Chapter 1 Coding Mathematics
1.1 Set Theory
1.1.1 The Rudiments of Set Theory
1.1.2 The Operation of Sets
1.1.3 Mapping
1.1.4 The Equivalence of Sets
1.1.5 The Classification of Sets
1.2 Abstract Algebra
1.2.1 Group
1.2.2 Ring
1.2.3 Field
1.2.4 Finite Field
1.2.5 Extension Fields
1.3 Vector Space
1.4 Probability Theory
1.4.1 Random Events and Probability
1.4.2 Random Variables
1.4.3 Numerical Characteristics of Random Variables
Chapter 2 Classical Information Theory
2.1 Introduction
2.2 Discrete Information Source and Discrete Entropy
2.2.1 The Discrete Entropy
2.2.2 The Average Mutual Information
2.2.3 Discrete Lossless Source Coding
2.2.4 Huffman Code
2.3 Discrete Channel and Channel Capacity
2.3.1 The Classification of Channel
2.3.2 Channel Capacity
2.4 Noisy Channel Coding
2.4.1 Decoding Rule of Channels
2.4.2 Channel Coding
2.5 Linear Block Code
2.5.1 G Matrix and H Matrix
2.5.2 Error Detection and Correction
2.5.3 Standard Array and Syndrome Decoding
Chapter 3 Network Coding
3.1 Fundamentals of Network Coding
3.2 Linear Network Coding
3.2.1 Deterministic LNC
3.2.2 Random LNC
3.3 Polynomial Time Algorithm for Linear Network Coding
3.3.1 Polynomial Time Algorithm
3.3.2 LNCBSD
Chapter 4 Network Capacity
4.1 Network Flows
4.2 Network Rate Region and Uniform Fractional Network Model
4.2.1 Network Rate Region
4.2.2 Uniform Fractional Network Model
4.3 Routing Rate Region
4.3.1 Multiple Unicast Routing Networks
4.3.2 Single Multicast Routing Networks
4.3.3 Mixed Patterns of Unicast and Multicast
4.4 Coding Rate Region
4.4.1 Theoretical Solution of the Coding Rate Region
4.4.2 The Cut Set Bound of Coding Rate Region
Chapter 5 Network Security Coding
5.1 Basics of Network Security
5.2 Security of Network Coding – An Overview
5.3 NC Security against Passive Attacks
5.3.1 Wiretap Model and Security Grade
5.3.2 Basic Security
5.3.3 Weak Security
5.3.4 Perfect Security
5.3.5 Strong Security
5.3.6 Security of Multisource Networks
5.3.7 Security Against TAAs
5.4 Secure Error Correcting Codes
5.5 NC Security against Active Attacks
5.6 Future Developing of NC Security
Chapter 6 Network Storage Coding
6.1 Basics of Network Storage Code
6.2 A Network Coding Based Cloud Storage Scheme
6.3 Subspace Storage Code
6.3.1 The Theoretical Framework of Subspace Storage Code
6.3.2 A Subspace Regenerating Storage Code with Minimum Decoding Bandwidth
6.3.3 Comparisons and Discussions
References
