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

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.