The single-mirror small-size telescope (SST-1M) is one of the three proposed designs for the small-size telescopes (SSTs) of the Cherenkov Telescope Array (CTA) project. The SST-1M will be equipped with a 4 m-diameter segmented reflector dish and an innovative fully digital camera based on silicon photo-multipliers. Since the SST sub-array will consist of up to 70 telescopes, the challenge is not only to build telescopes with excellent performance, but also to design them so that their components can be commissioned, assembled and tested by industry. In this paper we review the basic steps that led to the design concepts for the SST-1M camera and the ongoing realization of the first prototype, with focus on the innovative solutions adopted for the photodetector plane and the readout and trigger parts of the camera. In addition, we report on results of laboratory measurements on real scale elements that validate the camera design and show that it is capable of matching the CTA requirements of operating up to high moonlight background conditions.