The data processing inequality and stochastic resonance

Abstract

The data processing inequality of information theory states that given random variables X, Y and Z which form a Markov chain in the order X-->Y-->Z, then the mutual information between X and Y is greater than or equal to the mutual information between X and Z. That is I(X) >= I(X;Z) . In practice, this means that no more information can be obtained out of a set of data then was there to begin with, or in other words, there is a bound on how much can be accomplished with signal processing. However, in the field of stochastic resonance, it has been reported that a signal to noise ratio gain can occur in some nonlinear systems due to the addition of noise. Such an observation appears to contradict the data processing inequality. In this paper, we investigate this question by using an example model system.