by Hau Ka Pun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 102-[103]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- A General Review of MDCS --- p.1 / Chapter 1.2 --- MDCS with Independent Data Streams --- p.4 / Chapter 1.3 --- Admissible Coding Rate Region --- p.5 / Chapter 1.4 --- Distribution of Information in Different Encoders --- p.6 / Chapter 1.5 --- Multilevel Diversity Coding by Superposition --- p.8 / Chapter 1.6 --- Optimality of Superposition --- p.11 / Chapter 1.7 --- Different MDCS coding schemes --- p.17 / Chapter 2 --- MDCS's with Three Encoders --- p.20 / Chapter 2.1 --- 2-level-3-encoder MDCS --- p.21 / Chapter 2.2 --- 3-level-3-encoder MDCS --- p.31 / Chapter 3 --- Symmetrical Multilevel Diversity Coding System --- p.49 / Chapter 3.1 --- Introduction --- p.49 / Chapter 3.2 --- "SMDCS[2,m,(l,m)]" --- p.53 / Chapter 3.3 --- "SMDCS[3， m,(l,2,m)]" --- p.56 / Chapter 3.4 --- "SMDCS[3,m,(l,3,m)]" --- p.62 / Chapter 3.5 --- "SMDCS[4,4, (1,2,3,4)]" --- p.66 / Chapter 4 --- Convex Analysis of Coding Rate Region of DCS --- p.72 / Chapter 4.1 --- Introduction --- p.72 / Chapter 4.2 --- Polyhedral Sets --- p.73 / Chapter 4.3 --- Addition of Polyhedral Sets --- p.75 / Chapter 4.4 --- Algorithms to Enumerate Extreme Points and Decompose Tuples --- p.86 / Chapter 5 --- Conclusion and Further Research --- p.90 / Chapter 5.1 --- Conclusion --- p.90 / Chapter 5.2 --- Suggestions for Further Research --- p.91 / Appendix --- p.93 / Chapter A --- Proof of Equivalence of rsp and Rsp in Chapter3 --- p.93 / Chapter A.1 --- r2m1m and R2m1m --- p.93 / Chapter A.2 --- r33123 and R33123 --- p.94 / Chapter A.3 --- r441234 and. R441234 --- p.96 / Chapter B --- A Class of MDCS Where Superposition is Always Not Optimal --- p.99 / Bibliography --- p.102

