Numerical evaluation of error probabilities of self-synchronizing chaotic communications

Based on stochastic calculus, we provide a rigorous formulation of the numerical evaluation of the error probabilities of two modulation techniques for the chaotic Lorenz communication system with additive white Gaussian noise disturbance, These results provide further understanding on the robust self-synchronization ability of the Lorenz system to noise. An approximate model of the variance of the sufficient statistic of the chaotic communication is derived, which permits a comparison of the chaotic communication system performance to the conventional binary pulse position modulation (PAM) communication system.