Diversity gain of one-shot communication over molecular timing channels

TL;DR

This paper analyzes the diversity gain in one-shot molecular timing communication channels, comparing different detection methods and showing the effectiveness of the first arrival detector in various propagation scenarios.

Contribution

It introduces the concept of system diversity gain in molecular timing channels and compares the performance of ML, linear, and first arrival detectors.

Findings

FA detector matches ML performance for unimodal densities with zero mode

FA detector outperforms linear detector significantly

Diversity gain is high for FA detector even with positive mode densities

Abstract

We study diversity in one-shot communication over molecular timing channels. In the considered channel model the transmitter simultaneously releases a large number of information particles, where the information is encoded in the time of release. The receiver decodes the information based on the random time of arrival of the information particles. We characterize the asymptotic exponential decrease rate of the probability of error as a function of the number of released particles. We denote this quantity as the system diversity gain, as it depends both on the number of particles transmitted as well as the receiver detection method. Three types of detectors are considered: the maximumlikelihood (ML) detector, a linear detector, and a detector that is based on the first arrival (FA) among all the transmitted particles. We show that for random propagation characterized by right-sided unimodal densities with zero mode, the FA detector is equivalent to the ML detector, and significantly outperforms the linear detector. Moreover, even for densities with positive mode, the diversity gain achieved by the FA detector is very close to that achieved by the ML detector and much higher than the gain achieved by the linear detector.