Free space optical (FSO) communication is an emerging technology which can fulfil the current demands of additional broadband channels. It offers enormous bandwidth, less expensive setup and highly secure links. But it has some potential drawbacks as well i.e. its links deteriorate significantly due to the atmospheric turbulence and weather conditions (fog or cloud). The detection of the incoming light signals in FSO communications is done by photodiodes. The most preferable photodiodes are the photodetectors (avalanche photodiodes (APD)/positive-intrinsic-negative (PIN)). APDs are normally used in high performance FSO links where the noise shows different distribution for bits Os and Is rather than the Gaussian distribution. A signal dependent Gaussian noise (SDGN) model is proposed that incorporate the implementation of APDs for high performance communication links. We investigate the use of ON-OFF keying (OOK) which shows a good performance in terms of achieving optical power gains. Expressions are derived for the log-likelihood ratio (LLR) mapping of a received bit, the uncoded bit error rate (BER) and the ergodic capacity. We also provide the analysis of the FSO optimum/sub-optimum detectors.