Arithmetic coding revisited

Over the last decade, arithmetic coding has emerged as an important compression tool. It is now the method of choice for adaptive coding on multisymbol alphabets because of its speed, low storage requirements, and effectiveness of compression. This article describes a new implementation of arithmetic coding that incorporates several improvements over a widely used earlier version by Witten, Neal, and Cleary, which has become a de facto standard. These improvements include fewer multiplicative operations, greatly extended range of alphabet sizes and symbol probabilities, and the use of low-precision arithmetic, permitting implementation by fast shift/add operations. We also describe a modular structure that separates the coding, modeling, and probability estimation components of a compression system. To motivate the improved coder, we consider the needs of a word-based text compression program. We report a range of experimental results using this and other models. Complete source code is available

New Algorithms and Lower Bounds for Sequential-Access Data Compression

This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by character, outputting each character's self-delimiting codeword before reading the next one. We show how to encode and decode each character in constant worst-case time while producing an encoding whose length is worst-case optimal. In another chapter we consider one-pass compression with memory bounded in terms of the alphabet size and context length, and prove a nearly tight tradeoff between the amount of memory we can use and the quality of the compression we can achieve. In a third chapter we consider compression in the read/write streams model, which allows us passes and memory both polylogarithmic in the size of the input. We first show how to achieve universal compression using only one pass over one stream. We then show that one stream is not sufficient for achieving good grammar-based compression. Finally, we show that two streams are necessary and sufficient for achieving entropy-only bounds.Comment: draft of PhD thesi

Three dimensional DCT based video compression.

