عنوان

Mathematics of information and coding /

0821805347 (alk. paper)

9780821805343 (alk. paper)

dltt

Mathematics of information and coding /

[Book]

Te Sun Han, Kingo Kobayashi.

Providence, RI :

American Mathematical Society,

c2002.

xii, 286 p. :

ill. ;

26 cm.

Translations of mathematical monographs ;

v. 203

Includes bibliographical references (p. 277-281) and index.

Machine generated contents note: Preface to the English Edition xi -- Chapter 1. What is Information Theory? 1 -- 1.1. Introduction 1 -- 1.2. Information Theory So Far 2 -- 1.3. Basic Elements and Related Fields 6 -- 1.4. About this Book 16 -- Chapter 2. Basics of Information Theory 19 -- 2.1. Entropy 19 -- 2.2. Divergence 25 -- 2.3. Mutual Information 31 -- 2.4. Data Processing Inequality 37 -- 2.5. Fano's Inequality 40 -- 2.6. Type of Sequences, Typical Sequences, and AEP 41 -- Exercises 51 -- Chapter 3. Source and Coding 73 -- 3.1. Various Information Sources 73 -- 3.2. Entropy Rate of Source 79 -- 3.3. Various Codes 84 -- 3.4. AEP and Source Coding Theorem 86 -- 3.5. Separable Codes and Prefix Codes 88 -- 3.6. Converse Theorem for FV Coding 93 -- 3.7. Direct Theorem for FV Coding 95 -- 3.8. Huffman Code 99 -- 3.9. Coding for Arbitrarily Varying Sources 106 -- 3.10. Reliability Function for Source Coding 109 -- Exercises 115 -- Chapter 4. Arithmetic Code 127 -- 4.1. Elias Code 127 -- 4.2. Algorithm of Arithmetic Code 131 -- 4.3. Asymptotic Optimality of Arithmetic Code 139 -- 4.4. Arithmetic Code as Number System 142 -- 4.5. Enumerative Code 145 -- 4.6. Arithmetic Code as Tree Code 148 -- Exercises 151 -- Chapter 5. Universal Coding of Integers 157 -- 5.1. Universal Codes of Integers 157 -- 5.2. Search Tree of Bentley-Yao 166 -- 5.3. Bounds for Elias Codeword Length Functions 170 -- 5.4. Properties of the Log-Star Function 180 -- 5.5. Modified Log-Star Functions 182 -- Exercises 188 -- Chapter 6. Universal Coding of Texts 193 -- 6.1. Lempel-Ziv Code based on Incremental Parsing 193 -- 6.2. Lempel-Ziv Code based on Recurrence Time 202 -- Exercises 214 -- Chapter 7. Universal Coding of Compound Sources 219 -- 7.1. Compound Source 219 -- 7.2. Sub-Probability and Codeword Length 220 -- 7.3. Universal Code for Compound Source 222 -- 7.4. Estimation of Probability Distribution 223 -- 7.5. Rissanen's Two-Step Coding 225 -- 7.6. Rissanen's Predictive Coding 231 -- 7.7. Stochastic Complexity 233 -- 7.8. Bayes Code 234 -- 7.9. Model Selection and Universal Code 239 -- 7.10. Consistency of Model Selection 242 -- Exercises 248 -- Chapter 8. Data Analysis and MDL Principle 253 -- 8.1. Fitting of Experimental Data 254 -- 8.2. Histogram Approximation for Probability Density 257 -- 8.3. Self-Organization of Data 258 -- 8.4. Self-Formation of Category 262 -- 8.5. Category Classification by Decision Tree 263 -- 8.6. Probabilistic Category Classification 266 -- 8.7. About AIC Criterion 269 -- Exercises 273 -- Bibliography 277 -- Index 283.

8

Jōhō to fugōka no sūri.

English

Coding theory.

Information theory.

Han, Te Sun,1941-

Kobayashi, Kingo,1943-

20140220051832.0

[Book]

Y