The nonassociative algebras used to build fast-decodable space-time block codes
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 fas...
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| Format: | Article |
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American Institute of Mathematical Sciences
2015
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| Online Access: | https://eprints.nottingham.ac.uk/34232/ |
| _version_ | 1848794803804831744 |
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| author | Pumpluen, Susanne Steele, Andrew |
| author_facet | Pumpluen, Susanne Steele, Andrew |
| author_sort | Pumpluen, Susanne |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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). |
| first_indexed | 2025-11-14T19:22:00Z |
| format | Article |
| id | nottingham-34232 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:22:00Z |
| publishDate | 2015 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-342322020-05-04T20:06:35Z https://eprints.nottingham.ac.uk/34232/ The nonassociative algebras used to build fast-decodable space-time block codes Pumpluen, Susanne Steele, Andrew 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). American Institute of Mathematical Sciences 2015-11 Article PeerReviewed Pumpluen, Susanne and Steele, Andrew (2015) The nonassociative algebras used to build fast-decodable space-time block codes. Advances in Mathematics of Communications, 9 (4). pp. 449-469. ISSN 1930-5338 Space-time block codes fast-decodable MIMO code nonassociative algebra division algebra http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11938 doi:10.3934/amc.2015.9.449 doi:10.3934/amc.2015.9.449 |
| spellingShingle | Space-time block codes fast-decodable MIMO code nonassociative algebra division algebra Pumpluen, Susanne Steele, Andrew The nonassociative algebras used to build fast-decodable space-time block codes |
| title | The nonassociative algebras used to build fast-decodable space-time block codes |
| title_full | The nonassociative algebras used to build fast-decodable space-time block codes |
| title_fullStr | The nonassociative algebras used to build fast-decodable space-time block codes |
| title_full_unstemmed | The nonassociative algebras used to build fast-decodable space-time block codes |
| title_short | The nonassociative algebras used to build fast-decodable space-time block codes |
| title_sort | nonassociative algebras used to build fast-decodable space-time block codes |
| topic | Space-time block codes fast-decodable MIMO code nonassociative algebra division algebra |
| url | https://eprints.nottingham.ac.uk/34232/ https://eprints.nottingham.ac.uk/34232/ https://eprints.nottingham.ac.uk/34232/ |