We study communication over atmospheric turbulence channels based on LDPC-coded signaling using multidimensional orbital angular momentum (OAM) signal constellations. Multidimensional signal constellation is obtained as the N-dimensional Cartesian product of a one-dimensional signal constellation originating from non-negative pulse-amplitude modulation. This scheme represents an energy efficient alternative, since a larger number of bits per symbol can be transmitted using a given bandwidth. We evaluate the performance of this scheme by determining conditional symbol probability density functions (PDFs) from numerical propagation data. Two cases are considered: (i) when conditional PDFs are known on the receiver side, and (ii) when conditional PDFs are not known and Gaussian approximation is used instead. We show that the OAM modulation is more sensitive to atmospheric turbulence as the number of dimensions increases. We also describe several applications of interest ranging from indoor wireless communications to intersatellite communications.