Light-fidelity (Li-Fi) is a promising solution to provide high-rate, secure, and green communications to be used in the next generation of wireless networks. Since visible or infrared (IR) light-emitting diodes (LEDs) are used as the optical source and have a nonlinear transfer function, the transmitted modulated signal can be distorted if the signal has a high peak-to-average power ratio (PAPR). Recently, a new modulation scheme called Hadamard-coded modulation (HCM) is proposed which has a low PAPR and produces symbols with discrete levels. In the HCM technique, the symbol levels can be created using multiple LEDs. Therefore, each LED operates in its linear region and just switches on or off. In this paper, a low-complexity transceiver architecture for the HCM-based communication links is proposed and a complete synchronization procedure based on the spread spectrum techniques is presented. Finally, the bit error rate of the system is evaluated by Monte Carlo simulations, and effects of system parameters such as preamble length, fall and rise time of optical devices, and timing jitter on the bit error rate of the link are discussed.