. Tarokh, H. Jafarkhani, and A. R. Calderbank, "Space-time block codes from orthogonal designs," IEEE Trans. Inform. Theory, vol. 45, pp. 1456-1467, July 1999.
14. G. Ganesan and P. Stoica, "Space-time block codes: A maximum SNR," IEEE Trans. Inform. Theory, vol. 47, pp. 1650-1656, May 2001.
15. H. Jafarkhani, "A quasiorthogonal space-time block code," IEEE Trans. Commun., vol. 49, pp. 1-4, Jan. 2001.
16. O. Tirkkonen, A. Boariu, and A. Hottinen, "Minimal nonorthogonality rate 1 space-time block code for 3 + Tx antennas," in Proc. IEEE 6th Int. Symp. Spread-Spectrum Techniques and Applications (ISSSTA 2000 , Sept. 2000, pp. 429-432.
17. B. Hassibi and B. M. Hochwald, "High-rate codes that are linear in space and time," IEEE Trans. Inform. Theory, vol. 48, pp. 1473-1484, June 2002.
18. H. Wang and X.-G. Xia, "Upper bounds of rates of complex orthogonal designs," IEEE Trans. Inform. Theory, vol. 49, pp. 2788-2796, Oct. 2003.
19. W. Su and X.-G. Xia, "Two generalized complex orthogonal space-time block codes of rates 7/11 and 3/5 for 5 and 6 transmit antennas," IEEE Trans. Inform. Theory, vol. 49, pp. 313-316, Jan. 2003.
20. W. Su and X.-G. Xia, "Signal constellations for quasiorthogonal space-time block codes with full diversity," IEEE Trans. Inform. Theory, to be published.
21. X.-B. Liang, "Orthogonal designs with maximal rates," IEEE Trans. Inform. Theory, vol. 49, pp. 2468-2503, Oct. 2003.
22. W. Su, X.-G. Xia, and K. J. R. Liu, "A systematic design of high-rate complex orthogonal space-time block codes," IEEE Commun. Letters, vol. 8, no. 6, pp. 380-382, June 2004.
23. K. Lu, S. Fu, and X.-G. Xia, "Closed form designs of complex orthogonal space-time block codes of rates (k + 1)/(2k) for 2k or 2k + 1 transmit antennas," IEEE Trans. Inform. Theory, submitted for publication.
24. B. L. Hughes, "Differential space-time modulation," IEEE Trans. Inform. Theory, vol. 46, pp. 2567-2578, Nov. 2000.
25. B. L. Hughes, "Optimal space-time constellations from groups," IEEE Trans. Inform. Theory, vol. 49, pp. 401-410, Feb. 2003.
26. B. M. Hochward and W. Sweldens, "Differential unitary space-time modulation," IEEE Trans. Commun., vol. 48, pp. 2041-2052, Dec. 2000.
27. A. Shokrollahi, B. Hassibi, B. M. Hochward, and W. Sweldens, "Representation theory for high-rate multiple-antenna code design," IEEE Trans. Inform. Theory, vol. 47, pp. 2335-2367, Sept. 2001.
28. B. Hassibi and B. M. Hochwald, "Cayley differential unitary space-time codes," IEEE Trans. Inform. Theory, vol. 48, pp. 1485-1503, June 2002.
29. X.-B. Liang and X.-G. Xia, "Unitary signal constellations for space-time modulation with two transmit antennas: Parametric codes, optimal designs, and bounds," IEEE Trans. Inform. Theory, vol. 48, pp. 2291-2322, Aug. 2002.
30. W. H. Mow, "Maximum likelihood sequence estimation from the lattice viewpoint," IEEE Trans, Inform. Theory, vol. 40, pp. 1591-1600, Oct. 1994.
31. W. H. Mow, "Universal lattice decoding: Principle and recent advances," Wireless Commun. Mobile Comput., vol. 3, pp. 553-569, Aug. 2003.
32. M. O. Damen, K. Abed-Meraim, and J. C. Belfiore, "Generalized sphere decoder for asymmetrical space-time communication architecture," IEE Electron. Lett., vol. 36, pp. 166-166, Jan. 2000.
33. M. O. Damen, A. Chkeif, and J. C. Belfiore, "Lattice code decoder for space-time codes," IEEE Commun. Lett., vol. 4, pp. 161-163, May 2000.
34. H. Vikalo and B. Hassibi, "Maximum-likelihood sequence detection of multiple antenna systems over dispersive channels via sphere decoding," EURASIP J. Appl. Signal Processing, no. 5, pp. 525-531, 2002.
35. A. R. Hammons Jr and H. El Gamal, "On the theory of space time codes for PSK modulation," IEEE Trans. Inform. Theory, vol. 46, pp. 524-542, Mar. 2000.
36. H. El Gamal and A. R. Hammons Jr, "On the design of algebraic space-time codes for MIMO block-fading channels," IEEE Trans. Inform. Theory, vol. 49, pp. 151-163, Jan. 2003.
37. Y. Liu, M. P. Fitz, and O. Y. Takeshita, "A rank criterion for QAM space-time codes," IEEE Trans. Inform. Theory, vol. 48, pp. 3062-3079, Dec. 2002.
38. H.-F. Lu and P. V. Kumar, "A unified construction of space-time codes with optimal rate-diversity tradeoff," IEEE Trans. Inform. Theory submitted for publication.
39. H.-F. Lu and P. V. Kumar, "Rate-diversity tradeoff of space-time codes with fixed alphabet and optimal constructions for PSK modulation," IEEE Trans. Inform. Theory, vol. 49, pp. 2747-2751, Oct. 2003.
40. S. Lang, Algebraic Number Fields. New York: Springer-Verlag, 1986.
41. D. A. Marcus, Number Fields. New York: Springer-Verlag, 1977.
42. J. Rotman, Galois Theory. New York: Springer-Verlag, 1990.
43. P. Morandi, Field and Galois Theory. New York: Erlag, 1996.
44. I. Stewart and D. Tall, Algebraic Number Theory and Fermat's Last Theorem, 3rd ed. Natick, MA: A. K. Peters, 2002.
45. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed. New York: Springer-Verlag, 1998.
46. G. Wang and X.-G. Xia, "On optimal cyclotomic lattices and diagonal/single-layer space-time block codes," in Proc. IEEE Int. Symp. Information Theory (ISIT 2004), Chicago, IL, June/July 2004, p. 188.
47. G. Wang and X.-G. Xia, "On optimal multi-layer cyclotomic space-time code designs," IEEE Trans. Inform. Theory, submitted for publication.
48. G. Wang, H. Liao, H. Wang, and X.-G. Xia. Systematic and Optimal Cyclotomic Lattices and Diagonal Space-Time Block Code Designs. [Online]. Available: http://www.ee.udel.edu/~xxia/Pub.html