  This work studies optimal detection for communication over diffusion-based
molecular timing (DBMT) channels. The transmitter simultaneously releases
multiple information particles, where the information is encoded in the time of
release. The receiver decodes the transmitted information based on the random
time of arrival of the information particles, which is modeled as an additive
noise channel. For a DBMT channel without flow, this noise follows the L\'evy
distribution. Under this channel model, the maximum-likelihood (ML) detector is
derived and shown to have high computational complexity. It is also shown that
under ML detection, releasing multiple particles improves performance, while
for any additive channel with $\alpha$-stable noise where $\alpha<1$ (such as
the DBMT channel), under linear processing at the receiver, releasing multiple
particles degrades performance relative to releasing a single particle. Hence,
a new low-complexity detector, which is based on the first arrival (FA) among
all the transmitted particles, is proposed. It is shown that for a small number
of released particles, the performance of the FA detector is very close to that
of the ML detector. On the other hand, error exponent analysis shows that the
performance of the two detectors differ when the number of released particles
is large.
