Algebraic reduction for the Golden Code

Laura Luzzi; Ghaya Rekaya-Ben Othman; Jean-Claude Belfiore

doi:10.3934/amc.2012.6.1

Article Contents

2012, Volume 6, Issue 1: 1-26. Doi: 10.3934/amc.2012.6.1

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Algebraic reduction for the Golden Code

1.
Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ
2.
Département COMELEC, Télécom-ParisTech, 46, rue Barrault, 75013 Paris

Received: February 2010

Revised: October 2011

Published: February 2012

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Abstract

We introduce a new right preprocessing approach, called algebraic reduction, for the decoding of algebraic space-time block codes which are designed using maximal orders in division algebras. Unlike existing lattice-reduction aided decoding techniques, algebraic reduction exploits the multiplicative structure of the code. Its principle is to absorb part of the channel into the code, by approximating the channel matrix with a unit of the maximal order of the corresponding algebra.
In the case of $2 \times 2$ space-time codes, we propose a low-complexity algorithm to approximate a channel with a unit, and apply it to the Golden Code. Simulation results for the Golden Code evidence that algebraic reduction has the same performance of LLL reduction but significantly lower complexity.
We also show that for MIMO systems with $n$ receive and $n$ transmit antennas, algebraic reduction attains the receive diversity when followed by a simple ZF detection. However, establishing the approximation algorithm for higher dimensional codes remains an open problem.

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Mathematics Subject Classification: Primary: 94B35; Secondary: 16H10.

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