臺灣博碩士論文加值系統

在本篇論文中，我們探討一個相當新的通道模型，此通道是藉由原子在液體中的交換來傳輸訊號。而我們假設原子在傳輸過程中，是在一維的空間做移動。像是我們將奈米級的儀器放入血管中，而此儀器在人體內和其他儀器交換訊息就是一個很典型的通訊應用。一旦原子被釋放在液體中，將會在液體中進行布朗運動，進而造成我們無法預估原子到達傳輸端的時間，換句話說，布朗運動造成接收時間的不確定性，而此不確定性就是我們的雜訊，而我們用反高斯分布來描述此雜訊。此篇研究重點是相加性雜訊通道，在有平均以及最大延遲的限制下，基本的通道容量趨勢。
我們深入研究此模型，並且分析出新的通道容量的上界與下界，而這些界線是逐漸靠近的，也就是說，如果我們允許平均以及最大延遲放寬到無限到，亦或是介質的流體速度趨近無限大，我們可以得到準確的通道容量。

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. The molecules 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 electromagnetic waves, but we encode our information into 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 with average and peak delay constraints.
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 and peak-delay constraints are loosened to infinity, the corresponding asymptotic capacities are derived precisely.

Contents
1 Introduction 1
1.1 General Molecular Communication Channel Model . . . . . . . . . . 1
1.2 MathematicalModel........................... 2
1.3 Capacity.................................. 4
2 Mathematical Preliminaries 7
2.1 Properties of the Inverse Gaussian Distribution . . . . . . . . . . . . 7 2.2 RelatedLemmasandPropositions ................... 10
3 Known Bounds to the Capacity of the AIGN Channel with Only
an Average Delay Constraint 13
4 Main Result 17
5 Derivations 25
5.1 ProofofUpper-BoundofCapacity ................... 25 5.1.1 For0<α<0.5.......................... 25 5.1.2 For0.5≤α≤1.......................... 29
5.2 ProofofLower-BoundofCapacity ................... 30 5.2.1 For0<α<0.5.......................... 30 5.2.2 For0.5≤α≤1.......................... 34
5.3 AsymptoticCapacityofAIGNChannel ................ 35 5.3.1 WhenTLarge........................... 36 5.3.2 vLarge .............................. 37
6 Discussion and Conclusion 41
List of Figures 43
Bibliography 45

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