This paper studies the high-power capacity scaling of additive noise channels whose noise arises from the first-hitting location of a multidimensional drift-diffusion process on an absorbing hyperplane. By identifying the underlying stochastic transport mechanism as a Gaussian variance-mixture, we introduce and analyze the Normally-Drifted First-Hitting Location (NDFHL) family as a geometry-driven model for boundary-induced noise. Under a second-moment constraint, we derive an exact high-SNR capacity expansion and show that the asymptotic upper and lower bounds coincide at the constant level, yielding a vanishing capacity gap. As a consequence, isotropic Gaussian signaling is asymptotically capacity-achieving for all fixed drift strengths, despite the non-Gaussian and semi-heavy-tailed nature of the noise. The pre-log factor is determined solely by the dimension of the receiving boundary, revealing a geometric origin of the channel's degrees of freedom. The refined expansion further uncovers an entropy-dominant universality, whereby all physical parameters of the transport process -- including drift strength, diffusion coefficient, and boundary separation -- affect the capacity only through the differential entropy of the induced noise. Although the NDFHL density does not admit a simple closed form, its entropy is shown to be finite and to vary continuously as the drift vanishes, thereby connecting the finite-variance regime with the singular infinite-variance Cauchy limit. Together, these results provide a unified geometric and information-theoretic characterization of boundary-hitting channels across both regular and singular transport regimes.

翻译：本文研究了加性噪声信道在高功率下的容量缩放特性，该噪声源于多维漂移扩散过程在吸收超平面上的首达位置。通过识别底层随机传输机制为高斯方差混合模型，我们引入并分析了正态漂移首达位置（NDFHL）族作为边界诱导噪声的几何驱动模型。在二阶矩约束下，我们推导了精确的高信噪比容量展开式，并证明渐近上下界在常数项上重合，从而产生趋于零的容量间隙。因此，尽管噪声具有非高斯性和半重尾特性，各向同性高斯信令对于所有固定漂移强度均是渐近容量可达的。前对数因子完全由接收边界的维度决定，揭示了信道自由度的几何起源。精细化展开进一步揭示了熵主导的普适性：传输过程的所有物理参数——包括漂移强度、扩散系数和边界间距——仅通过诱导噪声的微分熵影响信道容量。尽管NDFHL概率密度函数不存在简单的闭合形式，但其熵被证明是有限的，并在漂移趋于零时连续变化，从而将有限方差区域与奇异的无限方差柯西极限联系起来。这些结果共同为边界击中信道在正则与奇异传输区域提供了统一的几何与信息论刻画。