在這篇論文中，我們想利用基因演算法(Genetic Algorithm, GA)去建構在訊號源-通道聯合編碼(Jointly Source-Channel Coding, JSCC)的傳輸架構下的可變長度錯誤更正碼(Variable- Length Error-Correcting Code, VLEC)，並針對某些自由距離下界(Free Distance Lower Bound)來建構一組平均碼長(Average Codeword Length)較小的碼字簿。為了達到此目的，我們修改不能適用在變長度碼的傳統型基因演算法，針對降低演化複雜度與符元錯誤率(Symbol Error Rate, SER)提出能適用在演化可變長度錯誤更正碼的改良式基因演算法。模擬分析結果中，比較文獻與我們的碼字簿之符元錯誤率，結果我們所建構碼字簿的錯誤率不管在可加性高斯白雜訊(Additive White Gaussian Noise, AWGN)或雷利衰減通道(Rayleigh Fading Channel)的錯誤率兩方都差不多，甚至更好；在建構相同條件的碼字簿方面，我們的碼字簿其平均碼長與文獻比較幾乎比他們更短，顯然有更好的解被我們找出。

In this thesis, we want to use genetic algorithms (GA) to construct the variable length error correcting codes (VLEC) in the transmission system of joint source-channel coding (JSCC) and construct codebooks with smaller average codeword length for some free distance lower bound. To achieve this goal, we modify the traditional genetic algorithm for variable length codes. For reducing the evolution of complexity and symbol error rate(SER) which proposed new genetic algorithm can be applied in the evolution of variable length error correcting codes. Simulation results, we compare the SER of our codebooks with reference and have almost error performance in additive white Gaussian noise (AWGN) channel and Rayleigh fading channel, even have better error performance in tern of same condition. We find some codebooks’ average codeword length that shorter than reference, obviously we have a better solution is to find out.

論文審定書 i
誌謝 ii
中文摘要 iii
Abstract iv
目錄 v
圖次 vii
表格目次 viii
第一章 導論 1
1.1 研究背景 2
1.2 研究動機 2
1.3 論文架構 3
第二章 編碼與演算法介紹 4
2.1 訊號源與通道聯合編碼 4
2.2 可變長度錯誤更正碼 6
2.3 基因演算法 7
第三章 可變長度錯誤更正碼 8
3.1 自由距離 8
3.2 序列最大事後機率解碼 9
3.3 建立可變長度錯誤更正碼樹狀圖 11
3.4 變長度錯誤前置更正碼的理論錯誤率 14
第四章 建構可變長度錯誤更正碼 15
4.1 基因演算法基本架構 15
4.1.1 交配 16
4.1.2 突變 18
4.1.3 選擇 18
4.2 使用改良型基因演算法建構VLEC 19
4.2.1 建構符元數量不同的VLEC碼字簿 19
4.2.2 碼長演化 25
4.2.3 演算法總體流程 26
第五章 模擬結果 29
5.1 符元錯誤率分析 29
5.2 比較VLEC各項數值 32
第六章 結論 44
參考文獻 45
中英對照表 51
縮寫對照表 55

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