# 臺灣博碩士論文加值系統

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 在本篇論文的第一部份，我們探討可逆變異長度編碼在遭遇編碼資料發生錯誤下的解碼特性。我們提出一個可以分析變異長度編碼的正向解碼錯誤偵測與正向解碼錯誤回復特性的數學模型。透過此數學模型，我們推導出描述變異長度編碼的六種錯誤特性的數學公式：正向解碼錯誤偵測機率、正向解碼錯誤回復機率、正向解碼錯誤偵測延遲長度的期望值與變異數、正向解碼錯誤回復延遲長度的期望值與變異數。當此數學模型套用在可逆變異長度編碼時，我們發現先前的六個數學公式中，有三個公式可以進行簡化。我們也推導出描述可逆變異長度編碼的另外六種錯誤特性的數學公式：逆向解碼錯誤偵測機率、逆向解碼錯誤回復機率、逆向解碼錯誤偵測延遲長度的期望值與變異數、逆向解碼錯誤回復延遲長度的期望值與變異數。在本篇論文的第二部份，我們探討可逆變異長度編碼的建構演算法。可逆變異長度編碼的建構演算法可分為兩大類：第一類是以霍夫曼編碼為基礎的建構演算法，第二類是反覆更新編碼的建構演算法。我們在這兩大類各別提出兩個建構演算法：第一個演算法著重在減少編碼累贅，第二個演算法同時考慮減少編碼累贅及提高錯誤偵測機率。
 In part I of this dissertation, we present a model for analyzing the error detection anderror synchronization characteristics of nonexhaustive VLCs. Six indices, the error detectionprobability, the mean and the variance of forward error detection delay length, the errorsynchronization probability, the mean and the variance of forward error synchronizationdelay length are formulated based on this model. When applying the proposed model to thecase of nonexhaustive RVLCs, these formulations can be further simplified. Since RVLCs canbe decoded in backward direction, the mean and the variance of backward error detectiondelay length, the mean and the variance of backward error synchronization delay lengthare also introduced as measures to examine the error detection and error synchronizationcharacteristics of RVLCs. In addition, we found that error synchronization probabilities ofRVLCs with minimum block distance greater than 1 are 0.We study the topics of RVLC construction algorithms in part II of this dissertation.RVLC construction algorithms can be classified into two categories : 1. Huffman codebased RVLC construction algorithms, 2. Iterative RVLC construction algorithms. In eachcategory, we proposed two algorithms : one of them aims at minimizing average codewordlengths while the other proposed algorithm jointly considers minimizing average codewordlengths and maximizing error detection probabilities.
 1 Introduction 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Part I:Characteristics of Error Detection and Error Synchronization ofRVLCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2 Part II:The Construction Algorithms of RVLCs . . . . . . . . . . . . 41.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5I Characteristics of RVLCs 72 Error Detection and Error Synchronization of VLCs and RVLCs 92.1 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Error Detection and Error Synchronization of VLCs . . . . . . . . . . . . . . 102.3 Error Detection and Error Synchronization of RVLCs . . . . . . . . . . . . . 212.4 Comparison of the Error Detection and Error Synchronization Characteristicsof Various RVLCs for a benchmark English Alphabet Source . . . . . . . . . 242.5 Phase Error Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24II RVLC Construction Algorithms 273 Huffman-Code Based RVLC Construction Algorithms 29i3.1 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.2 Algorithms For RVLC Construction . . . . . . . . . . . . . . . . . . . 303.1.3 Algorithms For Constructing Error-Correcting RVLCs . . . . . . . . . 323.2 The Proposed Huffman-code Based Construction Algorithms . . . . . . . . . 343.2.1 A Generic Algorithm for Construction of RVLCs . . . . . . . . . . . . 343.2.2 A Generic Algorithm for Constructing RVLC with Error-CorrectingCapability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 Iterative RVLC Construction Algorithms 514.1 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.1.1 Tseng and Chang’s Algorithm . . . . . . . . . . . . . . . . . . . . . . 514.2 The Proposed Iterative RVLC Construction Algorithms . . . . . . . . . . . . 534.2.1 The Proposed Generic Algorithm for Construction of SymmetricalRVLCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.2 The Proposed Generic Algorithm for Constructing Symmetrical RVLCswith Error Correcting Capabilities . . . . . . . . . . . . . . . . . . . . 544.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56III Future Work 615 Conclusion And Future Works 635.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2.1 Issues on the Construction of RVLCs . . . . . . . . . . . . . . . . . . 645.2.2 Issues on the Decoding of RVLCs in Video Coding Standards . . . . . 645.2.3 Issues on the Theoretical Results of RVLCs . . . . . . . . . . . . . . 65iiAppendix 71A Publication List 71
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(1995) Variable-length error-correcting codes. Ph.D. dissertation, Univ. ofManchester, Manchester, U.K..[22] Y. Takishima, M. Wada, and H. Murakami, ”Reversible variable length codes,” IEEETransactions on Communications, 43, 158-162, 1952.[23] C. -W. Tsai and J. -L. Wu ”On Constructing the Huffman-Code-Based ReversibleVariable-Length Codes,” IEEE Transactions on Communications, vol. 49, pp. 1506-1509, 2001.[24] C. -W. Tsai and J. -L. Wu ”Modified Symmetrical Reversible Variable-Length Codeand Its Theoretical Bounds,” IEEE Transactions on Information Theory, vol. 47, pp.2543-2548, 2001.[25] Lakovi´c, K. and Vallasenor, J, ”An Algorithm for Construction of Efficient Fix-FreeCodes,” IEEE Communications Letters, vol. 7, no. 2, pp. 391-393, 2003.[26] Lakovi´c, K. and Vallasenor, J, ”On Design of Error-Correcting Reversible VariableLength Codes,” IEEE Communications Letters, 6, pp. 337-339, 2004.[27] D. A. Huffman, ”A Method for the Construction of Minimum Redundancy Codes,”Proceeding of the IRE 40, pp. 1098-1101, 1952.[28] Tseng, H. -W. and Chang, C. -C.. ”Construction of Symmetrical Reversible VariableLength Codes Using Backtracking,” The Computer Journal, 46, 100-105, 2003.[29] C. -W. Lin and Y. -J. Chuang and J. -L. Wu ”Generic construction algorithms for symmetricand asymmetric RVLCs,” Proceedings of ICCS ’02, Singapore, 25-28 November,vol. 2, pp. 968-972, 2002.[30] Tseng, H. -W. and Chang, C. -C.. ”A Branch-and-Bound Algorithm for the Construcitonof Reversible Variable Length Codes,” The Computer Journal, 47, pp. 701-707, 2004.[31] Jin Wang, Lie-Liang Yang and Lajos Hanzo, ”Iterative Construction of ReversibleVariable-Length Codes and Variable-Length Error-Correcting Codes,” IEEE CommunicationsLetters, 6, pp. 671-673, 2004.[32] Sunil Kumar and Liyang Xu, ”RVLC decoding scheme for improved data recovery inMPEG-4 video coding standard,” Real-Time Imaging, pp. 315V323, 2004.[33] Jennifer L. H. Webb, ”Efficient table access for reversible variable-length decoding”,IEEE Trans. Circuits and Systems for Video Technology, vol. 11, pp. 981-985, 2001.[34] K-L Chung and H-N Chen, ”On decoding MPEG-4 reversible variable length codes,”Signal Processing: Image Communication, 20(2), pp. 187-192, 2005.
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