Constellation design for color-shift keying using billiards algorithms

Light-emitting diodes (LEDs) have the potential to replace traditional devices in a variety of lighting applications, offering the possibility of simultaneous modulation for communications. One modulation method, color-shift keying (CSK), has been recently proposed specifically for red/green/blue (RGB) LEDs. We examine the design of CSK signaling constellations for an additive white Gaussian noise channel, incorporating the common requirement that the RGB LED outputs a specific, possibly time-varying, perceived color. In particular, we equate this design problem to that of disk packing and employ modified billiards algorithms that rely on the “thermodynamic” settling of the disks to obtain constellation points with good minimum distance. Simulation results are presented that illustrate the design approach.