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Most of the basic concepts of algebraic coding theory are derived for the memoryless binary symmetric channel. These concepts do not necessarily hold for time-varying channels or for channels with memory. However, errors in real-life channels seem to occur in bursts rather than independently, suggesting that these channels exhibit some statistical dependence or memory. Nonetheless, the same algebraic codes are still commonly used in current communication systems that employ interleaving to spread channel error bursts over the set of received codewords to make the channel appear memoryless to the block decoder. This method suffers from immediate shortcomings as it fails to exploit the channel’s memory while adding delay to the system. We study optimal maximum likelihood block decoding of binary codes sent over several binary additive channels with infinite and finite memory. We derive conditions on general binary codes and channels parameters under which maximum likelihood and minimum distance decoding are equivalent. The channels considered in this work are the infinite and finite memory Polya contagion channels, the queue-based channel, and the Gilbert-Elliott channel. We also present results on the optimality of classical perfect and quasi-perfect codes when used over the aforementioned channels under maximum likelihood decoding. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2013-07-12 13:45:35.294

Rate 1/2 systematic recursive convolutional codes over integer rings modulo-q are investigated for their performance. The investigation examines the performance in severe fading and additive white Gaussian noise for codes with various constraint lengths. The arithmetic for the codes is modulo-q. where the value of q is within the range of 2 to 16. An exhaustive search is carried out for codes with short constraint lengths. A reduced search is developed for larger constraint lengths which restricts the tap polynomials to irreducible polynomials over Zq. The irreducible polynomials are generated and the ones not found in the literature are presented in tables. The search algorithms are outlined and the results for the codes are tabulated. The performance of selected codes are verified by Monte-Carlo simulation techniques. Several codes have better performance than comparable codes presented in the literature for the Rayleigh fading channel. In sme of cases, the codes found have better performance on the AWGN channel than the best known ring codes. The characteristics of rotationally invariant (RI) ring codes presented in the literature are used in an exhaustive search for codes over Zq which are invariant to phase shifts of 2[pi]/q. Tables of RI codes optimized for the Rayleigh fading channel are presented along with codes which are optimized for the AWGN channel. / Graduate

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