A Study of Chemical Reactions in Point-to-Point Diffusion-Based Molecular Communication

The differential equations describing reaction-diffusion systems in molecular communication are non-linear and do not admit closed-form solutions in general. Consequently, characterizing optimal modulation and coding strategies is a key challenge in molecular communication. In this paper, we consider a concrete example and illustrate the application of tools from real and complex analysis to study this difficult problem. We show that the optimal release pattern is a finite sum of Dirac’s delta functions in our working example. Simulation results validate the discrete nature of the optimal release pattern. We also provide an upper bound on the numbers of delta functions under some assumptions.