Redundancy of Lossless Data Compression for Known Sources by Analytic Methods PDF Download
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Author: Michael Drmota
Publisher:
ISBN: 9781680832853
Category : Coding theory
Languages : en
Pages : 140
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Book Description
Lossless data compression is a facet of source coding and a well studied problem of information theory. Its goal is to find a shortest possible code that can be unambiguously recovered. Here, we focus on rigorous analysis of code redundancy for known sources. The redundancy rate problem determines by how much the actual code length exceeds the optimal code length. We present precise analyses of three types of lossless data compression schemes, namely fixed-to-variable (FV) length codes, variable-to-fixed (VF) length codes, and variable to- variable (VV) length codes. In particular, we investigate the average redundancy of Shannon, Huffman, Tunstall, Khodak and Boncelet codes. These codes have succinct representations as trees, either as coding or parsing trees, and we analyze here some of their parameters (e.g., the average path from the root to a leaf). Such trees are precisely analyzed by analytic methods, known also as analytic combinatorics, in which complex analysis plays decisive role. These tools include generating functions, Mellin transform, Fourier series, saddle point method, analytic poissonization and depoissonization, Tauberian theorems, and singularity analysis. The term analytic information theory has been coined to describe problems of information theory studied by analytic tools. This approach lies on the crossroad of information theory, analysis of algorithms, and combinatorics.
Author: Michael Drmota
Publisher:
ISBN: 9781680832853
Category : Coding theory
Languages : en
Pages : 140
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Book Description
Lossless data compression is a facet of source coding and a well studied problem of information theory. Its goal is to find a shortest possible code that can be unambiguously recovered. Here, we focus on rigorous analysis of code redundancy for known sources. The redundancy rate problem determines by how much the actual code length exceeds the optimal code length. We present precise analyses of three types of lossless data compression schemes, namely fixed-to-variable (FV) length codes, variable-to-fixed (VF) length codes, and variable to- variable (VV) length codes. In particular, we investigate the average redundancy of Shannon, Huffman, Tunstall, Khodak and Boncelet codes. These codes have succinct representations as trees, either as coding or parsing trees, and we analyze here some of their parameters (e.g., the average path from the root to a leaf). Such trees are precisely analyzed by analytic methods, known also as analytic combinatorics, in which complex analysis plays decisive role. These tools include generating functions, Mellin transform, Fourier series, saddle point method, analytic poissonization and depoissonization, Tauberian theorems, and singularity analysis. The term analytic information theory has been coined to describe problems of information theory studied by analytic tools. This approach lies on the crossroad of information theory, analysis of algorithms, and combinatorics.
Author: Michael Drmota
Publisher: Cambridge University Press
ISBN: 1108474446
Category : Computers
Languages : en
Pages : 381
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Book Description
Explores problems of information and learning theory, using tools from analytic combinatorics to analyze precise behavior of source codes.
Author: Volker Diekert
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110416328
Category : Mathematics
Languages : en
Pages : 424
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Book Description
The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents: Algebraic structures Cryptography Number theoretic algorithms Polynomial time primality test Elliptic curves Combinatorics on words Automata Discrete infinite groups
Author: Mark Nelson
Publisher:
ISBN: 9788170297291
Category :
Languages : en
Pages : 0
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Book Description
Described by Jeff Prosise of PC Magazine as one of my favorite books on applied computer technology, this updated second edition brings you fully up-to-date on the latest developments in the data compression field. It thoroughly covers the various data compression techniques including compression of binary programs, data, sound, and graphics. Each technique is illustrated with a completely functional C program that demonstrates how data compression works and how it can be readily incorporated into your own compression programs. The accompanying disk contains the code files that demonstrate the various techniques of data compression found in the book.
Author: Faxin Yu
Publisher: Springer Science & Business Media
ISBN: 3642126510
Category : Computers
Languages : en
Pages : 434
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Book Description
With the increasing popularization of the Internet, together with the rapid development of 3D scanning technologies and modeling tools, 3D model databases have become more and more common in fields such as biology, chemistry, archaeology and geography. People can distribute their own 3D works over the Internet, search and download 3D model data, and also carry out electronic trade over the Internet. However, some serious issues are related to this as follows: (1) How to efficiently transmit and store huge 3D model data with limited bandwidth and storage capacity; (2) How to prevent 3D works from being pirated and tampered with; (3) How to search for the desired 3D models in huge multimedia databases. This book is devoted to partially solving the above issues. Compression is useful because it helps reduce the consumption of expensive resources, such as hard disk space and transmission bandwidth. On the downside, compressed data must be decompressed to be used, and this extra processing may be detrimental to some applications. 3D polygonal mesh (with geometry, color, normal vector and texture coordinate information), as a common surface representation, is now heavily used in various multimedia applications such as computer games, animations and simulation applications. To maintain a convincing level of realism, many applications require highly detailed mesh models. However, such complex models demand broad network bandwidth and much storage capacity to transmit and store. To address these problems, 3D mesh compression is essential for reducing the size of 3D model representation.
