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Cyclic division algebras: a tool for space-time coding

Oggier, Frédérique and Belfiore, Jean-Claude and Viterbo, Emanuele (2007) Cyclic division algebras: a tool for space-time coding. Foundations and Trends in Communications and Information Theory, 4 (1). pp. 1-95. ISSN 1567-2328.

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Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. 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. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes.

Item Type:Article
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Oggier, Frédérique0000-0003-3141-3118
Additional Information:2007 F. Oggier, J.-C. Belfiore and E. Viterbo. This work was supported in part by the STREP project No. IST-026905 (MASCOT) within the Sixth Framework Program of the European Commission.
Funding AgencyGrant Number
European CommissionIST-026905 (MASCOT)
Subject Keywords:Cyclic algebras; division algebras; full diversity; golden code; non-vanishing determinant; perfect space–time codes; space–time coding
Issue or Number:1
Record Number:CaltechAUTHORS:FOftcit07
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Official Citation:Frédérique Oggier, Jean-Claude Belfiore and Emanuele Viterbo (2007) "Cyclic Division Algebras: A Tool for Space-Time Coding", Foundations and Trends® in Communications and Information Theory: Vol. 4: No 1, pp 1-95. http:/
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9468
Deposited By: Kristin Buxton
Deposited On:23 Jan 2008
Last Modified:03 Oct 2019 00:00

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