The DMT of Real and Quaternionic Lattice Codes and DMT Classification of Division Algebra Codes

In this paper we consider the diversity-multiplexing gain tradeoff (DMT) of so-called minimum delay asymmetric space-time codes. Such codes are less than full dimensional lattices in their natural ambient space. Apart from multiple input single output (MISO) channel there exist very few methods to analyze DMT such Further, apart MISO case, no optimal known. We first discuss previous criteria used and comment on why these fail when applied then two special classes where code-words restricted either real or quaternion matrices. prove separate trade-off upper bounds for provide a criterion lattice code achieve bounds. also show that based Q-central division algebras satisfy optimality criterion. As corollary result provides classification all algebra standard embeddings. While largest possible space, they still fall short case.