Coded Modulation with Rotated Multidimensional Constellations in Block-Fading Channels

AbstractWe 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 probabilitywhen 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 decodingcomplexity, and in some cases it might be beneficial to use multiple rotations of smaller dimension. We alsostudy the diversity reliability exponent in this case, which yields the optimal rate-diversity-complexity tradeoff inblock-fading channels with discrete inputs.Index TermsBlock-fading channels, diversity, linear rotations, maximum distance-separable (MDS) codes, outage probability. A. Guillen i F´ `abregas is with the Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK,e-mail: guillen@ieee.org.G. Caire is with the Electrical Engineering Department, University of Southern California, 3740 McClintock Ave., Los Angeles, CA90089, USA, e-mail: caire@usc.edu.The work by A. Guill´en i F abregas work has been supported in part by the Australian Research Council under ARC grants DP0558861`and RN0459498.