On the Capacity of Zero-Drift First Arrival Position Channels in Diffusive Molecular Communication

TL;DR

This paper characterizes the capacity of zero-drift first arrival position channels in diffusive molecular communication, revealing a capacity doubling from 2D to 3D and providing a simplified estimation formula.

Contribution

It introduces a novel capacity characterization for zero-drift FAP channels in 2D and 3D, overcoming challenges posed by heavy-tailed distributions.

Findings

3D capacity is twice the 2D capacity

New capacity estimation formula similar to Gaussian case

Modified constraints simplify capacity calculation

Abstract

Recent advancements in understanding the impulse response of the first arrival position (FAP) channel in molecular communication (MC) have illuminated its Shannon capacity. While Lee et al. shed light on FAP channel capacities with vertical drifts, the zero-drift scenario remains a conundrum, primarily due to the challenges associated with the heavy-tailed Cauchy distributions whose first and second moments do not exist, rendering traditional mutual information constraints ineffective. This paper unveils a novel characterization of the zero drift FAP channel capacity for both 2D and 3D. Interestingly, our results reveal a 3D FAP channel capacity that is double its 2D counterpart, hinting at a capacity increase with spatial dimension growth. Furthermore, our approach, which incorporates a modified logarithmic constraint and an output signal constraint, offers a simplified and more intuitive formula (similar to the well-known Gaussian case) for estimating FAP channel capacity.