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Preface
1 Introduction
2 Definitions£¬Concepts£¬and Fundamental Characteristics of LDPC Codes
2£®1 Matrices and Matrix Dispersions of Finite Field Elements
2£®2 Fundamental Structural Properties and Performance Characteristics of LDPC Codes
2£®3 Discussion and Remarks

3 A Review of PTG-Based Construction of LDPC Codes
3£®1 PTG-LDPC Code Construction
3£®2 Conclusion and Remarks

4 An Algebraic Method for Constructing
QC-PTG-LDPC Codes and Code Ensembles
4£®1 Construction of QC-PTG-LDPC Codes by Decomposing Base Matrices
4£®2 Construction of RC-Constrained PTG Parity-Check Matrices
4£®3 Examples
4£®4 Construction of the Ensemble of PTG-LDPC Codes from an Algebraic Point of View
4£®5 Discussion and Remarks

5 Superposition Construction of LDPC Codes
5£®1 SP-Construction of LDPC Codes and Its Graphicallnterpretation
5£®2 Ensembles of SP-LDPC Codes
5£®3 Constraints on the Construction of SP-LDPC Codes Free of Cycles of Length 4
5£®4 SP-Construction ofQC-LDPC Codes
5£®5 SP-Base Matrices over Nonnegative Integers
5£®6 Discussion and Remarks

6 Construction of Base Matrices and RC-Constrained Replacement Sets for SP-Construction
6£®1 RC-Constrained Base Matrices
6£®2 Construction of RC-Constrained Replacement Sets Based on Hamming Codes
6£®3 Construction of RC-Constrained Replacement Sets Based on m-dimensional Euclidean Geometry EG(m£¬2) over GF(2)
6£®4 Construction of RC-Constrained Replacement Sets Based on RC-Constrained Arrays of CPMs
6£®5 Discussion and Remarks

7 SP-Construction of QC-LDPC Codes Using Matrix
Dispersion and Masking
7£®1 A Deterministic SP-Construction of QC~LDPC Codes
7£®2 Conditions on Girth of CPM-QC-SP-LDPC Codes
7£®3 A Finite Field Construction of 2x2 SM-Constrained SP-Base
Matrices and Their Associated CPM-QC SP-LDPC Codes
7£®4 Masking
7£®5 Design ofMasking Matrices
7£®6 Construction of CPM-QC-SP-LDPC Codes for Correcting
Bursts of Erasures by Masking
7£®7 Discussion and Remarks

8 Doubly QC-LDPC Codes
8£®1 Base Matrices with Cyclic Structure
8£®2 CPM-D-SP-Construction of Doubly QC-LDPC Codes
8£®3 Masking and Variations
8£®4 SP-Construction of CPM-QC-SP-LDPC Codes
8£®5 Discussion and Remarks

9 SP-Construction of Spatially Coupled QC-LDPC Codes
9£®1 Base Matrices and Their Structural Properties
9£®2 Type-l QC-SC-LDPC Codes
9£®3 Type-2 QC-SC-LDPC Codes
9£®4 Terminated and Tailbiting CPM-QC-SC-LDPC Codes
9£®5 A More General Construction of Type-l CPM-QC-SC-LDPC Codes
9£®6 A More General Construction of Type-2 CPM-QC-SC-LDPC Codes
9£®7 Discussion and Remarks
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10 Globally Coupled QC-LDPC Codes
11 SP-Construction of Nonbinary LDPC Codes
12 Conclusion and Remarks