Orthogonal Designs and a Cubic Binary Function

Orthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is to construct designs maximizing the rate and minimizing the...

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Bibliographic Details
Published in:IEEE transactions on information theory 2013-03, Vol.59 (3), p.1583-1589
Main Authors: Morier-Genoud, S., Ovsienko, V.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Applied sciences
Block codes
Codes
Coding, codes
Decoding
Decoding delay
Delay
Exact sciences and technology
generalized octonions
Information theory
Information, signal and communications theory
Mathematical functions
Mathematical Physics
Mathematics
Matrix
Matrix decomposition
maximal rate
orthogonal designs
peak-to-average power ratio
Signal and communications theory
space-time codes
Telecommunications and information theory
Wireless communication
Zirconium
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Summary:Orthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is to construct designs maximizing the rate and minimizing the decoding delay. All known constructions of CODs are inductive or algorithmic. In this paper, we present an explicit construction of optimal CODs. We do not apply recurrent procedures and do calculate the matrix elements directly. Our formula is based on a cubic function in two binary n -vectors. In our previous work (Comm. Math. Phys., 2010, and J. Pure and Appl. Algebra, 2011), we used this function to define a series of non-associative algebras generalizing the classical algebra of octonions and to obtain sum of squares identities of Hurwitz-Radon type.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2012.2229335