Full-rank, full-rate STBCs from division algebras

Construction of rate-optimal full-diversity space-time block codes (STBC) over symmetric PSK signal sets using cyclotomic field extensions of the field of rational Q was reported previously, and for a variety of other signal sets using non-cyclotomic field extensions. Fields are commutative division algebras. Construction of full-rate STBCs with full-diversity using a class of non-commutative division algebras (cyclic division algebras) was also reported previously and the Alamouti code was shown to be a special case with an algebraic uniqueness property. In this paper, we present the basic principle behind these constructions and also obtain full-diversity, full-rate STBCs using a different class of non-commutaive division algebra constructed by Brauer. The interrelationship between codes constructed from division algebras, linear dispersion codes and codes from orthogonal designs is discussed.