Algebraic reduction for space-time codes based on quaternion algebras

TL;DR

This paper introduces an algebraic reduction method for decoding 2x2 space-time block codes that leverages algebraic structures to improve decoding efficiency while maintaining high diversity, with minimal performance loss.

Contribution

The paper presents a novel algebraic reduction technique that exploits quaternion algebra structures for decoding space-time codes, enhancing performance with simple detection methods.

Findings

Achieves full receive diversity with simple ZF detection after algebraic reduction.

Only 3 dB loss compared to ML decoding when using MMSE-GDFE preprocessing.

Effective decoding method for the Golden Code demonstrated through simulations.

Abstract

In this paper we introduce a new right preprocessing method for the decoding of 2x2 algebraic STBCs, called algebraic reduction, which exploits the multiplicative structure of the code. The principle of the new reduction is to absorb part of the channel into the code, by approximating the channel matrix with an element of the maximal order of the algebra. We prove that algebraic reduction attains the receive diversity when followed by a simple ZF detection. Simulation results for the Golden Code show that using MMSE-GDFE left preprocessing, algebraic reduction with simple ZF detection has a loss of only $3 \dB$ with respect to ML decoding.