臺灣博碩士論文加值系統

在本篇論文中,我們研究一個相當新且近代的通道模型,該通道利用 常速流體當中的化學粒子交換來做為溝通的訊息。這些粒子由傳送端出發 至接收端的路徑,我們將其視為一維空間來做模擬。很典型的通訊應用像 是我們將奈米級的儀器置入血管中,以完成傳遞訊息的任務。在這個情況 下,我們不再依賴電磁波傳遞訊息,而是將訊息放在釋放粒子的時間點上。 一旦粒子被傳送端釋放進入流體中時,會在介質中行布朗運動,這將會對 粒子到達接收端的時間產生不確定性,這樣的不確定性就是我們的雜訊。 我們用反高斯分布來描述這樣的雜訊。此篇研究將重點放在相加性雜訊通 道以描述基本的通道容量趨勢。
我們深入研究此模型,並分析出新的通道容量上界與下界。 這些界線 是漸進緊的,也就是說,如果平均延遲的限制可放寬至無限大,或是介質 流體流速趨近無限大,則相對應的漸進通道容量可被精確的推導出來。

In this thesis a very recent and new channel model is investigated that describes communication based on the exchange of chemical molecules in a liquid medium with constant drift. They travel from the transmitter to the receiver at two ends of a one-dimensional axis. A typical application of such communication are nano- devices inside a blood vessel communicating with each other. In this case, we no longer transmit our signal via electromegnetic waves, but we put our information on the emission time of the molecules. Once a molecule is emitted in the fluid medium, it will be affected by Brownian motion, which causes uncertainty of the molecule’s arrival time at the receiver. We characterize this noise with an inverse Gaussian distribution. Here we focus solely on an additive noise channel to describe the fundamental channel capacity behavior.
This new model is investigated and new analytical upper and lower bounds on the capacity are presented. The bounds are asymptotically tight, i.e., if the average- delay constraint is loosened to infinity or if the drift velocity of the liquid medium tends to infinity, the corresponding asymptotic capacities are derived precisely.

1 Introduction 1
1.1 General Molecular Communication Channel Model . . . . .. . . . .1 1.2 Mathematical Model . . . . . . . . . . . . . . . .. . . . . . . 2
1.3 Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 MathematicalPreliminaries 5
2.1 Properties of the Inverse Gaussian Distribution . . . . . . . . . . . . 5
2.2 Power Inverse Gaussian and Its Properties . . . . . . . . . . . . . . . 10
2.3 Related Lemmas and Propositions . . . . . . . . . . . . . . . . . . . 11
3 Known Bounds to the Capacity of the AIGN Channel 13
4 OurDifferent Trials of Lower Bounds 16
4.1 Lower Bounds of h(Y ) Based on h(X) . . . . . . . . . . . . . . . . . 16
4.2 Capacity Lower Bounds Based on Theorem 4.1 . . . . . . . . . . . . 18
4.2.1 Lower Bound 1: Taylor Expansion . . . . . . . . . . . . . . . 18
4.2.2 Lower Bound 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Lower Bound Based on the Convolution of Exponential and Inverse
Gaussian Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5 OurDifferent Trials of Upper Bounds 27
5.1 Exponential Distribution as Output Distribution . . . . . . . . . . . 27
5.2 Inverse Gaussian Distribution as Output Distribution . . . . . . . . 28
5.3 PIG Distribution as Output Distribution . . . . . . . . . . . . . . . . 32
5.4 Shifted Gamma Distribution as Output Distribution . . . . . . . . . 35
6 Asymptotic Capacity of AIGN Channel 37
6.1 When v Large . . . . . . . . . . . . . . . . . . . . . . . . . 37
6.2 When m Large . . . . . . . . . . . . . .. . . . . . . . . . . . 38
IV
7 Discussion and Conclusion 41
Bibliography 41
V

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