Stable Distributions as Noise Models for Molecular Communication

TL;DR

This paper models diffusion-based molecular communication timing channels using stable distributions for noise, providing analytical expressions and highlighting the heavy-tailed nature of the noise compared to Gaussian models.

Contribution

It introduces three novel timing channel models with stable distribution noise, offering analytical PDFs and demonstrating their heavy-tailed characteristics.

Findings

Noise follows stable distribution subclasses

Expressions for PDFs and CDFs are derived

Tails are longer than Gaussian distributions

Abstract

In this work, we consider diffusion-based molecular communication timing channels. Three different timing channels are presented based on three different modulation techniques, i.e., i) modulation of the release timing of the information particles, ii) modulation on the time between two consecutive information particles of the same type, and iii) modulation on the time between two consecutive information particles of different types. We show that each channel can be represented as an additive noise channel, where the noise follows one of the subclasses of stable distributions. We provide expressions for the probability density function of the noise terms, and numerical evaluations for the probability density function and cumulative density function. We also show that the tails are longer than Gaussian distribution, as expected.