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How to obtain division algebras used for fast-decodable space-time block codes
1. | School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD |
References:
[1] |
A. A. Albert, On the power-associativity of rings, Summa Brazil. Math., 2 (1948), 21-33. |
[2] |
G. Berhuy and F. Oggier, Space-time codes from crossed product algebras of degree 4, in AAECC 2007 (eds. S. Boztaş and H.F. Lu), 2007, 90-99.
doi: 10.1007/978-3-540-77224-8_13. |
[3] |
G. Berhuy and F. Oggier, On the existence of perfect space-time codes, IEEE Trans. Inf. Theory, 55 (2009), 2078-2082.
doi: 10.1109/TIT.2009.2016033. |
[4] |
G. Berhuy and F. Oggier, Introduction to Central Simple Algebras and their Applications to Wireless Communication, AMS, 2013. |
[5] |
A. Deajim and D. Grant, Space-time codes and nonassociative division algebras over elliptic curves, Contemp. Math., 463 (2008), 29-44.
doi: 10.1090/conm/463/09044. |
[6] |
L. E. Dickson, Linear Algebras with associativity not assumed, Duke Math. J., 1 (1935), 113-125.
doi: 10.1215/S0012-7094-35-00112-0. |
[7] |
P. Elia, A. Sethuraman and P. V. Kumar, Perfect space-time codes with minimum and non-minimum delay for any number of antennas, in International Conference on Wireless Networks, Communications and Mobile Computing, IEEE, 2005, 722-727. |
[8] |
C. Hollanti, J. Lahtonen, K. Rauto and R. Vehkalahti, Optimal lattices for MIMO codes from division algebras, IEEE International Symposium on Information Theory, Seattle, 2006, 783-787. |
[9] | |
[10] |
N. Markin and F. Oggier, Iterated space-time code constructions from cyclic algebras, IEEE Trans. Inf. Theory, 59 (2013), 5966-5979.
doi: 10.1109/TIT.2013.2266397. |
[11] |
F. Oggier, G. Rekaya, J.-C. Belfiore and E. Viterbo, Perfect space-time block codes, IEEE Trans. Inf. Theory, 32 (2006), 3885-3902.
doi: 10.1109/TIT.2006.880010. |
[12] |
S. Pumplün, Tensor products of central simple algebras and fast-decodable space-time block codes, preprint, available from: http://molle.fernuni-hagen.de/~loos/jordan/index.html |
[13] |
S. Pumplün and V. Astier, Nonassociative quaternion algebras over rings, Israel J. Math., 155 (2006), 125-147.
doi: 10.1007/BF02773952. |
[14] |
S. Pumplün and T. Unger, Space-time block codes from nonassociative division algebras, Adv. Math. Commun., 5 (2011), 609-629.
doi: 10.3934/amc.2011.5.449. |
[15] |
R. D. Schafer, An introduction to nonassociative algebras, Dover Publ. Inc., New York, 1995. |
[16] |
B. A. Sethuraman, B. S. Rajan and V. Sashidhar, 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. |
[17] |
K. P. Srinath and B. S. Rajan, Fast decodable MIDO codes with large coding gain, in 2013 IEEE International Symposium on Information Theory Proceedings (ISIT), 2013, 2910-2914.
doi: 10.1109/TIT.2013.2292513. |
[18] |
A. Steele, Nonassociative cyclic algebras, Israel J. Math., 200 (2014), 361-387.
doi: 10.1007/s11856-014-0021-7. |
[19] |
A. Steele, S. Pumplün and F. Oggier, MIDO space-time codes from associative and non-associative cyclic algebras, Information Theory Workshop, IEEE, 2012, 192-196. |
[20] |
R. Vehkalahti, C. Hollanti and F. Oggier, Fast-decodable asymmetric space-time codes from division algebras, IEEE Trans. Inf. Theory, 58 (2012), 2362-2385.
