The nonassociative algebras used to build fast-decodable space-time block codes

Pumpluen, Susanne; Steele, Andrew

Abstract

Let K/F and K/L be two cyclic Galois field extensions and D a cyclic algebra. Given an invertible element d in D, we present three families of unital nonassociative algebras defined on the direct sum of n copies of D. Two of these families appear either explicitly or implicitly in the designs of fast-decodable space-time block codes in papers by Srinath, Rajan, Markin, Oggier, and the authors. We present conditions for the algebras to be division and propose a construction for fully diverse fast decodable space-time block codes of rate-m for nm transmit and m receive antennas. We present a DMT-optimal
rate-3 code for 6 transmit and 3 receive antennas which is fast-decodable, with ML-decoding complexity at most O(M^15).

Citation

Pumpluen, S., & Steele, A. (2015). The nonassociative algebras used to build fast-decodable space-time block codes. Advances in Mathematics of Communications, 9(4), https://doi.org/10.3934/amc.2015.9.449

• Journal Article Type: Article
• Acceptance Date: Jul 9, 2015
• Publication Date: Nov 1, 2015
• 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: 9
• Issue: 4
• DOI: https://doi.org/10.3934/amc.2015.9.449
• Keywords: Space-time block codes, fast-decodable, MIMO code, nonassociative algebra, division algebra
• Public URL: https://nottingham-repository.worktribe.com/output/981486
• Publisher URL: http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11938
• 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, Steele, Andrew, The nonassociative algebras used to build fast-decodable space-time block codes, 2015, v. 9, no. 4, pp. 449-469 is available online at: http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11938.
• Contract Date: Jun 21, 2016