A new design criterion for spherically-shaped division algebra-based space-time codes

This work considers normalized inverse determinant sums as a tool for analyzing the performance of division algebra based space-time codes for multiple antenna wireless systems. A general union bound based code design criterion is obtained as a main result. In our previous work, the behavior of inverse determinant sums was analyzed using point counting techniques for Lie groups; it was shown that the asymptotic growth exponents of these sums correctly describe the diversity-multiplexing gain trade-off of the space-time code for some multiplexing gain ranges. This paper focuses on the constant terms of the inverse determinant sums, which capture the coding gain behavior. Pursuing the Lie group approach, a tighter asymptotic bound is derived, allowing to compute the constant terms for several classes of space-time codes appearing in the literature. The resulting design criterion suggests that the performance of division algebra based codes depends on several fundamental algebraic invariants of the underlying algebra.