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

Hassan Khodaiemehr | Zendy; Dariush Kiani | Zendy

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

Author(s) -

Hassan Khodaiemehr,

Dariush Kiani

Publication year - 2015

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2015.9.255

Subject(s) - laurent series , mathematics , crossed product , series (stratigraphy) , pure mathematics , space–time block code , product (mathematics) , algebraic structure , block code , block (permutation group theory) , space (punctuation) , algebra over a field , division (mathematics) , field (mathematics) , construct (python library) , discrete mathematics , combinatorics , arithmetic , algorithm , geometry , computer science , paleontology , decoding methods , operating system , programming language , biology

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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