Space-Time Codes from Structured Lattices

We present constructions of Space-Time (ST) codes based on lattice coset coding. First, we focus on ST code constructions for the short block-length case, i.e., when the block-length is equal to or slightly larger than the number of transmit antennas. We present constructions based on dense lattice packings and nested lattice (Voronoi) shaping. Our codes achieve the optimal diversity-multiplexing tradeoff of quasi-static MIMO fading channels for any fading statistics, and perform very well also at practical, moderate values of signal to noise ratios (SNR). Then, we extend the construction to the case of large block lengths, by using trellis coset coding. We provide constructions of trellis coded modulation (TCM) schemes that are endowed with good packing and shaping properties. Both short-block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean squared error generalized decision feedback equalizer (MMSE-GDFE) lattice decoding and a combination of this with a Viterbi TCM decoder for the TCM case. Beyond the interesting algebraic structure, we exhibit codes whose performance is among the state-of-the art considering codes with similar encoding/decoding complexity. The authors are with the Department of Electrical Engineering Systems, University of Southern California, Los Angeles, CA 90089, USA ({rkkrishn,caire}@usc.edu). The material in this paper was presented in part at the IEEE International Symposia on Information Theory ISIT-2006 in Seattle, USA and ISIT-2007 in Nice, France. This work has been partially funded by a gift from ST Microelectronics, NSF Grant No. CCF-0635326, the 2006 Okawa Foundation Research Grant and by an Oakley fellowship from the Graduate School at USC. April 10, 2008 DRAFT SUBMITTED TO IEEE TRANS. INFORM. THEORY, APR. 2008 2