差错控制编码（ESSENTIALS OF ERROR-CONTROL CODING）

1 Information and Coding Theory 1 1.1 Information 3 1.1.1 A Measure of Information 3 1.2 Entropy and Information Rate 4 1.3 Extended DMSs 9 1.4 Channels and Mutual Information 10 1.4.1 Information Transmission over Discrete Channels 10 1.4.2 Information Channels 10 1.5 Channel Probability Relationships 13 1.6 The A Prioriand A Posteriori Entropies 15 1.7 Mutual Information 16 1.7.1 Mutual Information: Definition 16 1.7.2 Mutual Information: Properties 17 1.8 Capacity of a Discrete Channel 21 1.9 The Shannon Theorems 22 1.9.1 Source Coding Theorem 22 1.9.2 Channel Capacity and Coding 23 1.9.3 Channel Coding Theorem 25 1.10 Signal Spaces and the Channel Coding Theorem 27 1.10.1 Capacity of the Gaussian Channel 28 1.11 Error-Control Coding 32 1.12 Limits to Communication and their Consequences 34 Bibliography and References 38 Problems 38 2 Block Codes 41 2.1 Error-Control Coding 41 2.2 Error Detection and Correction 41 2.2.1 Simple Codes: The Repetition Code 42 2.3 Block Codes: Introduction and Parameters 43 2.4 The Vector Space over the Binary Field 44 2.4.1 Vector Subspaces 46 2.4.2 Dual Subspace 48 2.4.3 Matrix Form 48 2.4.4 Dual Subspace Matrix 49 2.5 Linear Block Codes 50 2.5.1 Generator Matrix G 51 2.5.2 Block Codes in Systematic Form 52 2.5.3 Parity Check Matrix H 54 2.6 Syndrome Error Detection 55 2.7 Minimum Distance of a Block Code 58 2.7.1 Minimum Distance and the Structure of the H Matrix 58 2.8 Error-Correction Capability of a Block Code 59 …………………… ……………………