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In this paper, the dimensionality of the multilevel coded modulation (MLCM) scheme is addressed. This study is done for an MLCM scheme with a N-dimensional (ND) constellation constructed from the Cartesian product of N identical 1D constellations in the high SNR regime. It is demonstrated that multidimensional MLCM with Reed-Solomon code components has better trade-off between coding gain and complexity than a 1D scheme. Specifically, a 4D MLCM system gains 1.4 dB over a 1D MLCM system with lower complexity at a block error of 10-6. The gain increases to 2.5 dB asymptotically.