  We study the problem of constructing coded modulation schemes over
multidimensional signal sets in Nakagami-$m$ block-fading channels. In
particular, we consider the optimal diversity reliability exponent of the error
probability when the multidimensional constellation is obtained as the rotation
of classical complex-plane signal constellations. We show that multidimensional
rotations of full dimension achieve the optimal diversity reliability exponent,
also achieved by Gaussian constellations. Multidimensional rotations of full
dimension induce a large decoding complexity, and in some cases it might be
beneficial to use multiple rotations of smaller dimension. We also study the
diversity reliability exponent in this case, which yields the optimal
rate-diversity-complexity tradeoff in block-fading channels with discrete
inputs.
