極化碼現今多被應用在錯誤更正碼，是現今唯一被嚴格證明能達到香濃極限的編碼技術。而極化碼的解碼演算法中，列表連續消除解碼演算法相較於連續消除演算法，因有較好的解碼性能，於5G通訊之增強型行動頻寬通訊中被廣泛運用。 然而傳統列表連續消除解碼因其計算複雜度較複雜需花費更多的解碼時間，所以本文提出了新的定義列表大小的方法，使其能夠減少列表大小卻能達到相對應列表的解碼性能，以減少解碼所需的時間。 目前已被提出能減少列表連續消除解碼演算法之計算複雜度的方法有以下兩種類別: 提早終止解碼、適應性列表連續消除，本論文基於列表連續消除演算法進行改良，進行分析路徑度量值的範圍 (Path Metric Range) 和歸納出臨界集合(Critical Set)，綜合模擬分析，提出新的定義列表大小的方法，進而減少解碼過程中不必要的解碼路徑，降低整體解碼的計算複雜度。此解碼方法，相較傳統連續消除演算法能減少約$44\%$的計算複雜度。

Polar codes which had been proved to achieve Shannon limit, nowadays, have been applied for channel coding scheme for the enhanced mobile broadband (eMBB) scenario of 5G communication. The successive cancellation (SC) decoding and successive cancellation list (SCL) decoding have been adopted as polar code decoding. Compared to SC decoding, SCL decoding has a better error correction performance but it requires more computational complexity. The conventional SCL decoding splits the decoding path with fixed list size, and it will lead to split unnecessary path which makes the process of decoding increase unnecessary computational complexity. This thesis proposes a new method to redefine the list size in the polar code to reduce the average number of list size. According to the analysis of the path metric range (PMR) and the critical set (CS), the resizing range can be predefined in advance. By analysing the PMR and the critical set, it can be known that error occurs in some specific ranges. Therefore, compared to conventional SCL decoding, the total computational complexity of proposed SCL decoding can be decreased up to 44%.

Abstract I
中文摘要 II
Contents III
List of figures V
List of Tables VIII
1 Introduction 1
1.1 Introduction 1
1.2 Paper Format 2
2 Preliminary 3
2.1 Polar encoding 3
2.2 Successive cancellation decoding 4
2.2.1 Successive cancellation list decoding 5
2.2.2 CRC-aided SCL decoding 6
2.3 Review of efficient SCL decoding method 7
3 The Efficient List Resizing Scheme For SCL Decoding Using Off-line Analysis 11
3.1 Off-line analysis for the list size 12
3.2 Definition of path metric range 13
3.3 Definition of critical set 14
3.4 Proposed list resizing scheme 16
3.4.1 The first step for analysis of resizing range 16
3.4.2 Include critical set for the analysis of resizing range 18
3.4.3 Improvement for the base list size 20
3.5 The reduction of computational complexity 21
3.6 Simulation results 23
3.6.1 Resizing scheme with different conditions 23
3.6.2 Compared with the dynamic SCL decoding 27
3.6.3 Compared with the conventional SCL decoding 31
4 Conclusion 40
Bibliography 41

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