  This paper considers space-time coding over several independently Rayleigh
faded blocks. In particular we will concentrate on giving upper bounds for the
coding gain of lattice space-time codes as the number of blocks grow. This
problem was previously considered in the single antenna case by Bayer et al. in
2006. Crucial to their work was Odlyzko's bound on the discriminant of an
algebraic number field, as this provides an upper bound for the normalized
coding gain of number field codes. In the MIMO context natural codes are
constructed from division algebras defined over number fields and the coding
gain is measured by the discriminant of the corresponding (non-commutative)
algebra. In this paper we will develop analogues of the Odlyzko bounds in this
context and show how these bounds limit the normalized coding gain of a very
general family of division algebra based space-time codes. These bounds can
also be used as benchmarks in practical code design and as tools to analyze
asymptotic bounds of performance as the number of independently faded blocks
increases.
