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In this paper, we characterize the performance of a direct-detection, avalanche photodiode-based free-space optical (FSO) communication system in terms of the overall bit-error rate. The system of interest uses pulse-position modulation (PPM) and is subjected to scintillation due to optical turbulence. Two scenarios are considered. In one case, a weak turbulence (clear-air) scenario is considered, for which the received signal intensity may be modeled as a log-normal random process. In the other case, we consider a negative exponentially distributed received signal intensity. To arrive at the desired results, it is assumed that the system uses a binary PPM (BPPM) modulation scheme. Furthermore, it is assumed that the receiver thermal noise is nonnegligible, and that the average signal intensity is large enough to justify a Gaussian approximation at the receiver. Union bound is used to assess the performance of M-ary PPM systems using the results of the BPPM scenario. Numerical results are presented for the BPPM case to shed light on the impact of turbulence on the overall performance.