  This work introduces capacity limits for molecular timing (MT) channels,
where information is modulated in the release timing of small information
particles, and decoded from the time of arrivals at the receiver. It is shown
that the random time of arrival can be represented as an additive noise
channel, and for the diffusion-based MT (DBMT) channel this noise is
distributed according to the L\'evy distribution. Lower and upper bounds on the
capacity of the DBMT channel are derived for the case where the delay
associated with the propagation of the information particles in the channel is
finite, namely, when the information particles dissipate after a finite time
interval. For the case where a single particle is released per channel use,
these bounds are shown to be tight. When the transmitter simultaneously
releases a large number of particles, the detector at the receiver may not be
able to precisely detect the arrival time of all the particles. Therefore, two
alternative models are considered: detection based on the particle that arrives
first, or detection based on the average arrival times. Tight lower and upper
bounds are derived for these two models. It is shown that by controlling the
maximal delay of the information particles, the capacity can increase
poly-logarithmically with the number of released particles. As each particle
takes a random independent path, this diversity of paths is analogous to
receiver diversity and can be used to considerably increase the achievable data
rates.
