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High-rate space-time block codes from twisted Laurent series rings
1. | Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran, Iran |
References:
[1] |
P. M. Cohn, Introduction to Ring Theory, Springer-Verlag, London, 2000.
doi: 10.1007/978-1-4471-0475-9. |
[2] |
M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner and K. Wildanger, KANT V4, J. Symbolic Comp., 24 (1997), 267-283.
doi: 10.1006/jsco.1996.0126. |
[3] |
M. O. Damen, K. Abed-Merriam and J. C. Belfiore, Generalized sphere decoder for asymmetrical space-time communication architecture, IEEE Electron. Lett., 36 (2000), 16-20. |
[4] |
M. O. Damen, A. Chkeif and J. C. Belfiore, Lattice code decoder for space-time codes, IEEE Commun. Lett., 4 (2000), 161-163. |
[5] |
M. O. Damen, A. Tewfik and J. C. Belfiore, A construction of a space-time code based on number theory, IEEE Trans. Inf. Theory, 48 (2002), 753-760.
doi: 10.1109/18.986032. |
[6] |
P. K. Draxl, Skew Fields, Cambridge Univ. Press, Cambridge, 1983.
doi: 10.1017/CBO9780511661907. |
[7] |
U. Fincke and M. Pohst, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comput., 44 (1985), 463-471.
doi: 10.2307/2007966. |
[8] |
G. J. Foschini, Layered space-time architecture for wireless communications in a fading environment when using multi-element antennas, Bell Labs. Tech. J., 1 (1996), 41-59. |
[9] |
G. J. Foschini and M. Gans, On the limits of wireless communication in a fading environment when using multiple antennas, Wireless Personal Commun., 6 (1998), 311-335. |
[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, IEEE Trans. Commun., 47 (1999), 527-537. |
[11] |
T. Hanke, An explicit example of a noncrossed product division algebra, Math. Nachr., 271 (2004), 51-68.
doi: 10.1002/mana.200310181. |
[12] |
T. Hanke, A twisted Laurent series ring that is a noncrossed product, Israel J. Math., 150 (2005), 199-204.
doi: 10.1007/BF02762379. |
[13] |
B. Hassibi and B. Hochwald, High-rate codes that are linear in space and time, IEEE Trans. Inf. Theory, 48 (2002), 1804-1824.
doi: 10.1109/TIT.2002.1013127. |
[14] |
B. Hassibi and H. Vikalo, On the expected complexity of sphere decoding, in 35th Asilomar Conf. Sign. Syst. Comp., Pacific Grove, 2001, 1051-1055. |
[15] |
I. N. Herstein, Non-Commutative Rings, Math. Assoc. Amer., Washington, 1968. |
[16] |
B. M. Hochwald and S. T. Brink, Achieving near-capacity on a multiple-antenna channel, IEEE Trans. Commun., 51 (2003), 389-399. |
[17] |
T. W. Hungerford, Algebra, 3 edition, Springer-Verlag, Washington, 1980. |
[18] |
N. Jacobson, Basic Algebra I, 2nd edition, Freeman, New York, 1985. |
[19] |
T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4684-0406-7. |
[20] |
P. J. McCarthy, Algebraic Extensions of Filelds,, Dover Publications Inc., ().
|
[21] |
J. Neukirch, Algebraische Zahlentheorie, Springer-Verlag, Berlin, 1992. |
[22] |
R. S. Pierce, Associative Algebras, Springer-Verlag, Berlin, 1982. |
[23] |
B. A. Sethuraman and B. S. Rajan, An algebraic description of orthogonal designs and the uniqueness of the Alamouti code, in Proc. IEEE GLOBECOM (2002), Taipai, 2002, 1088-1092. |
[24] |
B. A. Sethuraman and B. S. Rajan, Optimal STBC over PSK signal sets from cyclotomic field extensions, in Proc. IEEE Int. Conf. Commun. (ICC 2002), New York, 2002, 1783-1787. |
[25] |
B. A. Sethuraman and B. S. Rajan, STBC from field extensions of the rational field, in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2002), Lausanne, 2002, p. 274. |
[26] |
B. A. Sethuraman, B. S. Rajan and V. Shashidhar, Full-diversity, high-rate space-time block codes from division algebras, IEEE Trans. Inf. Theory, 49 (2003), 2596-2616.
