臺灣博碩士論文加值系統

濾波器組有釵h的應用，在釵h成左瑰野峇丹p影音訊號和任意碼率錯誤更正碼，本論文最主要是討論在有限場中的泛正濾波器組，這濾波器組有節約能源的性質且有能夠完全重建的優點，並在2×2矩陣的狀況下，介紹利用基本建構塊和分解的方法，Wimax技術是利用IEEE802.16e空氣介面的標準建立，Wimax空氣介面是採用正交分頻多工存取技術，論文中主要是介紹OFDMA訊框的結構，LDPC碼近來被注意是因為編碼增益接近謝農極限，並且被應用在釵h地方如資料存取、CDMA，特別是在OFDM系統，利用幾何方法建立LDPC碼，這方法是基於有限幾何點和線的基礎，在有限場中分別有歐基理德幾何(EG)和投影幾何(PG)兩種方法，本論文最主要是討論投影幾何的LDPC Codes。

Filter banks have many applications. For many successful applications like video,audio signals and arbitrary-rate error-correcting codes. This thesis focuses on the class of paraunitary(PU) filter banks over finite fields. This filter banks have property of energy conservation and have the advantage that have a perfect reconstruction(PR).Introducing that use elementary building blocks and a factorization technique for the case 2×2 over fields of characteristic two.The Wimax technology is based on IEEE802.16e Air Interface Standard. The Wimax Air Interface adopts Orthogonal Frequency Division Multiple Access(OFDMA).In thesis major introduces OFDMA frame structure.LDPC codes recently be noted because it can achieve near Shannon limit error performance and applied to several applications such as data storage,CDMA,especially to OFDM systems. The construction of LDPC codes are from a geometric approach. The construction is based on the lines and points of a finite geometry. Well-known finite geometries are Euclidean and projective geometries over finite fields. This thesis focuses on the class of projective geometries.

誌謝 Ⅰ
中文摘要 Ⅱ
英文摘要 Ⅲ
圖片目錄 VIII
表格目錄 IX
第一章 緒論 1
1.1 簡介 1
1.2 研究動機 3
1.3 論文架構 4
第二章 有限場(Finite Fields) 5
2.1 場(Fields) 5
2.2 二位元場的計算 6
2.3 Galois Fields的建立 12
第三章 泛正濾波器組 17
3.1 有限場GF(2)中的泛正(paraunitary)濾波器組(filter banks)的介紹 17
3.2有限場GF(2r)中的泛正濾波器組的介紹 21
3.3 符號和定義 23
3.4 GF(2)中的正仁x陣 25
3.5在GF(2r)中的正仁x陣 26
3.6在GF(2)中的泛正矩陣和濾波器組 30
3.6.1 GF(2)中泛正的濾波器組 31
3.7在GF(2r)中的泛正矩陣 32
3.7.1 GF(2r)中2×2泛正矩陣的性質 34
3.8一階的泛正系統和分解 36
3.8.1 一階建構塊的基本性質 37
3.8.2利用D(z)簡化一階系統 38
3.9二階泛正系統的建構塊和分解 40
3.9.1 K(z)的基本性質 42
3.9.2用K(z)簡化二階系統 43
3.10 GF(2r)中泛正矩陣的分解 45
3.11 GF(2r)中的一階泛正矩陣 46
3.12 GF(2r)中的二階泛正矩陣 47
3.13 GF(2r)中2×2級數-2τ泛正建構塊 48
3.14 GF(2r)中2×2泛正矩陣的分解 50
第四章 802.16無限都會網路(WirelessMAN)OFDMA 實體層(PHY) 54
4.1 802.16介紹 54
4.2 實體層介紹 57
4.3 OFDMA符號描述 57
4.4 OFDMA重要的係數 59
4.5 OFDMA的基本項目定義 61
4.5.1 slot和資料區域 61
4.5.2 Segment 63
4.5.3 排列區域(Permutation Zone) 64
4.6訊框結構 64
4.7 符號結構 67
4.7.1 下行中PUSC的符號結構 70
4.7.2 下行中FUSC的符號結構 71
4.7.3 下行中OFUSC的符號結構 72
4.7.4 上行中PUSC的符號結構 73
4.7.5 上行中OPUSC的符號結構 74
第五章 PG-LDPC Codes 75
5.1 LDPC背景歷史 75
5.2 LDPC基礎介紹 77
5.3投射幾何(projective geometry)和投射幾何碼 78
5.4 PG-LDPC碼 85
第六章 結論 94
附錄一 3.14節中例3 matlab程式碼 95
附錄二 PG(2,23) LDPC codes 98
參考文獻 100

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