Coded Modulation with Rotated Multidimensional Constellations in Block-Fading Channels

We study the problem of constructing coded modulation schemes over multidimensional signal sets in Nakagamim 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. Index Terms Block-fading channels, diversity, linear rotations, maximum distance-separable (MDS) codes, outage probability. A. Guillén i Fàbregas is with the Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK, e-mail: [email protected]. G. Caire is with the Electrical Engineering Department, University of Southern California, 3740 McClintock Ave., Los Angeles, CA 90089, USA, e-mail: [email protected]. The work by A. Guillén i Fàbregas work has been supported in part by the Australian Research Council under ARC grants DP0558861 and RN0459498.