在現代通訊傳輸機制下，產生對碼率相容碼(Rate Compatible Code)的需求進而研究開發，而在碼率相容低密度奇偶檢查碼(RC-LDPC Code)的建造方法上，大致分為三大類型:穿刺(Puncturing)、延展(Extending)及拆分(Splitting)，其在建造上各有優缺點和限制，又以延展及拆分在建造順序上較符合通訊機制中混合式自動重送請求 (Hybrid Automatic Repeat reQuest)的要求，其目標為減少重傳次數來達到高吞吐量(Throughput)，而延展及拆分建造順序為從高碼率建造至低碼率碼容易在高碼率有最佳化碼，因此為了可以混和延展及拆分的優點以及破壞原本建造上的限制，本論文先提出一修改型拆分演算法，將拆分利用在多邊型原模圖碼(Multi Edge type Protograph Codes)上，讓拆分可以廣泛運在任何形式矩陣。本論文也提出了一個基於拆分及延展之建造方法，此建造方法較純拆分或純延展都有較大的彈性，且經由模擬實驗結果可以得到，利用本論文所提出方法與純拆分或純延展比較下有較優異的解碼門檻(Decoding threshold)且在吞吐量表現上亦是如此，再藉由所提出的方法再延伸開發提出一延遲交換方法，延伸運用下可以針對通道環境或者針對某個碼率下，去建造出擁有較優異解碼門檻的碼，並且接著提出一方法來改善實際錯誤率，且最後本論文也與現代通訊傳輸標準碼在不同通道及參數下做比較。

Splitting and extending are popular methods for constructing rate-compatible low-density parity-check (RC-LDPC) codes.
After the code with the highest rate is determined,
both of them can be used to design the low-rate codes,
and individual constraints on the code structures are introduced.
In this thesis,a code construction method based on the combination of splitting and extending is proposed,and a more flexible code structure can be selected for the low-rate codes.
The proposed method can be applied to design quasi-cyclic (QC)-LDPC codes with different length.
A comparable error-rate performance can be achieved compared to the best RC-LDPC codes presented in the previous literature.
When the designed RC-LDPC codes are applied to a variety of channel enviroments e.g.MIMO (multi-input multi-output) and Rayleigh fadding channels,a better error performance can be observed compared to the standard 3GPP Turbo code.

Abstract i

摘要 ii

第一章 簡介 1

第二章 利用延展建造碼率相容低密度奇偶檢查碼及解碼門檻預測方法介紹 3

第三章 利用拆分建造碼率相容低密度奇偶檢查碼介紹 11

第四章 基於拆分及延展碼率相容低密度奇偶檢查碼建構 27

第五章 總結 61

參考文獻 62

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