Characterizing First Arrival Position Channels: Noise Distribution and Capacity Analysis
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929246194106368 |
|---|---|
| author | Lee, Yen-Chi Lo, Yun-Feng Wu, Jen-Ming Hsieh, Min-Hsiu |
| author_facet | Lee, Yen-Chi Lo, Yun-Feng Wu, Jen-Ming Hsieh, Min-Hsiu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08353 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterizing First Arrival Position Channels: Noise Distribution and Capacity Analysis Lee, Yen-Chi Lo, Yun-Feng Wu, Jen-Ming Hsieh, Min-Hsiu Information Theory Emerging Technologies 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. |
| title | Characterizing First Arrival Position Channels: Noise Distribution and Capacity Analysis |
| topic | Information Theory Emerging Technologies |
| url | https://arxiv.org/abs/2306.08353 |