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.
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.
Michael Drmota is Professor for Discrete Mathematics at TU Wien. His research activities range from analytic combinatorics over discrete random structures to number theory. He has published several books, including 'Random Trees' (2009), and about 200 research articles. He was President of the Austrian Mathematical Society from 2010 to 2013, and has been Corresponding Member of the Austrian Academy of Sciences since 2013.
Inhaltsangabe
Part I. Known Sources: 1. Preliminaries 2. Shannon and Huffman FV codes 3. Tunstall and Khodak VF codes 4. Divide-and-conquer VF codes 5. Khodak VV codes 6. Non-prefix one-to-one codes 7. Advanced data structures: tree compression 8. Graph and structure compression Part II. Universal Codes: 9. Minimax redundancy and regret 10. Redundancy of universal memoryless sources 11. Markov types and redundancy for Markov sources 12. Non-Markovian sources: redundancy of renewal processes A. Probability B. Generating functions C. Complex asymptotics D. Mellin transform and Tauberian theorems E. Exponential sums and uniform distribution mod 1 F. Diophantine approximation References Index.
Part I. Known Sources: 1. Preliminaries 2. Shannon and Huffman FV codes 3. Tunstall and Khodak VF codes 4. Divide-and-conquer VF codes 5. Khodak VV codes 6. Non-prefix one-to-one codes 7. Advanced data structures: tree compression 8. Graph and structure compression Part II. Universal Codes: 9. Minimax redundancy and regret 10. Redundancy of universal memoryless sources 11. Markov types and redundancy for Markov sources 12. Non-Markovian sources: redundancy of renewal processes A. Probability B. Generating functions C. Complex asymptotics D. Mellin transform and Tauberian theorems E. Exponential sums and uniform distribution mod 1 F. Diophantine approximation References Index.
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