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Pumpluen, Susanne; Steele, Andrew (2015)
Publisher: American Institute of Mathematical Sciences
Languages: English
Types: Article
Subjects: Computer Science - Information Theory, 17A35, 94B05

Classified by OpenAIRE into

arxiv: Computer Science::Information Theory
Let $K/F$ and $K/L$ be two cyclic Galois field extensions and $D=(K/F,\sigma,c)$ a cyclic algebra. Given an invertible element $d\in D$, we present three families of unital nonassociative algebras over $L\cap F$ defined on the direct sum of $n$ copies of $D$. Two of these families appear either explicitly or implicitly in the designs of fast-decodable space-time block codes in papers by Srinath, Rajan, Markin, Oggier, and the authors. We present conditions for the algebras to be division and propose a construction for fully diverse fast decodable space-time block codes of rate-$m$ for $nm$ transmit and $m$ receive antennas. We present a DMT-optimal rate-3 code for 6 transmit and 3 receive antennas which is fast-decodable, with ML-decoding complexity at most $\mathcal{O}(M^{15})$.
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    • [1] N. Markin, F. Oggier, \Iterated Space-Time Code Constructions from Cyclic Algebras," IEEE Transactions on Information Theory, vol. 59, no. 9, September 2013.
    • [2] K. P. Srinath, B. S. Rajan, \Fast-decodable MIDO codes with large coding gain", IEEE Transactions on Information Theory (2) 60 2014, 992-1007.
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    • [4] S. Pumplun, A. Steele, \Fast-decodable MIDO codes from nonassociative algebras," Int. J. of Information and Coding Theory (IJICOT) 3 (1) 2015, 15-38.
    • [5] S. Pumplun, \How to obtain division algebras used for fast decodable space-time block codes", Adv. Math. Comm. 8 (3) (2014), 323 - 342.
    • [6] K. P. Srinath, B. S. Rajan, \DMT-optimal, low ML-complexity STBC-schemes for asymmetric MIMO systems." 2012 IEEE International Symposium on Information Theory Proceedings (ISIT), 2012 , 3043-3047.
    • [7] S. Pumplun, \Tensor products of nonassociative cyclic algebras." Available at http://molle.fernuni-hagen.de/~loos/jordan/index.html [8] A. Steele, S. Pumplun, F. Oggier, \MIDO space-time codes from associative and non-associative cyclic algebras," Information Theory Workshop (ITW) 2012 IEEE (2012), 192-196.
    • [9] S. Pumplun, T. Unger, \Space-time block codes from nonassociative division algebras." Adv. Math. Comm. 5 (3) (2011), 609-629.
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    • [15] A. Steele, \Nonassociative cyclic algebras", Israel J. Math. 200 (1) (2014), 361-387.
    • [16] G. R. Jithamitra, B. S. Rajan, \Minimizing the complexity of fast-sphere decoding of STBCs," IEEE Int. Symposium on Information Theory Proceedings (ISIT), 2011.
    • [17] L. P. Natarajan, B. S. Rajan, \Fast group-decodable STBCs via codes over GF(4)," Proc. IEEE Int. Symp. Inform. Theory, Austin, TX, June 2010 [18] L. P. Natarajan and B. S. Rajan, \Fast-Group-Decodable STBCs via codes over GF(4): Further Results," Proceedings of IEEE ICC 2011, (ICC'11), Kyoto, Japan, June 2011.
    • [19] C. Brown, PhD Thesis University of Nottingham, in preparation.
    • [20] R. Vehkalahti, C. Hollanti, F. Oggier, \Fast-Decodable Asymmetric Space-Time Codes from Division Algebras", IEEE Transactions on Information Theory, (4) 58, April 2012.
    • [21] L. P. Natarajan, B. S. Rajan, written communication, 2013.
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