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Cyclic division algebras in the space-time coding

Grant number: 11/12657-9
Support Opportunities:Scholarships abroad - Research
Effective date (Start): January 15, 2012
Effective date (End): July 14, 2012
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Carina Alves
Grantee:Carina Alves
Host Investigator: Jean-Claude Belfiore
Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
Research place: ParisTech, France  


Division algebras have been proposed as a new tool for constructing Space-Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. For transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion, comes from an appropriate outer code. When the inner code has a cyclic al gebra structure over a number field, as for perfect space-time codes, an outer code can be designed viacoset coding. More precisely, if we take the quotient of the algebra by a two-sided ideal this leads to a finite alphabet for the outer code, with a cyclic algebra structure over a finite field or a finite ring. We will establish a general framework for designing coset codes via a series of isomorphisms that allows to represent the outer code alphabet in three different ways: an algebra of matrices over a finite ring, a cyclic algebra over a finite ring, and the Cartesian product of finite rings. The decoding of algebraic space-time codes has been performed using their lattice point representation. Belfiore et al introduced a right preprocessing method for the decoding of space-time block codes based on quaternion algebras, which allows to improve the performance of suboptimal decoders and reduces the complexity of ML decoders. So another question related to cyclic division algebras is deal with the generalization of algebraic reduction to higher-dimensional space-time codes based on cyclic division algebras. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
ALVES, C.; BELFIORE, J. -C.. Lattices from maximal orders into quaternion algebras. Journal of Pure and Applied Algebra, v. 219, n. 4, p. 687-702, . (11/12657-9)

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