A Framework to Study the Molecular Communication System

Communication between a transmitter and a receiver using electromagnetic waves does not scale to nano-sizes. To enable communication between nano-sized devices separated by a short distance, molecular communication has recently been proposed as a feasible scheme. The transmitter disperses molecules into the medium, which propagate to, and are sensed by, the receiver. In this paper, we wish to mathematically model such a system and subsequently characterize the information theoretic capacity of this channel. We present basic results on characterizing the mutual information between the transmitter and the receiver when information is encoded in the time of release of the molecule. To do so, we model the propagation of the molecule in this medium as Brownian motion, and derive the probability density function of the arrival time of the molecule at the receiver.