by Chun-tat See. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / ACKNOWLEDGEMENTS --- p.i / ABSTRACT --- p.ii / NOTATIONS --- p.iv / TABLE OF CONTENTS --- p.vi / Chapter 1. --- INTRODUCTION --- p.1-1 / Chapter 1.1 --- Introduction --- p.1-1 / Chapter 1.2 --- A Basic Transform Coding System --- p.1-2 / Chapter 1.3 --- Thesis Organization --- p.1-5 / Chapter 2. --- DYADIC MATRICES AND THEIR APPLICATION --- p.2-1 / Chapter 2.1 --- Introduction --- p.2-1 / Chapter 2.2 --- Theory of Dyadic Matrix --- p.2-2 / Chapter 2.2.1 --- Basic Definitions --- p.2-3 / Chapter 2.2.2 --- Maximum Size of Dyadic Matrix --- p.2-8 / Chapter 2.3 --- Application of Dyadic Matrix in Generating Orthogonal Transforms --- p.2-13 / Chapter 2.3.1 --- Transform Performance Criteria --- p.2-14 / Chapter 2.3.2 --- "[T1] = [P]Diag([DM2(4)],[A(4)])[Q]" --- p.2-19 / Chapter 2.3.3 --- "[T2] = [P]Diag([DM2(4)],[DM2(4)])[Q]" --- p.2-21 / Chapter 2.4 --- Discussion and Conclusion --- p.2-26 / Chapter 3. --- LOW SEQUENCY COEFFICIENT TRUNCATION (LSCT) CODING SCHEME --- p.3-1 / Chapter 3.1 --- Introduction --- p.3-1 / Chapter 3.2 --- DC Coefficient Estimation Schemes --- p.3-2 / Chapter 3.2.1 --- Element Estimation --- p.3-2 / Chapter 3.2.2 --- Row Estimation --- p.3-4 / Chapter 3.2.3 --- Plane Estimation --- p.3-7 / Chapter 3.3 --- LSCT Coding Scheme 1 and Results --- p.3-11 / Chapter 3.4 --- LSCT Coding Scheme 2 and Results --- p.3-17 / Chapter 3.5 --- Discussions and Conclusions --- p.3-21 / Chapter 4. --- VARIABLE BLOCK SIZE (VBS) CODING SCHEME --- p.4-1 / Chapter 4.1 --- Introduction --- p.4-1 / Chapter 4.2 --- Chen's VBS Coding Scheme and Its Limitation --- p.4-3 / Chapter 4.3 --- VBS Coding Scheme With Block Size Determined Using Edge Discriminator --- p.4-6 / Chapter 4.4 --- Simulation Results --- p.4-8 / Chapter 4.5 --- Discussions and Conclusions --- p.4-12 / Chapter 5. --- ENHANCEMENT OF JPEG INTERNATIONAL STANDARD --- p.5-1 / Chapter 5.1 --- Introduction --- p.5-1 / Chapter 5.2 --- The Basic JPEG International Standard --- p.5-2 / Chapter 5.2.1 --- Level Shift and Discrete Cosine Transform --- p.5-4 / Chapter 5.2.2 --- Uniform Quantization --- p.5-5 / Chapter 5.2.3 --- Coefficient Coding --- p.5-7 / Chapter 5.3 --- Efficient DC Coefficients Encoding --- p.5-8 / Chapter 5.3.1 --- The Minimum Edge Difference (MED) Predictor --- p.5-8 / Chapter 5.3.2 --- Simulation Results --- p.5-9 / Chapter 5.3.3 --- Pixel Domain Predictors --- p.5-13 / Chapter 5.3.4 --- Discussion and Conclusion --- p.5-15 / Chapter 5.4 --- JPEG Scheme Using Variable Block Size Technique --- p.5-15 / Chapter 5.4.1 --- Scheme 1 --- p.5-16 / Chapter 5.4.2 --- Scheme 2 --- p.5-25 / Chapter 5.4.3 --- Scheme 3 --- p.5-27 / Chapter 5.4.4 --- Scheme 4 --- p.5-29 / Chapter 5.4.5 --- Scheme 5 --- p.5-32 / Chapter 5.4.6 --- Discussions and Conclusions --- p.5-32 / Chapter 5.5 --- Conclusions --- p.5-33 / Chapter 6. --- CONCLUSIONS --- p.6-1 / Chapter 6.1 --- Summary of Research Work --- p.6-1 / Chapter 6.2 --- Contributions of Work --- p.6-2 / Chapter 6.3 --- Suggestions for Further Research --- p.6-3 / Chapter 7. --- REFERENCES --- p.7-1 / RESULTS

by Pui-chiu Yip. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 92-94.

by Chunxuan Ye. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 74-[78]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Information Theory --- p.1 / Chapter 1.2 --- Source Coding --- p.2 / Chapter 1.3 --- Fixed Length Codes and Variable Length Codes --- p.4 / Chapter 1.4 --- Prefix Codes --- p.5 / Chapter 1.4.1 --- Kraft Inequality --- p.7 / Chapter 1.4.2 --- Huffman Coding --- p.9 / Chapter 2 --- Existence of Fix-Free Codes --- p.13 / Chapter 2.1 --- Introduction --- p.13 / Chapter 2.2 --- Previous Results --- p.14 / Chapter 2.2.1 --- Complete Fix-Free Codes --- p.14 / Chapter 2.2.2 --- Ahlswede's Results --- p.16 / Chapter 2.3 --- Two Properties of Fix-Free Codes --- p.17 / Chapter 2.4 --- A Sufficient Condition --- p.20 / Chapter 2.5 --- Other Sufficient Conditions --- p.33 / Chapter 2.6 --- A Necessary Condition --- p.37 / Chapter 2.7 --- A Necessary and Sufficient Condition --- p.42 / Chapter 3 --- Redundancy of Optimal Fix-Free Codes --- p.44 / Chapter 3.1 --- Introduction --- p.44 / Chapter 3.2 --- An Upper Bound in Terms of q --- p.46 / Chapter 3.3 --- An Upper Bound in Terms of p1 --- p.48 / Chapter 3.4 --- An Upper Bound in Terms of pn --- p.51 / Chapter 4 --- Two Applications of the Probabilistic Method --- p.54 / Chapter 4.1 --- An Alternative Proof for the Kraft Inequality --- p.54 / Chapter 4.2 --- A Characteristic Inequality for ´ب1´ة-ended Codes --- p.59 / Chapter 5 --- Summary and Future Work --- p.69 / Appendix --- p.71 / A Length Assignment for Upper Bounding the Redundancy of Fix-Free Codes --- p.71 / Bibliography --- p.74

