  Currently for the nt x nr MIMO channel, any explicitly constructed space-time
(ST) designs that achieve optimality with respect to the diversity multiplexing
tradeoff (DMT) are known to do so only when decoded using maximum likelihood
(ML) decoding, which may incur prohibitive decoding complexity. In this paper
we prove that MMSE regularized lattice decoding, as well as the computationally
efficient lattice reduction (LR) aided MMSE decoder, allows for efficient and
DMT optimal decoding of any approximately universal lattice-based code. The
result identifies for the first time an explicitly constructed encoder and a
computationally efficient decoder that achieve DMT optimality for all
multiplexing gains and all channel dimensions. The results hold irrespective of
the fading statistics.
