Information transfer with small-amplitude signals

TL;DR

This paper investigates optimal information transfer in systems with memory at low signal amplitudes, revealing that maximizing signal variance and Fisher information structure enhances mutual information, with applications to biological neurons.

Contribution

It derives optimality conditions for information transfer with small signals, linking mutual information to signal variance and Fisher information, and demonstrates relevance to neural coding.

Findings

Optimal mutual information corresponds to maximum signal variance.

Correlation structure is determined by Fisher information matrix.

Results apply to weakly stimulated neurons and biological coding efficiency.

Abstract

We study the optimality conditions of information transfer in systems with memory in the low signal-to-noise ratio regime of vanishing input amplitude. We find that the optimal mutual information is represented by a maximum-variance of the signal time course, with correlation structure determined by the Fisher information matrix. We provide illustration of the method on a simple biologically-inspired model of electro-sensory neuron. Our general results apply also to the study of information transfer in single neurons subject to weak stimulation, with implications to the problem of coding efficiency in biological systems.