  This work aims at providing new bounds for the diversity multiplexing gain
trade-off of a general class of division algebra based lattice codes. In the
low multiplexing gain regime, some bounds were previously obtained from the
high signal-to-noise ratio estimate of the union bound for the pairwise error
probabilities. Here these results are extended to cover a larger range of
multiplexing gains. The improvement is achieved by using ergodic theory in Lie
groups to estimate the behavior of the sum arising from the union bound. In
particular, the new bounds for lattice codes derived from Q-central division
algebras suggest that these codes can be divided into two subclasses based on
their Hasse invariants at the infinite places. Algebras with ramification at
the infinite place seem to provide better diversity-multiplexing gain tradeoff.
