Shannon capacity and codes for communicating with a chaotic laser

In this paper, we investigate a method of communicating with chaos described by Hayes, Grebogi, and Ott, which uses the idea of controlling chaos by small perturbations. Although allowing the electronics controlling the output signal to remain at the low-power level, this method unavoidably incurs a capacity loss, which we calculate for a chaotic CO2 laser model. We first determine an approximation to the laser language, by means of a forbidden set representation, and then find its Shannon capacity. Results indicate that, since the capacity loss is not significant, the tradeoff is worthwhile. Finally, we point to simple finite-state encoders that satisfy the constraints imposed by the language.