Upper and Lower Bounds of Constrained Capacity in Diffusion-based Molecular Communication

This paper investigates upper and lower bounds for the constrained capacity of a diffusive molecular communication (MC) system in the case where the information is associated with the concentration of molecules released by the transmitter.
The evaluation of channel capacity for the diffusive channel is an open problem in the context of MC. Here, two simple bounds of the constrained capacity are derived for a given number of input concentration levels. Numerical results are reported for binary and quadruple concentration-shift keying considering the Poisson and Gaussian distributions, which are two common approximations used to describe the statistics of the received signal. We show that for both the two statistical channel models the resulting bounds are tight and, therefore, this means that, at least for low modulation orders, it is not necessary to resort to numerical techniques or complicated analytical expressions to guess the capacity of the diffusive MC channel.