The propagation of an ON-OFF keying modulated optical signal through an optical atmospheric turbulent channel is considered. The intensity fluctuations of the signal observed at the receiver are modeled using a gamma-gamma distribution. The capacity of this channel is determined for a wide range of turbulence conditions. For a zero inner scale, the capacity decreases monotonically as the turbulence strengthens. For non-zero inner scale, the capacity is not monotonic with turbulence strength. Two error-correction schemes, based on low-density parity-check (LDPC) codes, are investigated as a means to improve the bit-error rate (BER) performance of the system. Very large coding gains - ranging from 5.5 to 14 dB, depending on the turbulence conditions - are obtained by these LDPC codes compared with Reed-Solomon error-correction codes of similar rates and lengths.