Molecular Communication Over a Non-linear Reaction-Diffusion Medium: A Tractable Model

One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or in the parameters of the medium requires one to redo the simulations. This makes it difficult to design modulation schemes and practically impossible to prove the optimality of a given transmission strategy. We provide an analytical technique for modeling non-linearity of chemical reaction equations based on the perturbation method. It is shown that at low reaction rates, instead of using a continuous transmission waveform, it is optimal for each transmitter to release molecules in a sequence of spikes.