On the Capacity of Zero-Drift First Arrival Position Channels in Diffusive Molecular Communication
This work provides the first capacity characterization for zero-drift FAP channels, addressing a long-standing gap in molecular communication theory.
The paper characterizes the Shannon capacity of zero-drift first arrival position (FAP) channels in molecular communication for 2D and 3D, finding that the 3D capacity is double the 2D capacity, suggesting capacity increases with spatial dimension.
Recent advancements in understanding the impulse response of the first arrival position (FAP) channel in molecular communication (MC) have illuminated its Shannon capacity. While Lee et al. shed light on FAP channel capacities with vertical drifts, the zero-drift scenario remains a conundrum, primarily due to the challenges associated with the heavy-tailed Cauchy distributions whose first and second moments do not exist, rendering traditional mutual information constraints ineffective. This paper unveils a novel characterization of the zero drift FAP channel capacity for both 2D and 3D. Interestingly, our results reveal a 3D FAP channel capacity that is double its 2D counterpart, hinting at a capacity increase with spatial dimension growth. Furthermore, our approach, which incorporates a modified logarithmic constraint and an output signal constraint, offers a simplified and more intuitive formula (similar to the well-known Gaussian case) for estimating FAP channel capacity.