Efficient maximum-likelihood decoding of spherical lattice space-time codes

This paper develops a framework for the efficient maximum-likelihood decoding of lattice codes. Specifically we apply it to the spherical Lattice Space-Time (LAST) codes recently put forward by El Gamal et al. that have been proven to achieve the optimal diversity-multiplexing tradeoff of MIMO channels. Our solution addresses the so-called boundary control problem within the same search tree structure as existing suboptimal LAST decoders. We demonstrate its performance and complexity by applying two of the most efficient tree-based ML detectors currently reported in the literature to the spherical LAST code proposed for the 2 x 2 MIMO channel of block length 2. Our optimal decoders exhibit improved performance over the naive lattice decoder with MMSE-GDFE pre-processing at a comparable complexity.