在本論文中，我們提出一種適用於自動重傳請求(HARQ)碼率相容低密度檢查碼(RC-LDPC Codes)的建造方式。碼率相容低密度檢查碼可由穿刺(Puncturing)、延展(Extension)、拆分(Splitting)等三種方法建構，但在需要多個碼率相容碼時，三種建造方式皆無法達到好的錯誤表現。

由於傳統分析解碼門檻(Threshold)的方式無法觀察低密度檢查碼(LDPC Codes)在錯誤平層(Error-Floor Region)的性能，我們的方法除了使用 P-EXIT Chart 分析解碼門檻之外，還加上漸進環外訊息度(ACE)的比較作為決碼設計的條件，並設計出結合延展碼與拆分碼的建碼機制。所完成的RC-LDPC碼從碼率4/5到1/3，不只解碼門檻更接近於沈農極限(Shannon Limit)，也有更低的錯誤平層性能，與純延展法以及純拆分法相比，在大範圍的訊雜比(SNR)變化中能達到更好的錯誤表現。

將本論文所建造的RC-LDPC碼應用到IR-HARQ系統中，為了能進一步改善吞吐量(Throughput)，提出增量解碼(incremental decoding)搭配解碼牌程(decoding scheduling)的設計，使用最大互消息增加(Maximum Mutual Information Increase)演算法製作適用於RC-LDPC碼的解碼排程，在使用增量解碼搭配解碼排程下，即使疊帶次數受限仍能達到高吞吐量。

Incremental Redundancy Hybrid Automatic Repeat reQuest (IR-HARQ) is a popular scheme to achieve high throughput and be used in many communication systems. The rate-compatible codes are suitable for IR-HARQ and usually can be realized using puncturing, extension or splitting. However, all of them can not provide a satisfactory error performance over a wide range of code rates.


In this thesis, the code construction scheme based on low density parity check (RC-LDPC) codes is proposed. In order to achieve a more flexible code construction over a wide range of code rates, the extension and splitting are combined in our design. The Approximate Cycle Extrinsic (ACE) message degree is also equiped to lower the error-floor, which is never considered in the previous RC-LDPC code construction scheme. The RC-LDPC codes from rate-4/5 to 1/3 which satisfactory error rate performance and low error-floor are demonstrated. In addition, the error-floor performance of the proposed RC-LDPC codes have been significiantly improved comparing to that the previous design using pure extension or splitting.

In order to further improve the throughput, the incremental decoding is introduced and the decoding schedules are arranged by Maximum Mutual Information Increase ($M^2I^2$)-based algorithm. The system can achieve high throughput even if the number of iterations is limited.

Abstract - I
中文摘要 - II
Chapter 1 Introduction - 1
Chapter 2 Reviews of RC-LDPC Codes Constructions - 3
Chapter 3 Constructions of RC-LDPC Codes based on Extension and Splitting - 13
Chapter 4 Scheduling for RC-LDPC Codes used in IR-HARQ - 31
Chapter 5 Conclusion - 49
Bibliography - 50

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