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Advances in Mathematics of Communications (AMC)
 

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

Pages: 255 - 275, Volume 9, Issue 3, August 2015      doi:10.3934/amc.2015.9.255

 
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Hassan Khodaiemehr - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran (email)
Dariush Kiani - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran (email)

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.

Keywords:  Space-time block codes(STBC), crossed product algebras, twisted Laurent series, iterated twisted Laurent series, noncrossed product algebras.
Mathematics Subject Classification:  11T71, 68P30, 17A35.

Received: December 2011;      Revised: February 2015;      Available Online: July 2015.

 References