  In this paper we consider space-time codes where the code-words are
restricted to either real or quaternion matrices. We prove two separate
diversity-multiplexing gain trade-off (DMT) upper bounds for such codes and
provide a criterion for a lattice code to achieve these upper bounds. We also
point out that lattice codes based on Q-central division algebras satisfy this
optimality criterion. As a corollary this result provides a DMT classification
for all Q-central division algebra codes that are based on standard embeddings.
