Analytic Information Theory

Analytic Information Theory

Author: Michael Drmota

Publisher: Cambridge University Press

Published: 2023-09-07

Total Pages: 382

ISBN-13: 1108647987

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Aimed at graduate students and researchers interested in information theory and the analysis of algorithms, this book explores problems of information and learning theory, demonstrating how to use tools from analytic combinatorics to discover and analyze precise behavior of source codes.


Information and Life

Information and Life

Author: Gérard Battail

Publisher: Springer Science & Business Media

Published: 2013-07-30

Total Pages: 264

ISBN-13: 9400770405

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Communication, one of the most important functions of life, occurs at any spatial scale from the molecular one up to that of populations and ecosystems, and any time scale from that of fast chemical reactions up to that of geological ages. Information theory, a mathematical science of communication initiated by Shannon in 1948, has been very successful in engineering, but biologists ignore it. This book aims at bridging this gap. It proposes an abstract definition of information based on the engineers' experience which makes it usable in life sciences. It expounds information theory and error-correcting codes, its by-products, as simply as possible. Then, the fundamental biological problem of heredity is examined. It is shown that biology does not adequately account for the conservation of genomes during geological ages, which can be understood only if it is assumed that genomes are made resilient to casual errors by proper coding. Moreover, the good conservation of very old parts of genomes, like the HOX genes, implies that the assumed genomic codes have a nested structure which makes an information the more resilient to errors, the older it is. The consequences that information theory draws from these hypotheses meet very basic but yet unexplained biological facts, e.g., the existence of successive generations, that of discrete species and the trend of evolution towards complexity. Being necessarily inscribed on physical media, information appears as a bridge between the abstract and the concrete. Recording, communicating and using information exclusively occur in the living world. Information is thus coextensive with life and delineates the border between the living and the inanimate.


DCC '95, Data Compression Conference

DCC '95, Data Compression Conference

Author: James Andrew Storer

Publisher:

Published: 1995

Total Pages: 528

ISBN-13:

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Contains the presentations from the March 1995 conference which was sponsored by the IEEE Computer Society Technical Committee on Computer Communications. Among the topics are hierarchical vector quantization of perceptually weighted block transforms; unbounded length contexts for PPM; quadtree based JBIG compression; parallel algorithms for the static dictionary compression; and CREW--compression with reversible embedded wavelets. Includes a poster session and abstracts from industry and NASA workshops. No subject index. Annotation copyright by Book News, Inc., Portland, OR.


The Minimum Description Length Principle

The Minimum Description Length Principle

Author: Peter D. Grünwald

Publisher: MIT Press

Published: 2007

Total Pages: 736

ISBN-13: 0262072815

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This introduction to the MDL Principle provides a reference accessible to graduate students and researchers in statistics, pattern classification, machine learning, and data mining, to philosophers interested in the foundations of statistics, and to researchers in other applied sciences that involve model selection.


Redundancy of Lossless Data Compression for Known Sources by Analytic Methods

Redundancy of Lossless Data Compression for Known Sources by Analytic Methods

Author: Michael Drmota

Publisher:

Published: 2017

Total Pages: 140

ISBN-13: 9781680832853

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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.