Capacity Bounds for Vertically-Drifted First Arrival Position Channels under a Covariance Constraint

TL;DR

This paper investigates the capacity limits of a molecular communication channel with vertically-drifted first arrival position noise under a covariance constraint, providing analytical bounds in a 3D setting.

Contribution

It introduces new analytical upper and lower bounds on channel capacity considering covariance constraints, inspired by vector Gaussian interference channel principles.

Findings

Derived capacity bounds for the channel

Analyzed stability properties of the system

Enhanced understanding of molecular communication limits

Abstract

In this paper, we delve into the capacity problem of additive vertically-drifted first arrival position noise channel, which models a communication system where the position of molecules is harnessed to convey information. Drawing inspiration from the principles governing vector Gaussian interference channels, we examine this capacity problem within the context of a covariance constraint on input distributions. We offer analytical upper and lower bounds on this capacity for a three-dimensional spatial setting. This is achieved through a meticulous analysis of the characteristic function coupled with an investigation into the stability properties. The results of this study contribute to the ongoing effort to understand the fundamental limits of molecular communication systems.