了得網自然科學_信息論基礎

內容簡介

本書繫統介紹了信息論基本原理及其在通信理論、統計學、計算機科學、概率論以及投資理論等領域的應用。作者以循序漸進的方式，介紹了信息量的基本定義、相對熵、互信息以及他們如何自然地用來解決數據壓縮、信道容量、信息率失真、統計假設、網絡信息流等問題。除此以外，本書還探討了很多教材中從未涉及的問題，如：
熱力學第二定律與馬爾可夫鏈之間的聯繫
·huffman編碼的*性
·數據壓縮的對偶性
·lempel ziv編碼
·kolmogorov復雜性
·porfolio理論
·信息論不等式及其數學結論等。
本書可作為通信、電子、計算機、自動控制、統計、經濟等專業高年級本科生和研究生的教材或參考書，也可供相關領域的科研人員和專業技術人員參考。

作者簡介

Thomas M．Cover斯坦福大學電氣工程繫、統計繫教授。曾任IEEE信息論學會主席，現任數理統計研究所研究員、IEEE高級會員。1 972年以論文“Broadcast Channels”榮獲信息論優秀論文獎，1990年被選為“Shannon Lecturer”，這是信息論領域的榮譽。近20年，他致力於研究信

list of figures
1 introduction and preview
1.1 preview of the book
2 entropy, relative entropy and mutual information
2.1 entropy
2.2 joint entropy and conditional entropy
2.3 relative entropy and mutual information
2.4 relationship between entropy and mutual information
2.5 chain rules for entropy, relative entropy and mutual information
2.6 jensen's inequality and its consequences
2.7 the log sum inequality and its applications
2.8 data processing inequality
2.9 the second law of thermodynamics
2.10 sufficient statisticslist of figures
1 introduction and preview
1.1 preview of the book
2 entropy, relative entropy and mutual information
2.1 entropy
2.2 joint entropy and conditional entropy
2.3 relative entropy and mutual information
2.4 relationship between entropy and mutual information
2.5 chain rules for entropy, relative entropy and mutual information
2.6 jensen's inequality and its consequences
2.7 the log sum inequality and its applications
2.8 data processing inequality
2.9 the second law of thermodynamics
2.10 sufficient statistics
2.11 fano's inequality
summary of chapter 2
problems for chapter 2
historical notes
3 the asymptotic equipartition property
3.1 the aep
3.2 consequences of the aep: data compression
3.3 high probability sets and the typical set
summary of chapter 3
problems for chapter 3
historical notes
4 entropy rates of a stochastic process
4.1 markov chains
4.2 entropy rate
4.3 example: entropy rate of a random walk on a weighted graph
4.4 hidden markov models
summary of chapter 4
problems for chapter 4
historical notes
5 data compression
6 gambling and data compression
7 kolmogorov complexity
8 channel capacity
9 differential entropy
10 the gaussian channel
11 maximum entropy and spectral estimation
12 information theory and statistics
13 rate distortion theory
14 network information theory
15 information theory and the stock market
16 inequalities in information theory
index

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