作者：Oliver Johnson[著]
页数：14,209页
出版社：世界图书出版公司
出版日期：2023
ISBN：9787519296872
电子书格式：pdf/epub/txt
内容简介
“香农信息科学经典”已引进了3本加拉格尔教授的经典名著：《麻省理工加拉格尔数字通信原理》、《信息论与可靠通信》和《数据网络（第2版）》。
“香农信息科学经典”书系的策划者曾在麻省理工学院多年亲聆加拉格尔教授授课并一起探讨前沿科技问题。书系的logo形象取材于麻省理工学院校园内的香农塑像。
“香农信息科学经典”包含信息科学各个领域的图书，如信息论、通信与网络、信号处理、机器学习、理论计算机科学、量子信息科学等。
作者简介
[英]奥利佛·约翰逊(Oliver Johnson)，是英国剑桥大学的教授，著名学者，深耕于信息论领域多年， 发表了多篇有关论文和著作。
目录
Preface
1.Introduction to Information Theory
1.1 Entropy and relative entropy
1.1.1 Discrete entropy
1.1.2 Differential entropy
1.1.3 Relative entropy
1.1.4 Other entropy-like quantities
1.1.5 Axiomatic definition of entropy
1.2 Link to thermodynamic entropy
1.2.1 Definition of thermodynamic entropy
1.2.2 Maximum entropy and the Second Law
1.3 Fisher information
1.3.1 Definition and properties
1.3.2 Behaviour on convolution
1.4 Previous information-theoretic proofs
1.4.1 Rényi’s method
1.4.2 Convergence of Fisher information
2.Convergence in Relative Entropy
2.1 Motivation
2.1.1 Sandwich inequality
2.1.2 Projections and adjoints
2.1.3 Normal case
2.1.4 Results of Brown and Barron
2.2 Generalised bounds on projection eigenvalues
2.2.1 Projection of functions in L
2.2.2 Restricted Poincaré constants
2.2.3 Convergence of restricted Poincaré constants
2.3 Rates of convergence
2.3.1 Proof of O(1/n) rate of convergence
2.3.2 Comparison with other forms of convergence
2.3.3 Extending the Cramér-Rao lower bound
3.Non-Identical Variables and Random Vectors
3.1 Non-identical random variables
3.1.1 Previous results
3.1.2 Improved projection inequalities
3.2 Random vectors
3.2.1 Definitions
3.2.2 Behaviour on convolution
3.2.3 Projection inequalities
4.Dependent Random Variables
4.1 Introduction and notation
4.1.1 Mixing coefficients
4.1.2 Main results
4.2 Fisher information and convolution
4.3 Proof of subadditive relations
4.3.1 Notation and definitions
4.3.2 _ Bounds on densities
4.3.3 Bounds on tails
4.3.4 Control of the mixing coefficients
5.Convergence to Stable Laws
1.Introduction to Information Theory
1.1 Entropy and relative entropy
1.1.1 Discrete entropy
1.1.2 Differential entropy
1.1.3 Relative entropy
1.1.4 Other entropy-like quantities
1.1.5 Axiomatic definition of entropy
1.2 Link to thermodynamic entropy
1.2.1 Definition of thermodynamic entropy
1.2.2 Maximum entropy and the Second Law
1.3 Fisher information
1.3.1 Definition and properties
1.3.2 Behaviour on convolution
1.4 Previous information-theoretic proofs
1.4.1 Rényi’s method
1.4.2 Convergence of Fisher information
2.Convergence in Relative Entropy
2.1 Motivation
2.1.1 Sandwich inequality
2.1.2 Projections and adjoints
2.1.3 Normal case
2.1.4 Results of Brown and Barron
2.2 Generalised bounds on projection eigenvalues
2.2.1 Projection of functions in L
2.2.2 Restricted Poincaré constants
2.2.3 Convergence of restricted Poincaré constants
2.3 Rates of convergence
2.3.1 Proof of O(1/n) rate of convergence
2.3.2 Comparison with other forms of convergence
2.3.3 Extending the Cramér-Rao lower bound
3.Non-Identical Variables and Random Vectors
3.1 Non-identical random variables
3.1.1 Previous results
3.1.2 Improved projection inequalities
3.2 Random vectors
3.2.1 Definitions
3.2.2 Behaviour on convolution
3.2.3 Projection inequalities
4.Dependent Random Variables
4.1 Introduction and notation
4.1.1 Mixing coefficients
4.1.2 Main results
4.2 Fisher information and convolution
4.3 Proof of subadditive relations
4.3.1 Notation and definitions
4.3.2 _ Bounds on densities
4.3.3 Bounds on tails
4.3.4 Control of the mixing coefficients
5.Convergence to Stable Laws
