How to obtain division algebras used for fast-decodable space-time block codes

Pumpluen, Susanne

Abstract

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D, employing a K-automorphism tau and an invertible element d in D. These algebras appear in the construction of iterated space-time block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly look at algebras (and codes) obtained from variations of this method.

Citation

Pumpluen, S. (2014). How to obtain division algebras used for fast-decodable space-time block codes. Advances in Mathematics of Communications, 8(3), https://doi.org/10.3934/amc.2014.8.323

• Journal Article Type: Article
• Acceptance Date: Apr 11, 2014
• Publication Date: Aug 1, 2014
• Deposit Date: Jun 21, 2016
• Publicly Available Date: Jun 21, 2016
• Journal: Advances in Mathematics of Communications
• Print ISSN: 1930-5346
• Electronic ISSN: 1930-5338
• Publisher: American Institute of Mathematical Sciences (AIMS)
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Issue: 3
• DOI: https://doi.org/10.3934/amc.2014.8.323
• Keywords: Space-time block code, fast-decodable, asymmetric, non-associative division algebra, iterated code
• Public URL: https://nottingham-repository.worktribe.com/output/731493
• Publisher URL: http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10204
• Additional Information: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Advances in Mathematics of Communications following peer review. The definitive publisher-authenticated version, Pumpluen, Susanne, How to obtain division algebras used for fast-decodable space-time block codes, v. 8, no. 3, 2014, pp. 323-342 is available online at: http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10204.