Evidence for stochastic resonance in threshold systems based on mutual information

This paper shows how noise can improve how threshold systems process signals and maximize their throughput information. Such favorable use of noise is the so-called "stochastic resonance" or SR effect. We present a theorem that shows that a threshold system can maximize its input-output mutual information for a large class of noise probability densities. The theorem shows that almost all noise probability density functions produce some SR effect in threshold systems even if the noise is impulsive and has infinite variance. We also show that a new statistically robust learning law can find this entropy-optimal noise level. These findings suggest that scientists and engineers should also consider the use of noise in their systems\´ designs.