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Using an accurate exponential bound for the Gaussian Q-function, we derive simple approximate closed-form expressions for the average symbol error probability (ASEP) of a free-space optical communication link using subcarrier intensity modulation (SIM) with general-order rectangular quadrature amplitude modulation (QAM) over atmospheric turbulence channels. To model the atmospheric turbulence conditions, the log-normal and the gamma-gamma distribution are used. Extensive numerical and computer simulation results are presented in order to verify the accuracy of the proposed mathematical analysis.