doi: 10.1109/TIT.2003.817831. |
[27] |
V. Shashidhar, High-Rate and Information-Lossless Space-Time Block Codes from Crossed-Product Algebras, Ph.D thesis, Indian Institute of Science, Bangalore, 2004. |
[28] |
V. Shashidhar, B. S. Rajan and B. A. Sethuraman, STBCs using capacity achieving designs from cyclic division Algebras, in Proc. IEEE GLOBECOM (2003), San Francisco, 2003, 1957-1962. |
[29] |
V. Shashidhar, B. S. Rajan and B. A. Sethuraman, Information lossless STBCs from crossed-product algebras, IEEE Trans. Inf. Theory, 52 (2006), 3913-3935.
doi: 10.1109/TIT.2006.880049. |
[30] |
V. Shashidhar, K. Subrahmanyam, R. Chandrasekharan, B. S. Rajan and B. A. Sethuraman, High-rate, full-diversity STBCs from field extensions, in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2003), Yokohama, 2003, p. 126. |
[31] |
V. Tarokh, N. Seshadri and A. R. Calderbank, Space-time codes for high data rate wireless communication: Performance criterion and code construction, IEEE Trans. Inf. Theory, 44 (1998), 744-765.
doi: 10.1109/18.661517. |
[32] |
E. Telatar, Capacity of multi-antenna Gaussian channels, Europ. Trans. Telecommun., 10 (1999), 585-595. |
[33] |
J. P. Tignol, Generalized crossed products, in Séminaire Mathématique (nouvelle série), UniversitéCatholique de Louvain, Belgium, 1987. |
[34] |
E. Viterbo and J. Boutros, A universal lattice code decoder for fading channel, IEEE Trans. Inf. Theory, 45 (1999), 1639-1642.
doi: 10.1109/18.771234. |
show all references
References:
[1] |
P. M. Cohn, Introduction to Ring Theory, Springer-Verlag, London, 2000.
doi: 10.1007/978-1-4471-0475-9. |
[2] |
M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner and K. Wildanger, KANT V4, J. Symbolic Comp., 24 (1997), 267-283.
doi: 10.1006/jsco.1996.0126. |
[3] |
M. O. Damen, K. Abed-Merriam and J. C. Belfiore, Generalized sphere decoder for asymmetrical space-time communication architecture, IEEE Electron. Lett., 36 (2000), 16-20. |
[4] |
M. O. Damen, A. Chkeif and J. C. Belfiore, Lattice code decoder for space-time codes, IEEE Commun. Lett., 4 (2000), 161-163. |
[5] |
M. O. Damen, A. Tewfik and J. C. Belfiore, A construction of a space-time code based on number theory, IEEE Trans. Inf. Theory, 48 (2002), 753-760.
doi: 10.1109/18.986032. |
[6] |
P. K. Draxl, Skew Fields, Cambridge Univ. Press, Cambridge, 1983.
doi: 10.1017/CBO9780511661907. |
[7] |
U. Fincke and M. Pohst, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comput., 44 (1985), 463-471.
doi: 10.2307/2007966. |
[8] |
G. J. Foschini, Layered space-time architecture for wireless communications in a fading environment when using multi-element antennas, Bell Labs. Tech. J., 1 (1996), 41-59. |
[9] |
G. J. Foschini and M. Gans, On the limits of wireless communication in a fading environment when using multiple antennas, Wireless Personal Commun., 6 (1998), 311-335. |
[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, IEEE Trans. Commun., 47 (1999), 527-537. |
[11] |
T. Hanke, An explicit example of a noncrossed product division algebra, Math. Nachr., 271 (2004), 51-68.
doi: 10.1002/mana.200310181. |
[12] |
T. Hanke, A twisted Laurent series ring that is a noncrossed product, Israel J. Math., 150 (2005), 199-204.
doi: 10.1007/BF02762379. |
[13] |
B. Hassibi and B. Hochwald, High-rate codes that are linear in space and time, IEEE Trans. Inf. Theory, 48 (2002), 1804-1824.
