  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.
