Complex low density lattice codes for the 2×2 MIMO fading channel

A transmission scheme for a 2 × 2 multiple-input multiple-output (MIMO) channel utilizing a complex low density lattice codes (CLDLC´s) is presented in this paper. The code is of small size and small degree, and the scheme reduces the number of dimensions per channel use from 2 to 4/3. For decoding, we derive an iterative max-product algorithm for the MIMO channel combined with the code. When the a-priori probabilities are Gaussians, there is an interesting connection between the passed messages and minimum mean square error estimation. Using the CLDLC structure and the reduced dimensionality of the transmission scheme, we present a very efficient parametric decoding algorithm for the 2×2 MIMO channel. At a rate of 8 bits per channel use the proposed simple and computationally efficient transmission scheme outperforms the Alamouti scheme by 3.5 dB, and has a gap of 1.7 dB from the golden code.