Information transmission in parallel threshold arrays: Suprathreshold stochastic resonance

Abstract

The information transmitted through a parallel summing array of noisy threshold elements with a common threshold is considered. In particular, using theoretical and numerical analysis, a recently reported [N. G. Stocks, Phys. Rev. Lett. 84, 2310 (2000)] form of stochastic resonance, termed suprathreshold stochastic resonance (SSR), is studied in detail. SSR is observed to occur in arrays with two or more elements and, unlike stochastic resonance (SR) in a single element, gives rise to noise-induced information gains that occur independent of the setting of the threshold or the size of the signal. The transmitted information is maximized when all thresholds are set to coincide with the signal mean. In this situation, and for large arrays, the noise can enhance performance up to approximately half the theoretical noiseless channel capacity. The theory is tested against digital simulation.

Nonlinear Devices Acting as SNR Amplifiers for a Harmonic Signal in Noise

“…into parallel arrays, instead of using a single one in isolation. For nonlinearities associated in parallel arrays, an interesting form of stochastic resonance consists in purposely injecting additional noises, on each device of the array, to induce more variability and richness in the responses of the devices [17]. A global response collected over the array of noisy devices can sometimes bring improvement over the performance of a single device with no extra added noise.…”

“…A global response collected over the array of noisy devices can sometimes bring improvement over the performance of a single device with no extra added noise. Various forms of enhanced processing through stochastic resonance in arrays have recently been demonstrated, essentially with two-state quantizers [17], [13], [15] corresponding to the nonlinearity of Figure 1c tuned at λ = 0. Saturating nonlinearities like those of Figures 1a and 1b, in terms of SNR gain with Gaussian noise, have been shown here to be superior to threshold nonlinearities like those of Figures 1c and 1d.…”

Noise-enhanced nonlinear detector to improve signal detection in non-Gaussian noise

“…This non-standard strategy to design suboptimal detectors based on two-state quantizers benefits from recent studies on the use of stochastic resonance and the constructive role of noise in nonlinear processes [9][10][11][12][13][14]. This paradoxical nonlinear phenomenon, has been intensively studied during the last two decades.…”

“…In these circumstances, the mechanism of improvement, qualitatively, is that the noise assists small signals in overcoming the threshold of the two-state quantizer. Recently, another form of stochastic resonance was proposed in [9,10], with parallel arrays of two-state quantizers, under the name of suprathreshold stochastic resonance. This form in [9][10][11][12][13][14] applies to signals of arbitrary amplitude, which do not need to be small and subthreshold, whence the name.…”

“…Recently, another form of stochastic resonance was proposed in [9,10], with parallel arrays of two-state quantizers, under the name of suprathreshold stochastic resonance. This form in [9][10][11][12][13][14] applies to signals of arbitrary amplitude, which do not need to be small and subthreshold, whence the name. Different measures of performance have been studied to quantify the suprathreshold stochastic resonance: general information measures like the input-output Shannon mutual information [9], the input-output correlation coefficient [11], signal-to-noise ratios [11,13], in an estimation context with the Fisher information contained in the array output [12] or in a detection context with a probability of error [14].…”