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Full-Diversity, High-Rate Space-Time Block Codes from Division Algebras (2003)
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| Venue: | IEEE TRANS. INFORM. THEORY |
| Citations: | 176 - 54 self |
BibTeX
@ARTICLE{Sethuraman03full-diversity,high-rate,
author = {B. A. Sethuraman and B. Sundar Rajan and V. Shashidhar},
title = {Full-Diversity, High-Rate Space-Time Block Codes from Division Algebras},
journal = {IEEE TRANS. INFORM. THEORY},
year = {2003},
volume = {49},
pages = {2596--2616}
}
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Abstract
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 embedded in matrix rings. The first half of the paper deals with constructions using field extensions of . 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 division algebras into matrices: left regular representation, and representation over maximal cyclic subfields. The 4 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 th 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.
Keyphrases
division algebra high-rate space-time block code maximal cyclic subfields noncommutative division algebra arbitrary number cyclic division algebra full rank transmit antenna signal set field extension commutative division algebra real orthogonal design arbitrary rate code space-time block code wide range special case later half matrix ring general principle th root paper deal regular representation coding gain transcendental element several family cyclotomic field extension several example rational field first half general technique left regular representation transcendental extension minimal delay certain algebraic uniqueness characteristic noncyclotomic field extension
