Color-shift keying (CSK) is a visible light modulation scheme that transmits data imperceptibly through the variation of output light color. In this work, a rigorous design framework for CSK constellations is presented based on interior point methods. A differentiable approximation to the CSK constellation design problem is presented which is compatible with commercial interior point optimization algorithms and is used to find locally optimal symbol sets. The benefits of the approach are that it can operate with a variety of peak and color-cross talk constraints (i.e., convex constraint regions), permits any desired operating color and is able to produce results for any size constellation. Design guidelines on tradeoffs between minimum distance and operating color as well a heuristic for handling larger constellations are also provided.
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