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Chapter 1 Coding Mathematics1.1 Set Theory1.1.1 The Rudiments of Set Theory1.1.2 The Operation of Sets1.1.3 Mapping1.1.4 The Equivalence of Sets1.1.5 The Classification of Sets1.2 Abstract Algebra1.2.1 Group1.2.2 Ring1.2.3 Field1.2.4 Finite Field1.2.5 Extension Fields1.3 Vector Space1.4 Probability Theory1.4.1 Random Events and Probability1.4.2 Random Variables1.4.3 Numerical Characteristics of Random VariablesChapter 2 Classical Information Theory2.1 Introduction2.2 Discrete Information Source and Discrete Entropy2.2.1 The Discrete Entropy2.2.2 The Average Mutual Information2.2.3 Discrete Lossless Source Coding2.2.4 Huffman Code2.3 Discrete Channel and Channel Capacity2.3.1 The Classification of Channel2.3.2 Channel Capacity2.4 Noisy Channel Coding2.4.1 Decoding Rule of Channels2.4.2 Channel Coding2.5 Linear Block Code2.5.1 G Matrix and H Matrix2.5.2 Error Detection and Correction2.5.3 Standard Array and Syndrome DecodingChapter 3 Network Coding3.1 Fundamentals of Network Coding3.2 Linear Network Coding3.2.1 Deterministic LNC3.2.2 Random LNC3.3 Polynomial Time Algorithm for Linear Network Coding3.3.1 Polynomial Time Algorithm3.3.2 LNCBSDChapter 4 Network Capacity4.1 Network Flows4.2 Network Rate Region and Uniform Fractional Network Model4.2.1 Network Rate Region4.2.2 Uniform Fractional Network Model4.3 Routing Rate Region4.3.1 Multiple Unicast Routing Networks4.3.2 Single Multicast Routing Networks4.3.3 Mixed Patterns of Unicast and Multicast4.4 Coding Rate Region4.4.1 Theoretical Solution of the Coding Rate Region4.4.2 The Cut Set Bound of Coding Rate RegionChapter 5 Network Security Coding5.1 Basics of Network Security5.2 Security of Network Coding ¨C An Overview5.3 NC Security against Passive Attacks5.3.1 Wiretap Model and Security Grade5.3.2 Basic Security5.3.3 Weak Security5.3.4 Perfect Security5.3.5 Strong Security5.3.6 Security of Multisource Networks5.3.7 Security Against TAAs5.4 Secure Error Correcting Codes5.5 NC Security against Active Attacks5.6 Future Developing of NC SecurityChapter 6 Network Storage Coding6.1 Basics of Network Storage Code6.2 A Network Coding Based Cloud Storage Scheme6.3 Subspace Storage Code6.3.1 The Theoretical Framework of Subspace Storage Code6.3.2 A Subspace Regenerating Storage Code with Minimum Decoding Bandwidth6.3.3 Comparisons and DiscussionsReferences