arXiv subjects

Yen-Chi Lee

Publications and source records attributed to Yen-Chi Lee.

13 recordsLinked to original sources

arXiv2026

Phase-Resolved Molecular Timing Channels under Pulsatile Drift: Volterra Characterization and Corrected Inverse-Gaussian Approximation

Pulsatile drift makes molecular arrival times depend on the release phase. We study a one-dimensional absorbing timing channel with constant diffusivity and positive-mean sinusoidal drift. A moving-boundary formulation yields an exact Volterra characterization of the phase-conditioned first-hitting law, with regularity, uniqueness, properness, and moment properties. Within this framework, we integrate and assess the corrected inverse-Gaussian (C-IG) approximation introduced in our conference work. Comparisons with a numerically validated Volterra reference distinguish raw-kernel mass discrepancy from normalized shape errors and show that close cumulative agreement can coexist with density and peak-count discrepancies, particularly under transient backflow. Phase-family analysis further shows that a small between-phase contribution to delay variance can coexist with substantial differences between conditional cumulative distributions. We connect these conditional laws and protocol-induced mixtures to timing likelihoods and absorption probabilities within a prescribed reception window, clarifying the arrival-time structures preserved by C-IG and the phase information concealed by averaging.

cs.IT↗

arXiv2026

First-Hitting Location Laws as Boundary Observables of Drift-Diffusion Processes

First-passage theory usually emphasizes when absorption occurs. Here, we instead treat where absorption occurs (the first-hitting location, or FHL) as a primary boundary observable of drift-diffusion processes. We formulate its law as the exit measure induced by the diffusion generator and recover its density from the normal derivative of an elliptic Green function. This yields exact half-space kernels in arbitrary ambient dimension $d$ for constant drift, with the two- and three-dimensional cases validated by Monte Carlo simulations. In the zero-drift limit, the kernels reduce to scale-free Cauchy-type laws with algebraic tails; drift introduces exponential screening and the characteristic length $\ell_u=σ^2/|\mathbf{v}|$, where $σ$ is the noise strength and $\mathbf{v}$ is the constant drift vector, thereby localizing the boundary footprint. An entropy-based effective width provides a finite diagnostic of this crossover. To test the geometric reach of the planar theory, we also analyze drift-free exterior hitting of a circle. Its exact Poisson kernel recovers the planar Cauchy law as a local near-boundary limit, admits an exact Cauchy-Poisson composition through an intermediate line, and yields a finite-time supporting-line bound. These results organize geometry, drift, and pathwise constraints within a unified description of first-hitting location laws.

cond-mat.stat-mech↗

arXiv2026

From Distance to Angle: One-Shot Detection Under Isotropic Multivariate Cauchy Noise

We study one-shot detection under isotropic multivariate Cauchy noise 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 (SEP), showing that this bound, and the associated reliability descriptor, retain 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 bound-based distance descriptors to angle-based reliability descriptors under heavy-tailed noise. Beyond asymptotic characterization, we show that these descriptors also admit a lightweight design interpretation for planar constellations under a common average power budget. The theory is further illustrated through an asymmetric four-point example exhibiting geometric collapse, a standard four-point Quadrature Amplitude Modulation (4QAM) sanity check, and finite-$γ$ numerical validation for both asymptotic regimes, together with descriptor-guided design comparisons that reveal collapse avoidance and reciprocal-distance burden as practically meaningful screening criteria.

cs.IT↗

arXiv2026

On the Tail Transition of First Arrival Position Channels: From Cauchy to Exponential Decay

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.

cs.IT↗

arXiv2026

Field-Assisted Molecular Communication: Girsanov-Based Channel Modeling and Dynamic Waveform Optimization

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 an effective stochastic modeling approach to address this challenge. By leveraging trajectory-reweighting techniques, we derive analytically tractable channel impulse response (CIR) expressions for both fully-absorbing and passive spherical receivers, where the latter serves as an exact theoretical baseline to validate our modeling accuracy. Building upon these models, we establish a dynamic waveform design framework for system optimization. Under a maximum \textit{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.

cs.IT↗

arXiv2026

Exact 3-D Channel Impulse Response Under Uniform Drift for Absorbing Spherical Receivers

An exact channel impulse response (CIR) for the three-dimensional point-to-sphere absorbing channel under drift has remained unavailable due to symmetry breaking. This letter closes this gap by deriving an exact analytical CIR for a fully absorbing spherical receiver under uniform drift with arbitrary direction. By formulating the problem in terms of joint first-hitting time-location statistics and applying a Girsanov-based measure change, drift effects are isolated into an explicit multiplicative factor, yielding an exact series representation. The resulting CIR provides a rigorous reference model and enables efficient, noise-free evaluation of key channel metrics without relying on Monte Carlo simulations.

cs.IT↗

arXiv2026

Capacity Scaling Laws for Boundary-Induced Drift-Diffusion Noise Channels

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.

