信息論基礎(chǔ)

內(nèi)容概要

《信息論基礎(chǔ)(英文版)》作者（楊偉豪）現(xiàn)為香港中文大學(xué)網(wǎng)絡(luò)編碼研究所主任，是網(wǎng)絡(luò)編碼理論的提出者之一。本書原版自2002年出版以來，被哥倫比亞大學(xué)、康奈爾大學(xué)、麻省理工學(xué)院、斯坦福大學(xué)等美國著名學(xué)府所采用，是信息理論方面的重要教材。本書首先介紹了信息論的經(jīng)典內(nèi)容，然后全面詳細(xì)地論述了，度量、網(wǎng)絡(luò)編碼、Shannon型與非Shannon型信息不等式等理論，以及熵函數(shù)與群論之間的關(guān)系?！缎畔⒄摶A(chǔ)(英文版)》中配有大量的實(shí)例、插圖和習(xí)題，適合作為通信、電子信息、計(jì)算機(jī)等專業(yè)的高年級本科生和研究生的教材，也可供相關(guān)領(lǐng)域的科研人員參考。

作者簡介

楊偉豪(Raymond
w．Yeung)教授1988年畢業(yè)于美國康奈爾大學(xué)。獲博士學(xué)位。之后曾在AT&T貝爾實(shí)驗(yàn)室工作3年，于1
991年加入香港中文大學(xué)，現(xiàn)為網(wǎng)絡(luò)編碼研究所主任，是網(wǎng)絡(luò)編碼理論的提出者之一，其主要研究領(lǐng)域?yàn)樾畔⒗碚撆c網(wǎng)絡(luò)編碼。他還是IEEE
Fellow和香港工程師學(xué)會(huì)會(huì)士。

書籍目錄

1. THE SCIENCE OF INFORMATION
2. INFORMATION MEASURES
 2.1 Independence and Markov Chai
 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
  3.2.1 Definition and Existence
  3.2.2 Huffman Codes
 3.3 Redundancy of Prefix Codes
 Problems
 Historical Notes
4. WEAK TYPICALITY
 4.1 The Weak AEP
 4.2 The Source Coding Theorem
 4.3 Efficient Source Coding
 4.4 The Shannon-McMiilan-BreimanTheorem
 Problems
 Historical Notes
5. STRONG TYPICALITY
 5.1 StrongAEP
 5.2 Strong Typicality Veus Weak Typicality
 5.3 Joint Typicality
 5.4 An Interpretation of the Basic Inequalities
 Problems
 Historical Notes
6. THE/-MEASURE
 6.1 Preliminaries
 6.2 The/-Measure for Two Random Variables
 6.3 Cotruction of the/-Measure ч*
 6.4 #* Can be Negative
 6.5 Information Diagrams
 6.6 Examples of Applicatio
 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 MemorylessChannels
 8.2 The Channel Coding Theorem
 8.3 The Convee
 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 Convee
 9.5 Achievability of RI(D)
 Problems
 Historical Notes
10. THE BLAHUT-ARIMOTO ALGORITHMS
 10.I Alternating Optimization
 10.2 The Algorithms
  10.2.1 Channel Capacity
  10.2.2 The Rate-Distortion Function
 10.3 Convergence
  10.3.1- A Sufficient Condition
  10.3.2 Convergence to the Channel Capacity
 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
  11.5.1 Acyclic Networks
  11.5.2 Cyclic Networks
 Problems
 Historical Notes
12. INFORMATION INEQUALITIES
 12.1 The Region Fn
 12.2 Information Expressio in Canonical Form
 12.3 A Geometrical Framework
  12.3.1 Uncotrained Inequalities
  12.3.2 Cotrained Inequalities
  12.3.3 Cotrained Identities
 12.4 Equivalence of Cotrained 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
  13.2.1 Uncotrained Inequalities
  13.2.2 Cotrained Inequalities and Identities
 13.3 A Duality
 13.4 Machine Proving - ITIP
 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
14. BEYOND SHANNON-TYPE INEQUALITIES
 14.1 Characterizatio of г2,г3, and гn
 14.2 A Non-Shannon-Type Uncotrained Inequality
 14.3 A Non-Shannon-Type Cotrained Inequality
 14.4 Applicatio
 Problems
 Historical Notes
15. MULTI-SOURCE NETWORK CODING
 15.1 Two Characteristics
  15.1.1 The Max-Flow Bounds
  15.1.2 Superposition Coding
 15.2 Examples of Application
  15.2.1 Multilevel Diveity Coding
  15.2.2 Satellite Communication Network
 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 Functio
 16.3 A Group Characterization of гn
 16.4 Information Inequalities and Group Inequalities
 Problems
 Historical Notes
Bibliography
Index

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