對於一個規則型準循環低密度奇偶檢查碼(regular QC-LDPC Code)，可藉由遮蔽矩陣(masking matrix)的應用，進而產生出新的規則型或非規則型之準循環低密度奇偶檢查碼。遮蔽矩陣的設計好壞對於建構出的新準循環低密度奇偶檢查碼影響非常大，一個結構優良的遮蔽矩陣，不僅只影響碼的行權重及列權重分布，且對於循環(cycle)數量及分布都能達到較好的結果，換句話說，透過精心設計的遮蔽矩陣，可以使規則型或非規則型準循環低密度奇偶檢查碼達到非常低的錯誤率，以符合特殊需求。本論文提出了三種方法來建構遮蔽矩陣，依據相同或接近的維度分布(degree distribution)分別比較其錯誤率優劣，並針對近似循環外信息度(ACE)及陷阱集(trapping set)作細部分析，以快速選取錯誤率表現較好的準循環低密度奇偶檢查碼。除此之外，本論文也對於重樣性取樣做修正，由於原始的重樣性取樣並未考量相同大小及定義的陷阱集對於錯誤率的貢獻不盡相同，若單使用陷阱集內的變量節點分布作為結構區分其實並不太準確，因為陷阱集內變量節點及檢查節點連線的方式也可能不同，因此提出利用錯誤邊界的概念將相同大小及定義的陷阱集分類，找出真正對錯誤率貢獻最多的陷阱集並套用重樣性取樣估計，修正原始重樣性取樣估計的誤差率。另外本論文也對使用循環差集族(CDF)及完美差集族(PDF)建構之行權重為三的準循環低密度奇偶檢查碼作探討，並且直接利用公式找出符合條件的完美差集族，最後討論循環矩陣(circulant)大小和完美差集族及特殊型式循環差集族之關係。

For a regular QC-LDPC code, we can construct a new regular or irregular QC-LDPC code by masking. A masking matrix with good structure not only affects column weights and row weights distribution but also achieves better results for the number of short cycles and cycles distribution in QC-LDPC codes. In other words, a well-design masking matrix could produce a very low error rate QC-LDPC code. This thesis proposes three ways to construct masking matrix based on the same or near degree distribution and compares the performance of them. Additionally, in order to find out the better QC-LDPC code quickly, this thesis also analysis the relationship between ACE, trapping sets and error floor. Furthermore, this thesis proposes a modified importance sampling to reduce to estimation error for error floor. Finally, we find the constrution of PDF with weight-3 by existing difference family formulas and discuss the constraint for circulant size of PDF-based QC-LDPC codes.

Abstract
摘要
第一章 簡介
第二章 基於有限域之準循環低密度奇偶檢查碼建構方法
第三章 錯誤地板現象與遮蔽矩陣介紹
第四章 遮蔽矩陣之設計
第五章 遮蔽矩陣應用於高碼率準循環低密度奇偶檢查碼
第六章 基於CDFs及PDFs建構之準循環低密度奇偶檢查碼
第七章 總結
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