doi: 10.1109/TIT.2002.1013127. |
[14] |
B. Hassibi and H. Vikalo, On the expected complexity of sphere decoding, in 35th Asilomar Conf. Sign. Syst. Comp., Pacific Grove, 2001, 1051-1055. |
[15] |
I. N. Herstein, Non-Commutative Rings, Math. Assoc. Amer., Washington, 1968. |
[16] |
B. M. Hochwald and S. T. Brink, Achieving near-capacity on a multiple-antenna channel, IEEE Trans. Commun., 51 (2003), 389-399. |
[17] |
T. W. Hungerford, Algebra, 3 edition, Springer-Verlag, Washington, 1980. |
[18] |
N. Jacobson, Basic Algebra I, 2nd edition, Freeman, New York, 1985. |
[19] |
T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4684-0406-7. |
[20] |
P. J. McCarthy, Algebraic Extensions of Filelds,, Dover Publications Inc., ().
|
[21] |
J. Neukirch, Algebraische Zahlentheorie, Springer-Verlag, Berlin, 1992. |
[22] |
R. S. Pierce, Associative Algebras, Springer-Verlag, Berlin, 1982. |
[23] |
B. A. Sethuraman and B. S. Rajan, An algebraic description of orthogonal designs and the uniqueness of the Alamouti code, in Proc. IEEE GLOBECOM (2002), Taipai, 2002, 1088-1092. |
[24] |
B. A. Sethuraman and B. S. Rajan, Optimal STBC over PSK signal sets from cyclotomic field extensions, in Proc. IEEE Int. Conf. Commun. (ICC 2002), New York, 2002, 1783-1787. |
[25] |
B. A. Sethuraman and B. S. Rajan, STBC from field extensions of the rational field, in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2002), Lausanne, 2002, p. 274. |
[26] |
B. A. Sethuraman, B. S. Rajan and V. Shashidhar, Full-diversity, high-rate space-time block codes from division algebras, IEEE Trans. Inf. Theory, 49 (2003), 2596-2616.
doi: 10.1109/TIT.2003.817831. |
[27] |
V. Shashidhar, High-Rate and Information-Lossless Space-Time Block Codes from Crossed-Product Algebras, Ph.D thesis, Indian Institute of Science, Bangalore, 2004. |
[28] |
V. Shashidhar, B. S. Rajan and B. A. Sethuraman, STBCs using capacity achieving designs from cyclic division Algebras, in Proc. IEEE GLOBECOM (2003), San Francisco, 2003, 1957-1962. |
[29] |
V. Shashidhar, B. S. Rajan and B. A. Sethuraman, Information lossless STBCs from crossed-product algebras, IEEE Trans. Inf. Theory, 52 (2006), 3913-3935.
doi: 10.1109/TIT.2006.880049. |
[30] |
V. Shashidhar, K. Subrahmanyam, R. Chandrasekharan, B. S. Rajan and B. A. Sethuraman, High-rate, full-diversity STBCs from field extensions, in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2003), Yokohama, 2003, p. 126. |
[31] |
V. Tarokh, N. Seshadri and A. R. Calderbank, Space-time codes for high data rate wireless communication: Performance criterion and code construction, IEEE Trans. Inf. Theory, 44 (1998), 744-765.
doi: 10.1109/18.661517. |
[32] |
E. Telatar, Capacity of multi-antenna Gaussian channels, Europ. Trans. Telecommun., 10 (1999), 585-595. |
[33] |
J. P. Tignol, Generalized crossed products, in Séminaire Mathématique (nouvelle série), UniversitéCatholique de Louvain, Belgium, 1987. |
[34] |
E. Viterbo and J. Boutros, A universal lattice code decoder for fading channel, IEEE Trans. Inf. Theory, 45 (1999), 1639-1642.
doi: 10.1109/18.771234. |
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