Algebraic reduction for the Golden Code

In this paper we introduce a new right preprocessing method for the decoding of 2 × 2 algebraic space-time codes, 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 code algebra. We prove that algebraic reduction attains the receive diversity when followed by a simple zero-forcing (ZF) detection. Simulation results for the Golden Code show that using minimum mean squared error generalized decision feedback equalization (MMSE-GDFE left preprocessing), algebraic reduction with simple ZF detection has a loss of only 3 dB with respect to optimal decoding.