本文提出了一種卷積編碼波以松接收器(Convolutional Coded Poisson Receivers, CCPRs)的框架，將空間耦合技術融入到波以松接收器的結構中。我們引入機率密度演化(density evolution)方程式，使用連續干擾消除(Successive Interference Cancellation, SIC)演算法追蹤封包解碼過程。此外，在通訊通道在可以使用阿羅哈接收器建模時，我們推導出穩定區域（編碼波以松接收器和卷積編碼波以松接收器均能以機率1成功接收每個封包的區域）之上界。同時，我們還利用位能理論專門分析了單一類別用戶的情形下穩定區域的上界。此上界推廣了空間耦合不規則重複時槽阿羅哈 (Irregular Repetition Slotted ALOHA, IRSA)協議的上界，且只要這些模型可以表示為波以松接收器，則同樣適用於具有多個流量類別的通訊通道模型。此外，我們通過位能理論確定了構建卷積編碼波以松接收器的窗口大小條件，以確保相對於傳統卷積編碼波以松接收器具有更大的滲透閾值(percolation threshold)。對於多類別接收器與多類別使用者的情型，我們遞歸地計算機率密度演化方程式，以確定穩定區域的邊界。數值結果表明，通過利用空間耦合方法，相較於編碼波以松接收器，卷積編碼波以松接收器的穩定區域可能會擴大。

In this paper, we present a framework for convolutional coded Poisson receivers (CCPRs) that incorporates spatial coupling into the architecture of coded Poisson receivers (CPRs). We use density evolution equations to track the packet decoding process with the successive interference cancellation (SIC) technique. When the underlying channel can be modeled by a $
hi$-ALOHA receiver, we derive outer bounds for the stability region of CPRs, which guarantee that every packet can be successfully received with a probability of 1. Our outer bounds extend those of the spatially-coupled Irregular Repetition Slotted ALOHA (IRSA) protocol and are applicable to channel models with multiple traffic classes. Like convolutional Low-Density Parity-Check (LDPC) codes and the spatially coupled IRSA, we prove that the stability region is not smaller than that of the conventional CPR and it converges as the number of stages of CCPRs goes to infinity. For CCPRs with a single class of users, such a stability region is reduced to an interval and it can be characterized by a percolation threshold. By deriving the potential function of the base CPR used for the construction of a CCPR, we prove that the CCPR is stable if the offered load is below its percolation threshold (under a technical condition for the window size). For the multiclass scenario, we recursively evaluate the density evolution equations to determine the boundaries of the stability region. Numerical results demonstrate that the stability region of CCPRs can be enlarged compared to that of CPRs by leveraging the spatial coupling method.

中文摘要i
Abstract ii
Acknowledgements iv
List of Figures vii
List of Tables viii
1 Introduction 1
2 Review of the framework of coded Poisson receivers 6
2.1 Poisson receivers and ALOHA receivers . . . . . . . . . 6
2.2 Coded Poisson receivers with multiple classes of users
and receivers . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Outer bounds for the stability region 16
4 Convolutional coded Poisson receivers 25
4.1 Circular convolutional coded Poisson receivers . . . . . 25
4.2 Stability and threshold saturation . . . . . . . . . . . . . 28
5 Percolation thresholds of systems with a single class of users 33
5.1 The percolation threshold of the (T,G,Λ(x),R,F)-CPR
with one class of users and one class of receivers . . . . 34
5.2 The saturation theorem for the convolutional (T,G,Λ(x),R,F,w)-
CPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3 An upper bound for the potential threshold . . . . . . . . 47
6 Numerical results 51
6.1 Convolutional coded Poisson receivers with one class of
users and one class of receivers . . . . . . . . . . . . . . 51
6.2 IRSA with two classes of users and two classes of receivers 53
7 Conclusion 57
Bibliography 59
A Density evolution for the circular convolutional CPR with L
stages in Corollary 13 68
B Proof of Theorem 23 73
C List of notations 87

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