Yen-Chi Lee

Yen-Chi Lee, Min-Hsiu Hsieh

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.

Po-Chun Chou, Yen-Chi Lee, Chun-An Yang et al.

Analytical modeling of field-assisted molecular communication under dynamic electric fields is fundamentally challenging due to the coupling between stochastic transport and complex boundary geometries, which renders conventional partial differential equation (PDE) approaches intractable. In this work, we introduce a stochastic framework based on the Cameron-Martin-Girsanov theorem to address this challenge. By leveraging a change-of-measure technique, we derive analytically tractable channel impulse response (CIR) expressions for both fully-absorbing and passive spherical receivers, where the latter serves as an exact mathematical baseline to validate our framework. Building upon these models, we establish a dynamic waveform design framework for system optimization. Under a maximum a posteriori decision-feedback equalizer (MAP-DFE) framework, we show that the first-slot received probability serves as the primary determinant of the bit error probability (BEP), while inter-symbol interference manifests as higher-order corrections. Exploiting the monotonic response of the fully-absorbing architecture and using the limitations of the passive model to justify this strategic focus, we reformulate BEP minimization into a distance-based optimization problem. We propose a unified, low-complexity Maximize Received Probability (MRP) algorithm, encompassing the Maximize Hitting Probability (MHP) and Maximize Sensing Probability (MSP) methods, to dynamically enhance desired signals and suppress inter-symbol interference. Numerical results validate the accuracy of the proposed modeling approach and demonstrate near-optimal detection performance.

Yen-Chi Lee

While the zero-drift first arrival position (FAP) channel exhibits a Cauchy-distributed lateral displacement, nonzero drift in practical systems introduces advective transport that regularizes this singular limit. This letter characterizes the drift-induced transition of FAP distribution from heavy-tailed algebraic regime to exponential regularization. By asymptotically examining the exact FAP density, we identify a characteristic propagation distance (CPD) that serves as the fundamental boundary separating diffusion-dominated and drift-dominated regimes. Numerical experiments demonstrate that in low-drift environments, variance-matched Gaussian approximations severely underestimate the true communication potential, whereas the zero-drift Cauchy law provides a robust, physically grounded performance baseline.

Yen-Chi Lee

This paper develops a tractable analytical channel model for first-hitting-time molecular communication (MC) systems under time-varying drift. While existing studies of nonstationary transport rely primarily on numerical solutions of advection-diffusion equations or parametric impulse-response fitting, they do not provide an explicit analytical description of trajectory-level arrival dynamics at absorbing boundaries. By adopting a change-of-measure formulation, we reveal a structural decomposition of the first-hitting-time density into a cumulative-drift displacement term and a stochastic boundary-flux modulation factor. This leads to a closed-form Corrected-Inverse-Gaussian (C-IG) density that generalizes the classical IG model to nonstationary drift while preserving O(1) evaluation complexity. Monte Carlo simulations under both smooth pulsatile and abrupt switching drift profiles confirm that the proposed C-IG model accurately captures complex transport phenomena, including phase modulation, multi-pulse dispersion, and transient backflow -- effects that traditionally complicate symbol synchronization and induce severe inter-symbol interference. The resulting framework provides a physics-informed, computationally efficient channel model suitable for system-level analysis and advanced receiver design, such as real-time maximum likelihood detection, in dynamic biological and MC environments.

Yen-Chi Lee

We study one-shot detection under additive white Cauchy noise (AWCN) using finite constellations, with emphasis on the geometric mechanisms governing symbol-level reliability. Under isotropic Cauchy noise, the maximum-likelihood rule induces the same Euclidean Voronoi decision regions as in the Gaussian case, so the distinction lies not in the decision geometry itself but in how probability mass is distributed over these fixed regions. In the small-noise regime, we derive a reciprocal distance-spectrum upper bound for the symbol error probability, showing that reliability retains a longer-range dependence on the global constellation geometry than under additive white Gaussian noise. In the large-noise regime, we prove that the correct-decision probability converges to a limit determined solely by the angular measure of the associated Voronoi recession cone. These results formalize a regime-dependent transition from distance-based to angle-based reliability descriptors under heavy-tailed noise. The theory is further illustrated through an asymmetric four-point example exhibiting geometric collapse and a standard 4QAM sanity check.