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.

翻译：在分子通信（MC）中首次到达位置（FAP）信道脉冲响应研究的最新进展揭示了其香农容量。尽管Lee等人阐明了存在垂直漂移的FAP信道容量，但零漂移场景仍是一个难题，主要源于重尾柯西分布（其不存在一阶和二阶矩）带来的挑战，使得传统互信息约束失效。本文首次揭示了二维和三维空间中零漂移FAP信道容量的新特征。有趣的是，我们的结果表明三维FAP信道容量是二维对应值的两倍，暗示着随着空间维度增加容量会提升。此外，我们提出的方法引入了修正的对数约束和输出信号约束，为估计FAP信道容量提供了简化且更直观的公式（类似于著名的高斯情形）。