by Chan Kwong Wing Raymond.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 115-123).Acknowledgments --- p.iTable of Contents --- p.ii-vList of Tables --- p.viList of Figures --- p.viiAbstract --- p.1Chapter Chapter 1 : --- IntroductionChapter 1.1 --- An Introduction to Video Compression --- p.3Chapter 1.2 --- Overview of Problems --- p.4Chapter 1.2.1 --- Analog Video and Digital Problems --- p.4Chapter 1.2.2 --- Low Bit Rate Application Problems --- p.4Chapter 1.2.3 --- Real Time Video Compression Problems --- p.5Chapter 1.2.4 --- Source Coding and Channel Coding Problems --- p.6Chapter 1.2.5 --- Bit-rate and Quality Problems --- p.7Chapter 1.3 --- Organization of the Thesis --- p.7Chapter Chapter 2 : --- Background and Related WorkChapter 2.1 --- Introduction --- p.9Chapter 2.1.1 --- Analog Video --- p.9Chapter 2.1.2 --- Digital Video --- p.10Chapter 2.1.3 --- Color Theory --- p.10Chapter 2.2 --- Video Coding --- p.12Chapter 2.2.1 --- Predictive Coding --- p.12Chapter 2.2.2 --- Vector Quantization --- p.12Chapter 2.2.3 --- Subband Coding --- p.13Chapter 2.2.4 --- Transform Coding --- p.14Chapter 2.2.5 --- Hybrid Coding --- p.14Chapter 2.3 --- Transform Coding --- p.15Chapter 2.3.1 --- Discrete Cosine Transform --- p.16Chapter 2.3.1.1 --- 1-D Fast Algorithms --- p.16Chapter 2.3.1.2 --- 2-D Fast Algorithms --- p.17Chapter 2.3.1.3 --- Multidimensional DCT Algorithms --- p.17Chapter 2.3.2 --- Quantization --- p.18Chapter 2.3.3 --- Entropy Coding --- p.18Chapter 2.3.3.1 --- Huffman Coding --- p.19Chapter 2.3.3.2 --- Arithmetic Coding --- p.19Chapter Chapter 3 : --- Existing Compression SchemeChapter 3.1 --- Introduction --- p.20Chapter 3.2 --- Motion JPEG --- p.20Chapter 3.3 --- MPEG --- p.20Chapter 3.4 --- H.261 --- p.22Chapter 3.5 --- Other Techniques --- p.23Chapter 3.5.1 --- Fractals --- p.23Chapter 3.5.2 --- Wavelets --- p.23Chapter 3.6 --- Proposed Solution --- p.24Chapter 3.7 --- Summary --- p.25Chapter Chapter 4 : --- Fast 3D-DCT AlgorithmsChapter 4.1 --- Introduction --- p.27Chapter 4.1.1 --- Motivation --- p.27Chapter 4.1.2 --- Potentials of 3D DCT --- p.28Chapter 4.2 --- Three Dimensional Discrete Cosine Transform (3D-DCT) --- p.29Chapter 4.2.1 --- Inverse 3D-DCT --- p.29Chapter 4.2.2 --- Forward 3D-DCT --- p.30Chapter 4.3 --- 3-D FCT (3-D Fast Cosine Transform Algorithm --- p.30Chapter 4.3.1 --- Partitioning and Rearrangement of Data Cube --- p.30Chapter 4.3.1.1 --- Spatio-temporal Data Cube --- p.30Chapter 4.3.1.2 --- Spatio-temporal Transform Domain Cube --- p.31Chapter 4.3.1.3 --- Coefficient Matrices --- p.31Chapter 4.3.2 --- 3-D Inverse Fast Cosine Transform (3-D IFCT) --- p.32Chapter 4.3.2.1 --- Matrix Representations --- p.32Chapter 4.3.2.2 --- Simplification of the calculation steps --- p.33Chapter 4.3.3 --- 3-D Forward Fast Cosine Transform (3-D FCT) --- p.35Chapter 4.3.3.1 --- Decomposition --- p.35Chapter 4.3.3.2 --- Reconstruction --- p.36Chapter 4.4 --- The Fast Algorithm --- p.36Chapter 4.5 --- Example using 4x4x4 IFCT --- p.38Chapter 4.6 --- Complexity Comparison --- p.43Chapter 4.6.1 --- Complexity of Multiplications --- p.43Chapter 4.6.2 --- Complexity of Additions --- p.43Chapter 4.7 --- Implementation Issues --- p.44Chapter 4.8 --- Summary --- p.46Chapter Chapter 5 : --- QuantizationChapter 5.1 --- Introduction --- p.49Chapter 5.2 --- Dynamic Ranges of 3D-DCT Coefficients --- p.49Chapter 5.3 --- Distribution of 3D-DCT AC Coefficients --- p.54Chapter 5.4 --- Quantization Volume --- p.55Chapter 5.4.1 --- Shifted Complement Hyperboloid --- p.55Chapter 5.4.2 --- Quantization Volume --- p.58Chapter 5.5 --- Scan Order for Quantized 3D-DCT Coefficients --- p.59Chapter 5.6 --- Finding Parameter Values --- p.60Chapter 5.7 --- Experimental Results from Using the Proposed Quantization Values --- p.65Chapter 5.8 --- Summary --- p.66Chapter Chapter 6 : --- Entropy CodingChapter 6.1 --- Introduction --- p.69Chapter 6.1.1 --- Huffman Coding --- p.69Chapter 6.1.2 --- Arithmetic Coding --- p.71Chapter 6.2 --- Zero Run-Length Encoding --- p.73Chapter 6.2.1 --- Variable Length Coding in JPEG --- p.74Chapter 6.2.1.1 --- Coding of the DC Coefficients --- p.74Chapter 6.2.1.2 --- Coding of the DC Coefficients --- p.75Chapter 6.2.2 --- Run-Level Encoding of the Quantized 3D-DCT Coefficients --- p.76Chapter 6.3 --- Frequency Analysis of the Run-Length Patterns --- p.76Chapter 6.3.1 --- The Frequency Distributions of the DC Coefficients --- p.77Chapter 6.3.2 --- The Frequency Distributions of the DC Coefficients --- p.77Chapter 6.4 --- Huffman Table Design --- p.84Chapter 6.4.1 --- DC Huffman Table --- p.84Chapter 6.4.2 --- AC Huffman Table --- p.85Chapter 6.5 --- Implementation Issue --- p.85Chapter 6.5.1 --- Get Category --- p.85Chapter 6.5.2 --- Huffman Encode --- p.86Chapter 6.5.3 --- Huffman Decode --- p.86Chapter 6.5.4 --- PutBits --- p.88Chapter 6.5.5 --- GetBits --- p.90Chapter Chapter 7 : --- "Contributions, Concluding Remarks and Future Work"Chapter 7.1 --- Contributions --- p.92Chapter 7.2 --- Concluding Remarks --- p.93Chapter 7.2.1 --- The Advantages of 3D DCT codec --- p.94Chapter 7.2.2 --- Experimental Results --- p.95Chapter 7.1 --- Future Work --- p.95Chapter 7.2.1 --- Integer Discrete Cosine Transform Algorithms --- p.95Chapter 7.2.2 --- Adaptive Quantization Volume --- p.96Chapter 7.2.3 --- Adaptive Huffman Tables --- p.96Appendices:Appendix A : The detailed steps in the simplification of Equation 4.29 --- p.98Appendix B : The program Listing of the Fast DCT Algorithms --- p.101Appendix C : Tables to Illustrate the Reording of the Quantized Coefficients --- p.110Appendix D : Sample Values of the Quantization Volume --- p.111Appendix E : A 16-bit VLC table for AC Run-Level Pairs --- p.113References --- p.11