為了隱藏物理層的複雜性，我們需要一種抽象的接收器幫助我們進行在Layer2的輸入與輸出流量分析。在先前的論文中，波以松接收器被視為能夠分析編碼隨機接取的數學架構。在本篇論文中，我們進一步提出了確定性且可合併到數學架構中的阿羅哈接收器。阿羅哈接收器的特徵在於成功接收的封包數量的成功函數。受網路演算理論的啟發，我們推導出成功函數的各種代數性質，而它們可以用來證明各種阿羅哈接收器的封閉特性，包括(1)串聯式阿羅哈接收器(2)合作式阿羅哈接收器，(3)帶有流量多路傳輸的阿羅哈接收器，以及(4)具有編碼的阿羅哈接收器。進行廣泛的模擬後，我們證明理論值與模擬值非常吻合。

Motivated by the need to hide the complexity of the physical layer from performance analysis in a layer 2 protocol, a class of abstract receivers, called Poisson receivers, was recently proposed as a probabilistic framework for providing differentiated services in uplink transmissions in 5G networks. In this paper, we further propose a deterministic framework of ALOHA receivers that can be incorporated into the probabilistic framework of Poisson receivers for analyzing coded multiple access with successive interference cancellation. An ALOHA receiver is characterized by a success function of the number of packets that can be successfully received. Inspired by the theory of network calculus, we derive various algebraic properties for several operations on success functions and use them to prove various closure properties of ALOHA receivers, including (i) ALOHA receivers in tandem, (ii) cooperative ALOHA receivers, (iii) ALOHA receivers with traffic multiplexing, and (iv) ALOHA receivers with packet coding. By conducting extensive simulations, we show that our theoretical results match extremely well with the simulation results.

Contents 1
List of Figures 3
List of Tables 4
1 Introduction 5
2 Poisson receivers 9
2.1 Review of the framework of Poisson receivers . . . . . . . . . . . . . . . . 9
2.2 Rayleigh block fading channel with capture . . . . . . . . . . . . . . . . . 11
3 ALOHA Receivers 14
3.1 Definitions and examples of ALOHA receivers . . . . . . . . . . . . . . . 14
3.2 Operations on functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Two ALOHA receivers in tandem . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Two cooperative ALOHA receivers . . . . . . . . . . . . . . . . . . . . . 23
3.5 ALOHA receivers with trac multiplexing . . . . . . . . . . . . . . . . . 25
3.6 ALOHA receivers with packet coding . . . . . . . . . . . . . . . . . . . . 27
3.7 Multiple cooperative D-fold ALOHA receivers . . . . . . . . . . . . . . . 31
4 Numerical results 35
4.1 Two cooperative D-fold ALOHA receivers with URLLC traffic and eMBB traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 Wireless channel model . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1.2 Coded random access for a use case . . . . . . . . . . . . . . . . . 36
4.2 Rayleigh block fading channel with URLLC traffic and eMBB traffic . . . 38
5 Conclusion 40

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