Author: Ida Mengyi Pu
Publisher: Butterworth-Heinemann
ISBN: 0080530265
Category : Computers
Languages : en
Pages : 269
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Book Description
Fundamental Data Compression provides all the information students need to be able to use this essential technology in their future careers. A huge, active research field, and a part of many people's everyday lives, compression technology is an essential part of today's Computer Science and Electronic Engineering courses. With the help of this book, students can gain a thorough understanding of the underlying theory and algorithms, as well as specific techniques used in a range of scenarios, including the application of compression techniques to text, still images, video and audio. Practical exercises, projects and exam questions reinforce learning, along with suggestions for further reading.* Dedicated data compression textbook for use on undergraduate courses* Provides essential knowledge for today's web/multimedia applications* Accessible, well structured text backed up by extensive exercises and sample exam questions
Author: Timothy C. Bell
Publisher: Englewood Cliffs, N.J. : Prentice Hall
ISBN:
Category : Computers
Languages : en
Pages : 344
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Book Description
M->CREATED
Author: Johannes Huber (Prof. Dr.-Ing.)
Publisher: Margret Schneider
ISBN: 3800728028
Category : Coding theory
Languages : en
Pages : 487
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Book Description
Author: Jiri Jan
Publisher: CRC Press
ISBN: 135138791X
Category : Medical
Languages : en
Pages : 599
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Book Description
Differently oriented specialists and students involved in image processing and analysis need to have a firm grasp of concepts and methods used in this now widely utilized area. This book aims at being a single-source reference providing such foundations in the form of theoretical yet clear and easy to follow explanations of underlying generic concepts. Medical Image Processing, Reconstruction and Analysis – Concepts and Methods explains the general principles and methods of image processing and analysis, focusing namely on applications used in medical imaging. The content of this book is divided into three parts: Part I – Images as Multidimensional Signals provides the introduction to basic image processing theory, explaining it for both analogue and digital image representations. Part II – Imaging Systems as Data Sources offers a non-traditional view on imaging modalities, explaining their principles influencing properties of the obtained images that are to be subsequently processed by methods described in this book. Newly, principles of novel modalities, as spectral CT, functional MRI, ultrafast planar-wave ultrasonography and optical coherence tomography are included. Part III – Image Processing and Analysis focuses on tomographic image reconstruction, image fusion and methods of image enhancement and restoration; further it explains concepts of low-level image analysis as texture analysis, image segmentation and morphological transforms. A new chapter deals with selected areas of higher-level analysis, as principal and independent component analysis and particularly the novel analytic approach based on deep learning. Briefly, also the medical image-processing environment is treated, including processes for image archiving and communication. Features Presents a theoretically exact yet understandable explanation of image processing and analysis concepts and methods Offers practical interpretations of all theoretical conclusions, as derived in the consistent explanation Provides a concise treatment of a wide variety of medical imaging modalities including novel ones, with respect to properties of provided image data
Author: Charles K. Chui
Publisher: Springer Science & Business Media
ISBN: 9462390096
Category : Mathematics
Languages : en
Pages : 567
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Book Description
This textbook, apart from introducing the basic aspects of applied mathematics, focuses on recent topics such as information data manipulation, information coding, data approximation, data dimensionality reduction, data compression, time-frequency and time scale bases, image manipulation, and image noise removal. The methods treated in more detail include spectral representation and “frequency” of the data, providing valuable information for, e.g. data compression and noise removal. Furthermore, a special emphasis is also put on the concept of “wavelets” in connection with the “multi-scale” structure of data-sets. The presentation of the book is elementary and easily accessible, requiring only some knowledge of elementary linear algebra and calculus. All important concepts are illustrated with examples, and each section contains between 10 an 25 exercises. A teaching guide, depending on the level and discipline of instructions is included for classroom teaching and self-study.
