聯合資訊源暨通道編碼(Joint Source-Channel Coding, JSCC)的系統架構可用於解決系統複雜度過高和編碼延遲的問題。若系統複雜度和延遲有嚴格的限制，JSCC優於傳統的分離資訊源暨通道編碼(Separate Source-Channel Coding, SSCC)的系統架構。JSCC的架構可被設計固定長度和可變長度的編碼，在此篇論文中，我們探討在JSCC架構下擁有可有效率地壓縮資訊源且兼顧一定程度的錯誤率表現的可變長度錯誤更正碼(Variable-Length Error-Correcting Codes, VLEC)，其中的自由距離(Free Distance)是影響錯誤率的關鍵參數。最佳化的VLEC設計可基於固定平均碼字長度(Average Codeword Length)下最大化VLEC的自由距離或是固定自由距離下，最小化VLEC的平均碼字長度。我們使用基於交叉熵方法(Cross-Entropy Method)改良成在各種不同的自由距離下界(Free Distance Lower Bound)建構最小化平均碼字長度VLEC的搜尋演算法，稱作交叉熵基底演算法(Cross-Entropy Based Algorithm)。在接收端解碼上，我們使用兩階段序列最大事後機率(Two-phase Sequence Maximum A Posteriori, TPSMAP)解碼器，此解碼器必須知道被傳送的碼字數量和總共位元數(Bit)。在模擬結果中，我們在各種不同的自由距離下界下建構26英文字母資訊源和美國資訊交換標準代碼(American Standard Code for Information Interchange, ASCII)128資訊源的碼字簿還有將碼字簿經過可加高斯白雜訊(Additive White Gussian Noise, AWGN)的符元錯誤率(Symbol Error Rate, SER)表現。

A joint source-channel coding(JSCC) scheme can be considered to solve the problem of system complexity and delay of coding and JSCC scheme performs better than traditional separate source-channel coding(SSCC) sheme under strict limitations of complexity and delay of system. JSCC scheme can be designed fixed length of codes and variable length of codes. In this way, we focus on variable-length error-correcting codes(VLEC) that is capable of compressing source data efficiently with reliable communication under JSCC structure. The free distance is the key parameter of affecting the error performance. The optimal VLECs can be based on maximizing free distance with fixed average codeword length and minimizing average codeword length with fixed free distance. We present cross-entropy based search algorithm at the transmitter and aim at constructing optimal VLECs with minimizing average codeword length satisfying different fixed free distance constraint. Two-phase sequence maximum a posteriori(TPSMAP) decoder is adopted at the receiver that must know the number of transmitted codewords and overall length of transmitted bitstreams. In our simulation result, we construct optimal VLECs for 26-symbol English alphabet source and 128-symbol ASCII source with different free distance constraint and show the symbol error rate performance of VLECs with different free distance constraint.

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 1
第一章 導論 2
1.1 研究背景 3
1.2 研究動機 3
1.3 論文架構 4
第二章VLEC的基本理論 5
2.1自由距離 5
2.2最大事後機率序列解碼 7
2.3建立解碼網狀圖 8
2.4符元錯誤率理論上界 11
第三章交叉熵方法 12
3.1交叉熵方法基本理論 12
3.2交叉熵方法之組合最佳化問題 13
3.3交叉熵方法之組合最佳化建構VLEC 14
第四章交叉熵演算法 17
4.1演算法的前置作業 17
4.2演算法的總體流程 19
4.3演算法的設計機制 23
第五章 模擬結果 25
5.1符元錯誤率表現 25
5.2 VLEC碼字薄 27
第六章 結論 47
參考文獻 48
中英對照表 51
縮寫對照表 54

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