In recent years, there has been a growing interest in exploring the application of single-photon avalanche diode (SPAD) in optical wireless communication (OWC). As a photon counting detector, SPAD can provide much higher sensitivity compared to the other commonly used photodetectors. However, SPAD-based receivers suffer from significant dead-time-induced non-linear distortion and signal dependent noise. In this work, we propose a novel SPAD-based OWC system in which the non-linear distortion caused by dead time can be successfully eliminated by the pre-distortion of the signal at the transmitter. In addition, another system with joint pre-distortion and noise normalization functionality is proposed. Thanks to the additional noise normalization process, for the transformed signal at the receiver, the originally signal dependent noise becomes signal independent so that the conventional signal detection techniques designed for AWGN channels can be employed to decode the signal. Our numerical results demonstrate the superiority of the proposed SPAD-based systems compared to the existing systems in terms of BER performance and achievable data rate.