Identification for Inverse Gaussian Channels

TL;DR

This paper investigates the identification capacity of inverse Gaussian channels, modeling molecular communication, and finds super-exponential growth in codebook size under certain conditions.

Contribution

It derives bounds on the identification capacity of inverse Gaussian channels and characterizes its super-exponential growth behavior.

Findings

Identification capacity grows super-exponentially as ~2^{(n log n) R}

Bounds on capacity are derived considering deterministic encoding and peak constraints

Asymptotic analysis of codebook sizes in molecular communication channels

Abstract

We derive lower and upper bounds on the identification capacity of inverse Gaussian channels, a fundamental model for molecular communications in fluid environments. The analysis considers deterministic encoding schemes under a peak time constraint and characterizes the asymptotic growth of codebook sizes. A central result reveals that, under a mild regularity condition on the noise, i.e., the stochastic first arrival time of an information-carrying molecule propagating via diffusion and drift to the receiver, the identification capacity exhibits super-exponential growth in the codeword length, $n,$ i.e., $\sim 2^{(n \log n)R},$ where $R$ is the coding rate.