Threshold detection of wideband signals: A noise-induced maximum in the mutual information

In some nonlinear dynamic systems, the addition of noise to a weak periodic signal can increase the detectability of the signal, a phenomenon belonging to a class of noise-induced cooperative behavior known as stochastic resonance (SR). There has been much recent speculation on the possible role of SR in signal processing by sensory neurons. However, most results have focused exclusively on increasing the output signal-to-noise ratio (SNR) of time-periodic signals, even though many real-world signals (e.g., those encountered in some neurophysiological and communications applications) are not of this form. Here we consider a generalization of SR, based on the Shannon mutual information between the transmitted and received signal. This generalization can be applied to cases (e.g., the information transmitted by the output spike train of an integrate-fire model neuron which we consider here), involving aperiodic input signals for which the output SNR might be ill-defined, uninformative, or irrelevant. Since the SR-like effect in the transmitted information disappears with the optimal choice of model parameters, we suggest that such an effect is likely to be particularly relevant to systems, e.g., neuronal populations, in which natural circuit constraints may render parameter optimization impractical.