  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.
