  We consider molecular communication, with information conveyed in the time of
release of molecules. The main contribution of this paper is the development of
a theoretical foundation for such a communication system. Specifically, we
develop the additive inverse Gaussian (IG) noise channel model: a channel in
which the information is corrupted by noise with an inverse Gaussian
distribution. We show that such a channel model is appropriate for molecular
communication in fluid media - when propagation between transmitter and
receiver is governed by Brownian motion and when there is positive drift from
transmitter to receiver. Taking advantage of the available literature on the IG
distribution, upper and lower bounds on channel capacity are developed, and a
maximum likelihood receiver is derived. Theory and simulation results are
presented which show that such a channel does not have a single quality measure
analogous to signal-to-noise ratio in the AWGN channel. It is also shown that
the use of multiple molecules leads to reduced error rate in a manner akin to
diversity order in wireless communications. Finally, we discuss some open
problems in molecular communications that arise from the IG system model.
