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Full-diversity, high-rate space-time block codes from division algebras

Sethuraman, BA and Sundar Rajan, B and Shashidhar, V (2003) Full-diversity, high-rate space-time block codes from division algebras. In: IEEE Transactions on Information Theory, 49 (10). pp. 2596-2616.

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We present some general techniques for constructing full-rank, minimal-delay, rate at least one space-time block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algebras of the rational field Q embedded in matrix rings. The first half of the paper deals with constructions using field extensions of Q. Working with cyclotomic field extensions, we construct several families of STBCs over a wide range of signal sets that are of full rank, minimal delay, and rate at least one appropriate for any number of transmit antennas. We study the coding gain and capacity of these codes. Using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas. We also present a method of constructing STBCs using noncyclotomic field extensions. In the later half of the paper, we discuss two ways of embedding noncommutative mdivision algebras into matrices: left regular representation, and representation over maximal cyclic subfields. The 4 x 4 real orthogonal design is obtained by the left regular representation of quaternions. Alamouti's code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it. Also, we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the STBCs obtained from this construction. Another family of cyclic division algebras discovered by Brauer is discussed and several examples of STBCs derived from each of these constructions are presented.

Item Type: Journal Article
Publication: IEEE Transactions on Information Theory
Publisher: IEEE
Additional Information: Copyright 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE
Keywords: division algebras;mutual information;space-time block codes (STBCs);transmit diversity;wireless communications
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 22 Jul 2009 10:06
Last Modified: 19 Sep 2010 04:54
URI: http://eprints.iisc.ac.in/id/eprint/16949

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