# Optimal stimulus and noise distributions for information transmission via suprathreshold stochastic resonance

## TL;DR

This paper investigates how noise can enhance information transmission in neural-like systems through suprathreshold stochastic resonance, deriving optimal noise and stimulus distributions that maximize channel capacity.

## Contribution

It provides a theoretical framework linking mutual information and Fisher information to identify optimal stimulus and noise distributions for SSR.

## Key findings

- Capacity is maximized when the signal distribution matches Jeffrey's prior.
- Optimal noise distribution relates to the signal distribution via a cosine function.
- Theoretical results support previous empirical and computational studies.

## Abstract

Suprathreshold stochastic resonance (SSR) is a form of noise enhanced signal transmission that occurs in a parallel array of independently noisy identical threshold nonlinearities, including model neurons. Unlike most forms of stochastic resonance, the output response to suprathreshold random input signals of arbitrary magnitude is improved by the presence of even small amounts of noise. In this paper the information transmission performance of SSR in the limit of a large array size is considered. Using a relationship between Shannon's mutual information and Fisher information, a sufficient condition for optimality, i.e. channel capacity, is derived. It is shown that capacity is achieved when the signal distribution is Jeffrey's prior, as formed from the noise distribution, or when the noise distribution depends on the signal distribution via a cosine relationship. These results provide theoretical verification and justification for previous work in both computational neuroscience and electronics.