Hyperbolic lattices: a new propose for space time coding theory

In the context of space-time block codes (STBCs), the theory of hyperbolic lattices over totally real number field is presented, as well as theoretic criteria to check if such algebras are division algebras from arithmetic Fuchsian groups. These can be used to obtain families of 2 × 2 STBCs that satisfies the properties of linear dispersion, full rate and full diversity.