M-ary suprathreshold stochastic resonance: Generalization and scaling beyond binary threshold nonlinearities

Abstract

Suprathreshold stochastic resonance is a form of noise-enhanced processing that is observed only when more than one noisy nonlinear signal processing element is combined in a parallel array, such as in biological and engineered sensory transduction. The case of binary threshold nonlinearities combined into arrays of independently noisy components has previously been studied extensively, and quantified in terms of how information transmission through the array varies with the input noise level, and the number of elements, N. Here we generalise this setup to arrays of N identical M-ary threshold nonlinearities. We show that enhanced suprathreshold stochastic resonance occurs for and N>1, implying that M identical quantizing sensors can be combined to provide higher resolution than a single sensor, provided they are independently noisy. We also study the system's scaling with M and N and conclude that although binary quantizing nonlinearities are superior to M-ary nonlinearities in the presence of large noise, the opposite holds in the presence of small noise. This suggests that multiple identical but coarse-resolution sensors can be useful for acquiring low SNR signals while few high-resolution identical sensors are superior for high SNR signals.