The DMT classification of real and quaternionic lattice codes

TL;DR

This paper establishes DMT upper bounds for real and quaternionic lattice space-time codes, providing criteria for optimality and classifying codes based on Q-central division algebras.

Contribution

It introduces new DMT bounds for these codes and identifies conditions under which lattice codes achieve these bounds, especially for Q-central division algebra codes.

Findings

DMT upper bounds for real and quaternionic lattice codes

Criterion for lattice codes to achieve DMT bounds

Q-central division algebra codes satisfy the optimality criterion

Abstract

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.