Multidimensional Coded Modulation in Block-Fading Channnels

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.