Exploiting Diversity in One-Shot Molecular Timing Channels via Order Statistics

Abstract

We study diversity in one-shot communication over molecular timing channels. We consider a channel model where the transmitter simultaneously releases a large number of information particles, while 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. The random propagation is characterized by the general class of right-sided unimodal densities. We characterize the asymptotic exponential decrease rate of the probability of error as a function of the number of released particles, and denote this quantity as the system diversity gain . Four types of detectors are considered: 1) the maximum-likelihood (ML) detector; 2) a linear detector; 3) a detector that is based on the first arrival (FA) among all the transmitted particles; and 4) a detector based on the last arrival (LA). When the density characterizing the random propagation is supported over a large interval, we show that the simple FA detector achieves a diversity gain very close to that of the ML detector. On the other hand, when the density characterizing the random propagation is supported over a small interval, we show that the simple LA detector achieves a diversity gain very close to that of the ML detector.