Analytic Information Theory

ISBN-13: 9781108474443 / Twarda / 2023 / 400 str.

Indiana) Szpankowski Wojciech (Purdue University

Opis

Explores problems of information and learning theory, using tools from analytic combinatorics to analyze precise behavior of source codes.

Recenzje

'Drmota and Szpankowski, leading experts in the mathematical analysis of discrete structures, present here a compelling treatment unifying modern and classical results in information theory and analytic combinatorics. This book is certain to be a standard reference for years to come.' Robert Sedgewick, Princeton University

Spis treści

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.