由於簡單性和可擴展性，對於含有大量物聯網設備的非協調性多重接取，使用連續干擾消除 (SIC) 技術的非正則重覆時槽式阿羅哈(IRSA)方案是一種很有前途的解決方法。然而，IRSA的迭代解碼器本質上是循序的，因此可能會因為不完善的SIC導致一連串的錯誤。在本論文中，我們提出了兩個對於IRSA在加性高斯白雜訊通道裡的平行解碼方案。我們的第一個演算法限制在與IRSA中的SIC解碼過程相對應的 SIC 解耦矩陣。為此，我們提出了一種訊息傳遞算法，此演算法可以在當IRSA系統的用戶-時槽二分圖是非循環式的情況下找到最佳的SIC解耦矩陣，此最佳的SIC解耦矩陣可以最小化累積的雜訊。這包含了競爭解決分集時槽式阿羅哈(CRDSA)系統，此系統恰好傳送兩個一模一樣的封包。我們的第二個演算法由第一個演算法進行拓展，將兩個SIC解耦矩陣進行最佳的組合來找到對於CRDSA而言最佳的解耦矩陣。使用隨機圖分析，我們推導出基於閾值的解碼模型下，競爭解決分集時槽式阿羅哈(CRDSA)使用兩種平行解碼演算法的吞吐量。我們也進行了各種數值實驗來說明有限迭代次數的循序解碼與預定義訊雜比(SNR)閾值的平行解碼之間的權衡。我們的數值實驗結果展示了當SNR比解碼閾值大得多時，可以利用平行解碼來顯著減少解碼時間並達到可比較的吞吐量。

Due to its simplicity and scalability, the Irregular Repetition Slotted ALOHA (IRSA) system that uses the successive interference cancellation (SIC) technique is a promising solution for uncoordinated multiple access of a massive number of Internet-of-Things (IoT) devices. However, the peeling (iterative) decoder for IRSA is sequential, and it might lead to cascading errors due to imperfect SIC. In this thesis, we propose two parallel decoding algorithms for IRSA in an additive white Gaussian noise channel. Our first algorithm is limited to SIC-decoupling matrices that correspond to the SIC decoding process in IRSA. For this, we propose a message-passing algorithm to find the optimal SIC-decoupling matrix that can minimize the accumulated noise power when the induced user-slot bipartite graph of an IRSA system is acyclic. This includes the Contention Res olution Diversity Slotted ALOHA (CRDSA) system that sends exactly two copies for each packet as a special case. Our second algorithm extends the first one by finding the optimal decoupling matrix for CRDSA through an optimal combination of two SIC decoupling matrices. Using a random graph analysis, we derive the throughput for the two parallel decoding algorithms of CRDSA in a threshold-based decoding model. We also conduct various numerical experiments to illustrate the tradeoffs between sequential decoding with a limited number of iterations and parallel decoding with a predefined signal-to-noise ratio (SNR) threshold. Our numerical results show that one can significantly reduce the decoding time and achieve comparable throughput by parallel decoding when the SNR is substantially larger than the decoding threshold.

Abstract
Contents-------------------------------------------------------------1
List of Figures------------------------------------------------------2
1 Introduction-------------------------------------------------------3
2 Parallel decoding of IRSA------------------------------------------7
2.1 Review of IRSA--------------------------------------------------7
2.2 Parallel decoding-----------------------------------------------9
2.2.1 The optimization problem-------------------------------------9
2.2.2 Solving the optimization problem for CRDSA------------------11
2.2.3 Solving the optimization problem for IRSA with an acyclic bipartite graph-----------------------------------------------------13
2.2.4 Throughput analysis for parallel decoding of CRDSA----------17
2.3 Compare the performance between sequential decoding and parallel decoding------------------------------------------------------------19
3 General decoupling matrices for CRDSA-----------------------------22
3.1 Further reduction of the accumulated noise power---------------22
3.2 The pseudoinverse for an acyclic bipartite graph of CRDSA------26
3.3 Throughput analysis for parallel decoding of CRDSA by using the pseudoinverse-------------------------------------------------------32
3.4 Performance comparsion between parallel decoding in Section 2.2.4 and parallel decoding by using the pseudoinverse in Section 3.3-----34
4 Conclusion--------------------------------------------------------37

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