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|a 9781441986085
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|a Yeung, Raymond W.
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|a A First Course in Information Theory
|h Elektronische Ressource
|c by Raymond W. Yeung
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|a 1st ed. 2002
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| 260 |
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|a New York, NY
|b Springer US
|c 2002, 2002
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| 300 |
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|a XXIII, 412 p
|b online resource
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|a 10.1 Alternating Optimization -- 10.2 The Algorithms -- 10.3 Convergence -- Problems -- Historical Notes -- 11. Single-Source Network Coding -- 11.1 A Point-to-Point Network -- 11.2 What is Network Coding? -- 11.3 A Network Code -- 11.4 The Max-Flow Bound -- 11.5 Achievability of the Max-Flow Bound -- Problems -- Historical Notes -- 12. Information Inequalities -- 12.1 The Region ?*n -- 12.2 Information Expressions in Canonical Form -- 12.3 A Geometrical Framework -- 12.4 Equivalence of Constrained Inequalities -- 12.5 The Implication Problem of Conditional Independence -- Problems -- Historical Notes -- 13. Shannon-Type Inequalities -- 13.1 The Elemental Inequalities -- 13.2 A Linear Programming Approach -- 13.3 A Duality -- 13.4 Machine Proving -- 13.5 Tackling the Implication Problem -- 13.6 Minimality of the Elemental Inequalities -- Appendix 13.A: The Basic Inequalities and the Polymatroidal Axioms -- Problems -- Historical Notes -- Problems -- Historical Notes --
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|a 1. The Science of Information -- Information Measures -- 2.1 Independence and Markov Chains -- 2.2 Shannon’s Information Measures -- 2.3 Continuity of Shannon’s Information Measures -- 2.4 Chain Rules -- 2.5 Informational Divergence -- 2.6 The Basic Inequalities -- 2.7 Some Useful Information Inequalities -- 2.8 Fano’s Inequality -- 2.9 Entropy Rate of Stationary Source -- Problems -- Historical Notes -- 3. Zero-Error Data Compression -- 3.1 The Entropy Bound -- 3.2 Prefix Codes -- 3.3 Redundancy of Prefix Codes -- Problems -- Historical Notes -- 4. Weak Typicality -- 4.1 The Weak -- 4.2 The Source Coding Theorem -- 4.3 Efficient Source Coding -- 4.4 The Shannon-McMillan-Breiman Theorem -- Problems -- Historical Notes -- 5. Strong Typicality -- 5.1 Strong -- 5.2 Strong Typicality Versus Weak Typicality -- 5.3 Joint Typicality -- 5.4 An Interpretation of the Basic Inequalities -- Problems -- Historical Notes -- The I-measure -- 6.1 Preliminaries --
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|a 14. Beyond Shannon-Type Inequalities -- 14.1 Characterizations of ?*2,?*3, and ?*n -- 14.2 A Non-Shannon-Type Unconstrained Inequality -- 14.3 A Non-Shannon-TypeConstrained Inequality -- 14.4 Applications -- Problems -- Historical Notes -- 978-1-4419-8608-5_15 -- 15.1 Two Characteristics -- 15.2 Examples of Application -- 15.3 A Network Code for Acyclic Networks -- 15.4 An Inner Bound -- 15.5 An Outer Bound -- 15.6 The LP Bound and Its Tightness -- 15.7 Achievability of Rin -- Appendix 15.A: Approximation of Random Variables with Infinite Alphabets -- Problems -- Historical Notes -- 16. Entropy and Groups -- 16.1 Group Preliminaries -- 16.2 Group-Characterizable Entropy Functions -- 16.3 A Group Characterization of ?*n -- 16.4 Information Inequalities and Group Inequalities -- Problems -- Historical Notes
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|a 6.2 The I-Measure for Two Random Variables -- 6.3 Construction of the I-Measure ?* -- 6.4 ?* Can be Negative -- 6.5 Information Diagrams -- 6.6 Examples of Applications -- Appendix 6.A: A Variation of the Inclusion-Exclusion Formula -- Problems -- Historical Notes -- 7. Markov Structures -- 7.1 Conditional Mutual Independence -- 7.2 Full Conditional Mutual Independence -- 7.3 Markov Random Field -- 7.4 Markov Chain -- Problems -- Historical Notes -- 8. Channel Capacity -- 8.1 Discrete Memoryless Channels -- 8.2 The Channel Coding Theorem -- 8.3 The Converse -- 8.4 Achievability of the Channel Capacity -- 8.5 A Discussion -- 8.6 Feedback Capacity -- 8.7 Separation of Source and Channel Coding -- Problems -- Historical Notes -- 9. Rate-Distortion Theory -- 9.1 Single-Letter Distortion Measures -- 9.2 The Rate-Distortion Function R(D) -- 9.3 The Rate-Distortion Theorem -- 9.4 The Converse -- 9.5 Achievability of RI(D) -- Problems -- Historical Notes -- The Blahut-Arimoto Algorithms --
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|a Group Theory and Generalizations
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|a Engineering
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|a Group theory
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|a Computer science / Mathematics
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|a Discrete Mathematics in Computer Science
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|a Electrical and Electronic Engineering
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|a Electrical engineering
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|a Control theory
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|a Probability Theory
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|a Systems Theory, Control
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|a System theory
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|a Discrete mathematics
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|a Technology and Engineering
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|a Probabilities
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|a eng
|2 ISO 639-2
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|b SBA
|a Springer Book Archives -2004
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|a Information Technology: Transmission, Processing and Storage
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|a 10.1007/978-1-4419-8608-5
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|u https://doi.org/10.1007/978-1-4419-8608-5?nosfx=y
|x Verlag
|3 Volltext
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|a 621.3
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|a A First Course in Information Theory is an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields
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