High-rate space-time block codes from twisted Laurent series rings

Hassan  Khodaiemehr; Dariush  Kiani

doi:10.3934/amc.2015.9.255

Article Contents

2015, Volume 9, Issue 3: 255-275. Doi: 10.3934/amc.2015.9.255

This issue Previous Article Next Article The weight distributions of some irreducible cyclic codes of length $p^n$ and $2p^n$

High-rate space-time block codes from twisted Laurent series rings

Hassan Khodaiemehr^1, and
Dariush Kiani^1,

1.
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914

Received: November 30, 2011

Revised: January 31, 2015

Published: October 2015

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Abstract

We construct full-diversity, arbitrary rate STBCs for specific number of transmit antennas over an apriori specified signal set using twisted Laurent series rings. Constructing full-diversity space-time block codes from algebraic constructions like division algebras has been done by Shashidhar et al. Constructing STBCs from crossed product algebras arises this question in mind that besides these constructions, which one of the well-known division algebras are appropriate for constructing space-time block codes. This paper deals with twisted Laurent series rings and their subrings twisted function fields, to construct STBCs. First, we introduce twisted Laurent series rings over field extensions of $\mathbb{Q}$. Then, we generalize this construction to the case that coefficients come from a division algebra. Finally, we use an algorithm to construct twisted function fields, which are noncrossed product division algebras, and we propose a method for constructing STBC from them.

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Mathematics Subject Classification: 11T71, 68P30, 17A35.

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