by Ho Kin Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 68-69). / Abstracts in English and Chinese. / Chapter 0 --- Introduction --- p.5 / Chapter 1 --- Introduction to Coding Theory --- p.9 / Chapter 1.1 --- Definition of a code --- p.10 / Chapter 1.2 --- Maximum Likelihood Decoding --- p.11 / Chapter 1.3 --- Syndrome Decoding --- p.12 / Chapter 1.4 --- Two Kinds of Errors and Concatenated Code --- p.14 / Chapter 2 --- Basic Knowledge of Algebraic Curve --- p.16 / Chapter 2.1 --- Affine and Projective Curve --- p.16 / Chapter 2.2 --- Regular Functions and Maps --- p.17 / Chapter 2.3 --- Divisors and Differential forms --- p.19 / Chapter 2.4 --- Riemann-Roch Theorem --- p.21 / Chapter 3 --- Construction of Algebraic Geometric Code --- p.23 / Chapter 3.1 --- L-construction --- p.23 / Chapter 3.2 --- Ω -construction --- p.24 / Chapter 3.3 --- Duality --- p.26 / Chapter 4 --- Basic Error Processing --- p.28 / Chapter 4.1 --- Error Locators and Syndromes --- p.28 / Chapter 4.2 --- Finding an Error Locator --- p.29 / Chapter 5 --- Full Error Processing for Code on Curve of Genus1 --- p.34 / Chapter 5.1 --- Syndrome table --- p.34 / Chapter 5.2 --- Syndrome table --- p.36 / Chapter 5.3 --- The algorithm of Full Error Processing --- p.38 / Chapter 5.4 --- A simple Example --- p.40 / Chapter 6 --- General Full Error Processing --- p.47 / Chapter 6.1 --- Row Candidate and Column Candidate --- p.47 / Chapter 6.2 --- Consistency --- p.49 / Chapter 6.3 --- Majority voting --- p.50 / Chapter 6.4 --- Example --- p.53 / Chapter 7 --- Application of Algebraic Geometric Code --- p.60 / Chapter 7.1 --- Communication --- p.60 / Chapter 7.2 --- Cryptosystem --- p.62 / Bibliography

Consumption and production of video signals drastically changed in recent years. Due to the advances in digital consumer technology and the growing availability of fast and reliable internet connections, an increasing amount of digital video sequences are being produced, stored and shared every day in different parts of the world. Video signals are inherently larger in size than other types of multimedia signals. For this reason in order to allow transmission and storage of such data, more efficient compression technology is needed. In this thesis novel methods for enhancing the efficiency of current and next generation video codecs are investigated. Several aspects of interest to video coding technology are taken into account, from computational complexity and compliance to standardisation efforts, to compression efficiency and quality of the decoded signals. Compression can be achieved exploiting redundancies by computing a prediction of a part of the signal using previously encoded portions of the signal. Novel prediction methods are proposed in this thesis based on analytical or statistical models with the aim of providing a solid theoretical basis to support the algorithmic implementation. It is shown in the thesis that appropriately defined synthetic content can be introduced in the signal to compensate for the lack of certain characteristics in the original content. Some of the methods proposed in this thesis aim to target a broader set of use cases than those typically addressed by conventional video coding methods, such as ultra high definition content or coding under high quality conditions.

