  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.