doi: 10.1109/TIT.2011.2176310. |
[21] |
W. C. Waterhouse, Nonassociative quaternion algebras, Algebras Groups Geom., 4 (1987), 365-378. |
show all references
References:
[1] |
A. A. Albert, On the power-associativity of rings, Summa Brazil. Math., 2 (1948), 21-33. |
[2] |
G. Berhuy and F. Oggier, Space-time codes from crossed product algebras of degree 4, in AAECC 2007 (eds. S. Boztaş and H.F. Lu), 2007, 90-99.
doi: 10.1007/978-3-540-77224-8_13. |
[3] |
G. Berhuy and F. Oggier, On the existence of perfect space-time codes, IEEE Trans. Inf. Theory, 55 (2009), 2078-2082.
doi: 10.1109/TIT.2009.2016033. |
[4] |
G. Berhuy and F. Oggier, Introduction to Central Simple Algebras and their Applications to Wireless Communication, AMS, 2013. |
[5] |
A. Deajim and D. Grant, Space-time codes and nonassociative division algebras over elliptic curves, Contemp. Math., 463 (2008), 29-44.
doi: 10.1090/conm/463/09044. |
[6] |
L. E. Dickson, Linear Algebras with associativity not assumed, Duke Math. J., 1 (1935), 113-125.
doi: 10.1215/S0012-7094-35-00112-0. |
[7] |
P. Elia, A. Sethuraman and P. V. Kumar, Perfect space-time codes with minimum and non-minimum delay for any number of antennas, in International Conference on Wireless Networks, Communications and Mobile Computing, IEEE, 2005, 722-727. |
[8] |
C. Hollanti, J. Lahtonen, K. Rauto and R. Vehkalahti, Optimal lattices for MIMO codes from division algebras, IEEE International Symposium on Information Theory, Seattle, 2006, 783-787. |
[9] | |
[10] |
N. Markin and F. Oggier, Iterated space-time code constructions from cyclic algebras, IEEE Trans. Inf. Theory, 59 (2013), 5966-5979.
doi: 10.1109/TIT.2013.2266397. |
[11] |
F. Oggier, G. Rekaya, J.-C. Belfiore and E. Viterbo, Perfect space-time block codes, IEEE Trans. Inf. Theory, 32 (2006), 3885-3902.
doi: 10.1109/TIT.2006.880010. |
[12] |
S. Pumplün, Tensor products of central simple algebras and fast-decodable space-time block codes, preprint, available from: http://molle.fernuni-hagen.de/~loos/jordan/index.html |
[13] |
S. Pumplün and V. Astier, Nonassociative quaternion algebras over rings, Israel J. Math., 155 (2006), 125-147.
doi: 10.1007/BF02773952. |
[14] |
S. Pumplün and T. Unger, Space-time block codes from nonassociative division algebras, Adv. Math. Commun., 5 (2011), 609-629.
doi: 10.3934/amc.2011.5.449. |
[15] |
R. D. Schafer, An introduction to nonassociative algebras, Dover Publ. Inc., New York, 1995. |
[16] |
B. A. Sethuraman, B. S. Rajan and V. Sashidhar, 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. |
[17] |
K. P. Srinath and B. S. Rajan, Fast decodable MIDO codes with large coding gain, in 2013 IEEE International Symposium on Information Theory Proceedings (ISIT), 2013, 2910-2914.
doi: 10.1109/TIT.2013.2292513. |
[18] |
A. Steele, Nonassociative cyclic algebras, Israel J. Math., 200 (2014), 361-387.
doi: 10.1007/s11856-014-0021-7. |
[19] |
A. Steele, S. Pumplün and F. Oggier, MIDO space-time codes from associative and non-associative cyclic algebras, Information Theory Workshop, IEEE, 2012, 192-196. |
[20] |
R. Vehkalahti, C. Hollanti and F. Oggier, Fast-decodable asymmetric space-time codes from division algebras, IEEE Trans. Inf. Theory, 58 (2012), 2362-2385.
doi: 10.1109/TIT.2011.2176310. |
[21] |
W. C. Waterhouse, Nonassociative quaternion algebras, Algebras Groups Geom., 4 (1987), 365-378. |
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