cs.IT↗

arXiv2026

Symmetry-Enforced Quadratic Degradability Beyond Low Dimensions

Approximate degradability provides a powerful framework for bounding the quantum and private capacities of noisy quantum channels in regimes where exact degradability fails. While generic low-noise channels exhibit a non-degradability parameter that decays as a fractional power of the noise strength, certain symmetric channels are known to display an enhanced quadratic suppression. In this work, we investigate the structural origin of this phenomenon through a family of high-dimensional, rotationally symmetric noise models constructed from angular momentum operators. We first establish that the pure noise component of these channels is maximally distinguishable from the identity channel in diamond norm, revealing a geometric orthogonality between signal and noise. Building on this structure, we construct an explicit symmetric degrading map and prove that the approximate degradability parameter scales quadratically with the noise parameter for all system dimensions. To clarify the mechanism behind this behavior, we identify algebraic conditions on the noise operators that guarantee the cancellation of leading-order non-degradability terms. These conditions apply not only to the rotationally symmetric model studied here, but also to a distinct family of high-dimensional depolarizing channels based on discrete unitary operator bases. Numerical evaluations of capacity lower bounds further illustrate the practical impact of the quadratic suppression. Together, these results demonstrate that enhanced approximate degradability arises from symmetry-induced orthogonality and invariance properties, rather than from low-dimensional or model-specific effects.

cs.IT↗

arXiv2025

Spatiotemporal First-Arrival Modeling and Parameter Estimation in Drift-Diffusion Molecular Channels

We derive a closed-form joint distribution of the first arrival time (FAT) and first arrival position (FAP) in drift-diffusion molecular communication (MC) channels. In contrast to prior studies that analyze FAT or FAP in isolation, our framework explicitly captures the spatiotemporal coupling inherent in multidimensional transport. Building on this derivation, we compute the Fisher information matrix (FIM) and demonstrate that estimation accuracy for diffusivity scales proportionally with the spatial dimension, enabling increased sensitivity in higher-dimensional environments. Furthermore, we show that lateral drift -- which is unobservable from timing data alone -- can be recovered via a closed-form Maximum Likelihood Estimator (MLE) with a simple physical interpretation. Leveraging this spatial degree of freedom, we propose Drift Shift Keying (DSK), proving that joint receivers can reliably detect signals that are undetectable to timing-only receivers due to identical marginal FAT distributions. These results highlight the significant potential of spatiotemporal processing for future nanoscale communication and sensing.

cs.IT↗

arXiv2024

Characterizing First Arrival Position Channels: Noise Distribution and Capacity Analysis

This paper introduces a novel mathematical model for Molecular Communication (MC) systems, utilizing First Arrival Position (FAP) as a fundamental mode of information transmission. We address two critical challenges: the characterization of FAP density and the establishment of capacity bounds for channels with vertically-drifted FAP. Our method relate macroscopic Partial Differential Equation (PDE) models to microscopic Stochastic Differential Equation (SDE) models, resulting in a precise expression that links FAP density with elliptic-type Green's function. This formula is distinguished by its wide applicability across any spatial dimensions, any drift directions, and various receiver geometries. We demonstrate the practicality of our model through case studies: 2D and 3D planar receivers. The accuracy of our formula is also validated by particle-based simulations. Advancing further, the explicit FAP density forms enable us to establish closed-form upper and lower bounds for the capacity of vertically-drifted FAP channels under a second-moment constraint, significantly advancing the understanding of FAP channels in MC systems.

cs.IT↗

arXiv2023

On the Capacity of Zero-Drift First Arrival Position Channels in Diffusive Molecular Communication

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.

cs.IT↗

arXiv2023

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

In this paper, we delve into the capacity problem of additive vertically-drifted first arrival position noise channel, which models a communication system where the position of molecules is harnessed to convey information. Drawing inspiration from the principles governing vector Gaussian interference channels, we examine this capacity problem within the context of a covariance constraint on input distributions. We offer analytical upper and lower bounds on this capacity for a three-dimensional spatial setting. This is achieved through a meticulous analysis of the characteristic function coupled with an investigation into the stability properties. The results of this study contribute to the ongoing effort to understand the fundamental limits of molecular communication systems.

cs.IT↗

arXiv2023

A Unified Framework for Calculating First Arrival Position Density in Molecular Communication

This paper introduces a novel unified framework for calculating the first arrival position (FAP) density in diffusion-based molecular communication (MC) systems with fully-absorbing receivers, applicable to any spatial dimension or receiver shape. We validate the effectiveness of our proposed method by presenting two concrete examples from the MC literature: the 2D line receiver and 3D spherical receiver. Our approach successfully reproduces existing results on FAP density and further enhances the original formula for the 2D line receiver by accommodating arbitrary drift directions. The proposed framework offers a comprehensive and versatile solution for determining FAP density in diffusive MC channels with fully-absorbing receivers, paving the way for more robust and efficient system designs.

cs.IT↗