目錄
Preface
1 Coding and Capacity
1.1 Digital Data Communication and Storage
1.2 Channel-Coding Overview
1.3 Channel-Code Archetype: The (7,4) Hamming Code
1.4 Design Criteria and Performance Measures
1.5 Channel-Capacity Formulas for Common Channel Models
1.5.1 Capacity for Binary-Input Memoryless Channels
1.5.2 Coding Limits for M-ary-Input Memoryless Channels
1.5.3 Coding Limits for Channels with Memory
Problems
References
2 Finite Fields, Vector Spaces, Finite Geometries, and Graphs
2.1 Sets and Binary Operations
2.2 Groups
2.2.1 Basic Concepts of Groups
2.2.2 Finite Groups
2.2.3 Subgroups and Cosets
2.3 Fields
2.3.1 Definitions and Basic Concepts
2.3.2 Finite Fields
2.4 Vector Spaces
2.4.1 Basic Definitions and Properties
2.4.2 Linear Independence and Dimension
2.4.3 Finite Vector Spaces over Finite Fields
2.4.4 Inner Products and Dual Spaces
2.5 Polynomials over Finite Fields
2.6 Construction and Properties of Galois Fields
2.6.1 Construction of Galois Fields
2.6.2 Some Fundamental Properties of Finite Fields
2.6.3 Additive and Cyclic Subgroups
2.7 Finite Geometries
2.7.1 Euclidean Geometries
2.7.2 Projective Geometries
2.8 Graphs
2.8.1 Basic Concepts
2.8.2 Paths and Cycles
2.8.3 Bipartite Graphs
Problems
References
Appendix A
3 Linear Block Codes
3.1 Introduction to Linear Block Codes
3.1.1 Generator and Parity-Check Matrices
3.1.2 Error Detection with Linear Block Codes
3.1.3 Weight Distribution and Minimum Hamming Distance of a Linear Block Code
3.1.4 Decoding of Linear Block Codes
3.2 Cyclic Codes
3.3 BCH Codes
3.3.1 Code Construction
3.3.2 Decoding
3.4 Nonbinary Linear Block Codes and Reed-Solomon Codes
3.5 Product, Interleaved, and Concatenated Codes
3.5.1 Product Codes
3.5.2 Interleaved Codes
3.5.3 Concatenated Codes
3.6 Quasi-Cyclic Codes
3.7 Repetition and Single-Parity-Check Codes
Problems
References
4 Convolutional Codes
4.1 The Convolutional Code Archetype
4.2 Algebraic Description of Convolutional Codes
4.3 Encoder Realizations and Classifications
4.3.1 Choice of Encoder Class
4.3.2 Catastrophic Encoders
4.3.3 Minimal Encoders
4.3.4 Design of Convolutional Codes
4.4 Alternative Convolutional Code Representations
4.4.1 Convolutional Codes as Semi-Infinite Linear Codes
4.4.2 Graphical Representations for Convotutional Code Encoders
……
5 Low-Density Parity-Check Codes
6 Computer-Based Design of LDPC Codes
7 Turbo Codes
8 Ensemble Enumerators for Turbo and LDPC Codes
9 Ensemble Decoding Thresholds for LDPC and Turbo Codes
10 Finite-Geometry LDPC Codes
11 Constructions of LDPC Codes Based on Finite Fields
12 LDPC Codes Based on Combinatorial Designs, Graphs, and Superposition
13 LDPC Codes for Binary Erasure Channels
14 Nonbinary LDPC Codes
15 LDPC Code Applications and Advanced Topics
Index
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