The models introduced in Chapter 5 give us a mathematical framework to describe the elements of a molecular communication system, particularly the molecules as they traverse the medium. We now take this idea one step further, by describing the statistical interaction between two terminals as they exchange signaling molecules. Since it is the randomness of molecular motion under Brownian motion that creates uncertainty in communication, the models we gave in Chapter 5 play the role of communication noise in this chapter.

There is a rich mathematical literature on information and communication theory. Though much existing work deals with electromagnetic communication, the theories are general enough that we can apply them to molecular communication. In this chapter, we briefly describe these theories, and show how they relate to molecular communication systems. However, we will also see that there exist many open problems in this field, and that solutions are only known for simplified cases.

Theoretical models for analysis of molecular communication

In Chapter 5, we gave models for diffusion, and discussed some ways in which those models could be used to discuss communication. We now present these models more formally, to allow mathematical analysis of the communication systems. To do so, we must specify not only what is happening as molecules propagate, but also the actions of the transmitter and receiver.

Both in this section and in the chapter as a whole, we will see examples where physically unrealistic assumptions are made to simplify the analysis.