臺灣博碩士論文加值系統

本文提出一個提高區塊渦輪碼（Block Turbo Codes，稱BTC）改錯效能之想法。在Ramesh Mahendra Pyndiah之「Near-Optimum Decoding of Product Codes：Block Turbo Codes」論文中，作者以最大事後機率（maximum a posteriori，MAP）去尋找競爭碼（competing codeword），但在尋找競爭碼的過程中，有可能無法找到競爭碼之情況發生，而以參數β來近似之，因此，相對的其改錯效能無法達到最佳化。

本文提出一個簡便、複雜度低的方法來找出計算渦輪區塊碼之extrinsic information所需要的競爭碼，而非以前述論文中之參數β來近似。我們在每次遞回運算中，藉由三個限制條件實際找出競爭碼而非近似的方式來計算軟式輸出，成功地在低複雜度下提升BTC之改錯效能。

In [18], Ramesh Mahendra Pyndiah uses the maximum a posteriori (MAP) theorem to search the competing codeword, but perhaps appeal the condition that can’t find the competing codeword, then he uses a parameter β, according to the iteration times increasing, extrinsic information is more correct and the value of parameter β also increasing, to approximate. Relatively, the performance of BER can’t achieve optimization.

It is an interest topic that how to use the simplest and lowest complex method to find the competing codeword of BTC without using parameter β. In each iteration, we use three limit criteria to find the competing codeword. We expect that the non- approximate method can promote the performance under low complex.

目錄
指導教授同意書…………………………………………………………I

口試委員會審定書……………………………………………………II

授權書…………………………………………………………………III

致謝……………………………………………………………………IV

中文摘要………………………………………………………………VI

Abstract………………………………………………………………VII

第一章 序論……………………………………………………………1
1.1研究背景………………………………………………………1
1.2研究方法………………………………………………………3
1.3論文架構………………………………………………………4


第二章 硬式與軟式解碼演算法簡介…………………………………5
2.1 高斯雜訊………………………………………………………8
2.2 硬式判斷………………………………………………………9
2.2.1 最大事後機率法則……………………………………9
2.2.2 最大概似機率法則……………………………………10
2.3 軟式判斷……………………………………………………11
2.4 硬式與軟式解碼演算法……………………………………12
2.4.1 硬式解碼演算法………………………………………13
2.4.2 軟式解碼演算法………………………………………13
2.5 硬式與軟式解碼效能之比較………………………………14

第三章 基於可靠度之解碼演算法……………………………………16
3.1 基於不可靠位元解碼演算法………………………………16
3.1.1 Chase-II解碼演算法…………………………………17
3.1.2 Chase-II演算法的解碼效能…………………………20
3.2 基於可靠位元解碼演算法…………………………………21
3.2.1 次序統計解碼演算法…………………………………21
3.2.2 次序統計演算法的解碼效能…………………………26

第四章 區塊渦輪碼……………………………………………………27
4.1 乘積碼………………………………………………………28
4.2 區塊渦輪碼…………………………………………………29
4.3 區塊渦輪碼之改錯效能……………………………………34

第五章 區塊渦輪碼之競爭碼搜尋技術………………………………35
5.1與最佳碼相對關係之競爭碼搜尋技術………………………35
5.2 模擬結果分析………………………………………………40
5.3 複雜度分析…………………………………………………42

第六章 結論與未來展望………………………………………………44
6.1結論……………………………………………………………44
6.2 未來展望……………………………………………………45

參考文獻………………………………………………………………46

圖目錄
圖2-1 數位通訊系統架構………………………………………………7
圖2-2 高斯雜訊之機率密度函數………………………………………8
圖2-3 接收訊號之機率密度函數………………………………………8
圖2-4 （7,4）漢明碼之硬式與軟式解碼演算法之效能比較………15
圖3-1 Chase演算法之幾何表示圖……………………………………18
圖3-2 Chase演算法之流程圖…………………………………………19
圖3-3 (23,12)格雷碼（Golay code）以Chase演算法解碼之效能…20
圖3-4次序統計解碼演算法次序之多寡所產生的碼字範圍幾何圖
…………………………………………………………………24
圖3-5 次序統計解碼演算法流程圖…………………………………25
圖3-6 （23,12）格雷碼利用次序統計解碼演算法之解碼效能…26
圖4-1 乘積碼之架構圖………………………………………………28
圖4-2碼字相對關係示意圖…………………………………………32
圖4-3 區塊渦輪碼之區塊圖…………………………………………32
圖4-4 區塊渦輪碼之流程圖…………………………………………33
圖4-5 [BCH(64,57,4)]2區塊渦輪碼之改錯效能……………………34
圖5-1 碼字相對關係示意圖…………………………………………36

圖5-2 區塊渦輪碼與最佳碼相對關係之競爭碼搜尋技術之流程圖
…………………………………………………………………39
圖5-3 [BCH(64,57,4)]2區塊渦輪碼之競爭碼搜尋技術之改錯效能
…………………………………………………………………40
圖5-4 [BCH(64,57,4)]2區塊渦輪解碼（虛線）與競爭碼搜尋技術解
碼（實線）改錯效能比較……………………………………41

表目錄
表5-1 格雷碼改錯的數目及碼字權重之相對關係表………………37
表5-2 [BCH(64,57,4)]2區塊渦輪碼找不到競爭碼的次數統計表
………………………………………………………………42

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