A Data-driven Approach to Optimize Bounds on the Capacity of the Molecular Channel

The study of channel capacity is a well-known problem in Digital Communication (DC) systems. Most of the channel models used to evaluate capacity consider the additive white Gaussian noise as the sole impairment. Analytical formulas for lower and upper bounds have been obtained considering such a statistical characterization and different constraints for the transmitted signal. The field of Molecular Communication (MC) shows several analogies with DC systems. However, to the best of our knowledge, it is not possible to determine a statistical model characterizing an MC channel that considers the nonlinear effects present in the system. This paper aims to develop a data-driven methodology that, starting from in-silico or in-vitro experiments, allows estimating bounds on the constrained channel capacity of any biological system and the corresponding distribution of the source message, e.g., finite concentration levels of a protein. As experiments are time consuming, the method includes a machine learning-based data augmentation step. Our proposal is illustrated for a biological circuit composed of two prokaryotic cells. Results highlight fast and stable convergence of the algorithm to tight capacity bounds.