by Yan Cho Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 122-124). / Abstract also in Chinese. / Chapter 1 --- Complex algebraic curves --- p.6 / Chapter 1.1 --- Foundations --- p.6 / Chapter 1.1.1 --- Hilbert Nullstellensatz --- p.6 / Chapter 1.1.2 --- Complex algebraic curves in C2 --- p.9 / Chapter 1.1.3 --- Complex projective curves in P2 --- p.11 / Chapter 1.1.4 --- Affine and projective curves --- p.13 / Chapter 1.2 --- Algebraic properties of complex projective curves in P2 --- p.16 / Chapter 1.2.1 --- Intersection multiplicity --- p.16 / Chapter 1.2.2 --- Bezout's theorem and its applications --- p.18 / Chapter 1.2.3 --- Cubic curves --- p.21 / Chapter 1.3 --- Topological properties of complex projective curves in P2 --- p.23 / Chapter 1.4 --- Riemann surfaces --- p.26 / Chapter 1.4.1 --- Weierstrass &-function --- p.26 / Chapter 1.4.2 --- Riemann surfaces and examples --- p.27 / Chapter 1.5 --- Differentials on Riemann surfaces --- p.28 / Chapter 1.5.1 --- Holomorphic differentials --- p.28 / Chapter 1.5.2 --- Abel's Theorem for tori --- p.31 / Chapter 1.5.3 --- The Riemann-Roch theorem --- p.32 / Chapter 1.6 --- Singular curves --- p.36 / Chapter 1.6.1 --- Resolution of singularities --- p.37 / Chapter 1.6.2 --- The topology of singular curves --- p.45 / Chapter 2 --- Coding theory --- p.48 / Chapter 2.1 --- An introduction to codes --- p.48 / Chapter 2.1.1 --- Efficient noiseless coding --- p.51 / Chapter 2.1.2 --- The main coding theory problem --- p.56 / Chapter 2.2 --- Linear codes --- p.58 / Chapter 2.2.1 --- Syndrome decoding --- p.63 / Chapter 2.2.2 --- Equivalence of codes --- p.65 / Chapter 2.2.3 --- An introduction to cyclic codes --- p.67 / Chapter 2.3 --- Special linear codes --- p.71 / Chapter 2.3.1 --- Hamming codes --- p.71 / Chapter 2.3.2 --- Simplex codes --- p.72 / Chapter 2.3.3 --- Reed-Muller codes --- p.73 / Chapter 2.3.4 --- BCH codes --- p.75 / Chapter 2.4 --- Bounds on codes --- p.77 / Chapter 2.4.1 --- Spheres in Zn --- p.77 / Chapter 2.4.2 --- Perfect codes --- p.78 / Chapter 2.4.3 --- Famous numbers Ar (n，d) and the sphere-covering and sphere packing bounds --- p.79 / Chapter 2.4.4 --- The Singleton and Plotkin bounds --- p.81 / Chapter 2.4.5 --- The Gilbert-Varshamov bound --- p.83 / Chapter 3 --- Algebraic curves over finite fields and the Goppa codes --- p.85 / Chapter 3.1 --- Algebraic curves over finite fields --- p.85 / Chapter 3.1.1 --- Affine varieties --- p.85 / Chapter 3.1.2 --- Projective varieties --- p.37 / Chapter 3.1.3 --- Morphisms --- p.89 / Chapter 3.1.4 --- Rational maps --- p.91 / Chapter 3.1.5 --- Non-singular varieties --- p.92 / Chapter 3.1.6 --- Smooth models of algebraic curves --- p.93 / Chapter 3.2 --- Goppa codes --- p.96 / Chapter 3.2.1 --- Elementary Goppa codes --- p.96 / Chapter 3.2.2 --- The affine and projective lines --- p.98 / Chapter 3.2.3 --- Goppa codes on the projective line --- p.102 / Chapter 3.2.4 --- Differentials and divisors --- p.105 / Chapter 3.2.5 --- Algebraic geometric codes --- p.112 / Chapter 3.2.6 --- Codes with better rates than the Varshamov- Gilbert bound and calculation of parameters --- p.116 / Bibliography

