Capacity Bounds for Vertically-Drifted First Arrival Position Channels under a Second-Moment Constraint

This paper explores the capacity of additive Vertically-Drifted First Arrival Position (VDFAP) noise channels, which are emerging as a new paradigm for diffusive molecular communication. Analogous to the capacity of parallel Gaussian channels, the capacity of VDFAP noise channels is defined as the supremum of the mutual information between the input and output signals subject to an overall second-moment constraint on input distributions. Upper and lower bounds for this capacity are derived for the case of three spatial dimensions, based on an analysis of the characteristic function of the VDFAP distribution and an investigation of its stability properties. The results of this study contribute to the ongoing effort to understand the fundamental limits of molecular communication systems.