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Cyclic Algebras for Noncoherent Differential Space–Time Coding

Oggier, Frédérique (2007) Cyclic Algebras for Noncoherent Differential Space–Time Coding. IEEE Transactions on Information Theory, 53 (9). pp. 3053-3065. ISSN 0018-9448. doi:10.1109/TIT.2007.903152.

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We investigate cyclic algebras for coding over the differential noncoherent channel. Cyclic algebras are an algebraic object that became popular for coherent space–time coding, since it naturally yields linear families of matrices with full diversity. Coding for the differential noncoherent channel has a similar flavor in the sense that it asks for matrices that achieve full diversity, except that these matrices furthermore have to be unitary. In this work, we give a systematic way to find infinitely many unitary matrices inside cyclic algebras, which holds for all dimensions. We show how cyclic algebras generalize previous families of unitary matrices obtained using the representation of fixed-point-free groups. As an application of our technique, we present families of codes for three and four antennas that achieve high coding gain.

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Oggier, Frédérique0000-0003-3141-3118
Additional Information:© Copyright 2007 IEEE. Reprinted with permission. Manuscript received June 3, 2006; revised March 22, 2007. [Posted online: 2007-08-27] This work was supported by the Swiss National Science Foundation under Grant PBEL2-110209, and was started while the author was still with Laboratoire de Mathématiques Algorithmiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. The author would like to thank Dr. E. Lequeu for his collaboration and useful discussions at the beginning of this work.
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)PBEL2-110209
Subject Keywords:Cyclic algebras, differential space–time coding, full diversity, involution, unitary matrices
Issue or Number:9
Record Number:CaltechAUTHORS:OGGieeetit07b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8920
Deposited By: Archive Administrator
Deposited On:01 Oct 2007
Last Modified:08 Nov 2021 20:54

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