在本篇論文中，我們開發了一個用於分析編碼隨機接取的數學架構。我們的架構是基於波以松接受器，其根據波以松負載給定一個封包一個成功機率函數。我們將波以松接收器的設定推廣到可以容許多個不同種類的輸入流量。透過分析，我們也給出了一個關於超可靠低延遲通訊與增強型的移動寬頻兩種不同流量的數值模擬結果。除此之外，我們也將加密方式推廣到更通用的方式。透過進行廣泛的實驗模擬之後，我們也驗證了我們的理論結果與模擬結果是非常吻合的。

In this thesis, we develop a mathematical framework for analyzing coded random access.
Our framework is based on a Poisson receiver, which is characterized by a success probability function of a tagged packet subject to a Poisson offered load.
We extend Poisson receivers to the setting with multiple classes of input traffic that can provide differentiated service between different classes of input traffic.
Then, we demonstrate that our theory that is useful to provide differentiated services between ultra-reliable low-latency communication (URLLC) traffic and enhanced mobile broadband (eMBB) traffic.
In particular, we extend the tree evaluation method to more general code, (n,k) code.
By conducting extensive simulations, we also verify that our theoretical results match well with the simulation results.

Contents 1
List of Figures 4
1 Introduction 5
2 Slotted ALOHA and Poisson receivers 8
2.1 Slotted ALOHA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Slotted ALOHA in the on-o fading channel with two receivers . . 9
2.2 Poisson receivers with single class of input trac . . . . . . . . . . . . . 11
2.2.1 coded Poisson receiver . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Poisson receivers with multiple classes of input trac 14
3.1 Denition and examples of Poisson receivers with multiple classes of input
trac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 SA with multiple cooperative receivers . . . . . . . . . . . . . . . . . . . 17
3.3 Poisson receivers with packet routing . . . . . . . . . . . . . . . . . . . . 20
1
3.4 Poisson receivers with packet coding . . . . . . . . . . . . . . . . . . . . 22
4 Numerical results 27
4.1 A use case for URLLC trac subject to eMBB cross trac . . . . . . . . 27
4.1.1 A single coded slotted ALOHA (CSA) receiver . . . . . . . . . . . 28
4.1.2 Two cooperative receivers with a common fading channel for both
eMBB trac and URLLC trac . . . . . . . . . . . . . . . . . . 33
4.2 Two cooperative receivers with dierent fading channels for eMBB trac
and URLLC trac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5 Coded Poisson Receiver with (n,k)-code 38
5.1 Tree analysis for (n,k)-code . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Numerial results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6 Conclusion 44

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