Inspired by biological communication systems, molecular communication has been proposed as a viable scheme to communicate between nano-sized devices separated by a very short distance. Here, molecules are released by the transmitter into the medium, which are then sensed by the receiver. This paper develops a preliminary version of such a communication system focusing on the release of either one or two molecules into a fluid medium with drift. We analyze the mutual information between transmitter and the receiver when information is encoded in the time of release of the molecule. Simplifying assumptions are required in order to calculate the mutual information, and theoretical results are provided to show that these calculations are upper bounds on the true mutual information. Furthermore, optimized degree distributions are provided, which suggest transmission strategies for a variety of drift velocities. Communications research has almost exclusively focused on systems based on electromagnetic propagation. However, at scales considered in nano-technology, it is not clear that these methods are viable. Inspired by the chemical-exchange communication performed by biological cells, this paper considers molecular communication [1] , in which information is transmitted by an exchange of molecules. Specifically we consider the propagation of individual molecules between closely spaced transmitters and receivers, both immersed in a fluid medium. The transmitter encodes a message in the pattern of release of the molecules into the medium; these molecules then propagate to the receiver where they are sensed. The receiver then attempts to recover the message by observing the pattern of the received molecules. It is well known that microorganisms exchange information by molecular communication, with quorum sensing [2] as but one example, where bacteria exchange chemical messages to estimate the local population of their species. The biological literature on molecular communication is vast, but there has been much recent work concerning these systems as engineered forms of communication. Several recent papers have described the design and implementation of engineered molecular communication systems, using methods such as: exchanging arbitrary molecules using Brownian motion in free space [3] ; exploiting gap junctions between cells to exchange calcium ions [4], [5] ; and using microtubules and molecular motors to actively drive molecules to their destination [6], [7] . A comprehensive overview of the molecular communication system is also given by [8], [9] and the references therein. Given this engineering interest, it is useful to explore the theoretical capabilities of molecular communication systems. To the authors' knowledge, the earliest effort towards information-theoretic analysis of these channels was given in [10] , which examined information flow in continuous diffusion. In [11] , [12] , physical models and achievable bounds on information rate were provided for diffusion-based systems.
In REF , the authors propose a slightly different scenario, in which both nano-nodes and emitted molecules propagate through a fluid medium, propelled by a drift velocity and Brownian motion.
Molecular Communication Using Brownian Motion with Drift
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