Kwok Pui Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 66-67). / Abstracts in English and Chinese. / Abstract --- p.i / Abstract (Chinese Version) --- p.ii / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Linear Network Coding --- p.7 / Chapter 2.1 --- Single Source Network Coding --- p.8 / Chapter 2.2 --- Descriptions of Linear Network Codes --- p.9 / Chapter 2.3 --- Desirable Properties of Linear Network Codes --- p.12 / Chapter 2.4 --- Linear Network Codes Constructions --- p.14 / Chapter 3 --- Node-based Characterization --- p.16 / Chapter 3.1 --- Channel-based characterization --- p.16 / Chapter 3.2 --- A Necessary Condition for the Existence of Linear Network Codes --- p.17 / Chapter 3.3 --- Insufficiency of the condition --- p.22 / Chapter 4 --- Relation between Linear Network Codes --- p.25 / Chapter 4.1 --- Relation between Multicast and Broadcast --- p.26 / Chapter 4.1.1 --- Auxiliary Graph --- p.26 / Chapter 4.2 --- Relation between Broadcast and Dispersion --- p.29 / Chapter 4.2.1 --- Expanded Graph --- p.29 / Chapter 4.3 --- Relation between Dispersion and Generic Net- work Code --- p.31 / Chapter 4.3.1 --- Edge Disjoint Path --- p.31 / Chapter 4.3.2 --- Path Rearrangement --- p.34 / Chapter 4.3.3 --- Extended Graph --- p.50 / Chapter 5 --- Upper Bound on the Size of the Base Field --- p.57 / Chapter 5.1 --- Base Field Size Requirement --- p.58 / Chapter 5.1.1 --- Linear Multicast --- p.58 / Chapter 5.1.2 --- Linear Broadcast --- p.58 / Chapter 5.1.3 --- Linear Dispersion --- p.59 / Chapter 5.1.4 --- Generic Network Code --- p.60 / Chapter 5.2 --- Upper Bounds Comparison for Generic Network Code --- p.61 / Chapter 6 --- Future Work --- p.62 / Bibliography --- p.66

Advances in digital camera technology have led to the development of image sensors that are capable of capturing High Dynamic Range (HDR) images. Although this has enabled the capture of greater depths of colour and illumination, there remain problems with regards to transmitting and displaying the HDR image data. Current consumer level displays are designed to only show images with a depth of 8-bits per pixel per channel. Typical HDR images can be 10-bits per pixel per channel and upwards, leading to the first problem, how to display HDR images on Standard Dynamic Range (SDR) displays. This is linked to a further problem, that of transmitting the HDR data to the SDR devices, due to the fact that most state-of-the-art image and video coding standards deal with only SDR data. Further, as with most technologies of this kind, current HDR displays are extremely expensive. Furthermore, media broadcast organisations have invested significant sums of money into their current architecture and are unwilling to completely change their systems at further cost.

Since the rediscovery, LDPC codes attract a large amount of research efforts. In 1998, nonbinary LDPC codes were firstly investigated and the results shown that they are better than their binary counterparts in performance. Recently, there is always a requirement from the industry to design applied nonbinary LDPC codes. In this dissertation, we firstly propose a novel class of quasi-cyclic (QC) LDPC codes. This class of QC-LDPC codes embraces both linear encoding complexity and excellent compatibility in various degree distributions and nonbinary expansions. We show by simulation results that our proposed QC-LDPC codes perform as well as their comparable counterparts. However, this proposed code structure is more flexible in designing. This feature may show its power when we change the code length and rate adaptively. Further more, we present two algorithms to generate codes with short girth and better girth distribution. The two algorithms are designed based on progressive edge growth (PEG) algorithm and they are specifically designed for quasi-cyclic structure. The simulation results show the improvement they achieved. In this thesis, we also investigate the believe propagation based iterative algorithms for decoding of nonbinary LDPC codes. The algorithms include sum-product (SP) algorithm, SP algorithm using fast Fourier transform, min-sum (MS) algorithm and complexity reduced extended min-sum (EMS) algorithm. In particular, we present the proposed modified min-sum algorithm with threshold filtering which further reduces the computation complexity.