On the optimality of lattice space-time (LAST) coding

In this paper, we introduce the class of lattice space-time (LAST) codes. We show that these codes achieve the optimal diversity-vs-multiplexing tradeoff defined by Zheng and Tse under generalized minimum Euclidean distance lattice decoding. Our scheme is based on a generalization of Erez and Zamir mod-Λ scheme to the MIMO case. This result settles the open problem posed by Zheng and Tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity-vs-multiplexing tradeoff. Moreover, our results shed more light on the structure of optimal coding/decoding techniques in delay limited MIMO channels. In particular: 1) we show that MMSE-GDFE plays a fundamental role in approaching the limits of delay limited MIMO channels in the high SNR regime, unlike the AWGN channel case and 2) our random coding arguments represent a major departure from traditional space-time code designs based on the rank and/or mutual information design criteria.