A Framework to Study the Molecular Communication System

Abstract

Communication between a transmitter and a re- ceiver 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. Communications research has largely focused on systems based on electromagnetic propagation. However, at scales con- sidered in nano-technology it is not clear that these concepts apply. In this paper we consider communication based on molecules (1). Specifically, we consider the propagation of individual molecules between closely spaced transmitters and receivers embedded in a fluid medium. The transmitter en- codes information in the pattern of release of the molecules it disperses into the fluid medium. These molecules then propa- gate to the receiver, where they are detected. The receiver then tries to decode the information from the pattern of received molecules. For a comprehensive overview of the molecular communication system, refer to (2) and the references therein. As in any communication system, the potential rate of communication is determined by the characteristics of the channel. Here, propagation is determined by a mean drift velocity and is uncertain due to the Brownian motion within the fluid. In this preliminary work, our goal is to analyze the mutual information between the transmitter and receiver and hence the capacity of the channel. We would like to emphasize that, in order to gain insight, and to make the problem mathematically tractable, we consider a fairly simple model of a molecular communication system. In (3), the authors compute information theoretic bounds to capacity for a general diffusion channel. Our work is along similar lines, although we lay a greater emphasis on the mathematical modeling of the system. In (4), the authors study a system where the receiver chemically reacts with the molecules and forms complexes. This is very different from the system model we consider. We assume that the receiver absorbs the molecule. Furthermore, we model the diffusion of the particle in the medium, and incorporate its effect in our calculations.