Light emitting diodes (LED) are becoming the dominant lighting elements due to their efficiency. Optical camera communications (OCC), the branch of visible light communications (VLC) that uses video cameras as receivers, is a suitable candidate in facilitating the development of new communication solutions for the broader public because video cameras are available on almost any smartphone nowadays. Unfortunately, most OCC systems that have been proposed until now require either expensive and specialized high-frame-rate cameras as receivers, which are unavailable on smartphones, or they rely on the rolling shutter effect, being sensitive to camera movement and pointing direction, they produce light flicker when low-frame-rate cameras are used, or they must discern between more than two light intensity values, affecting the robustness of the decoding process. This paper presents in detail the design of an OCC system that overcomes these limitations, being designed for receivers capturing 120 frames per second and being easily adaptable for any other frame rate. The system does not rely on the rolling shutter effect, thus making it insensitive to camera movement during frame acquisition and less demanding about camera resolution. It can work with reflected light, requiring neither a direct line of sight to the light source nor high resolution image sensors. The proposed communication is invariant to the moment when the transmitter and the receiver are started as the communication is self-synchronized, without any other exchange of information between the transmitter and the receiver, without producing light flicker, and requires only two levels of brightness to be detected (light on and light off). The proposed system overcomes the challenge of not producing light flicker even when it is adapted to work with very low-frame-rate receivers. This paper presents the statistical analysis of the communication performance and discusses its implementation in an indoor localization system.