目錄
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 Graphical Interpretation
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 of QC-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 2 x 2 SM-Constrained SP-Base Matrices and Their Associated CPM-QC-SP-LDPC Codes
7.4 Masking
7.5 Design of Masking 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-1 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-1 CPM-QC-SC-LDPC Codes
9.6 A More General Construction of Type-2 CPM-QC-SC-LDPC Codes
9.7 Discussion and Remarks
10 Globally Coupled QC-LDPC Codes
10.1 Construction of CN-Based QC-GC-LDPC Codes: Method-1
10.2 A Local/Global Two-Phase Decoding of CN-Based CPM-QC-GC-LDPC Codes
10.3 Construction of CN-Based GC-LDPC Codes: Method-2
10.4 CPM-Dispersion Construction of CN-Based Product QC-GC-LDPC Codes
10.5 Discussion and Remarks
11 SP-Construction of Nonbinary LDPC Codes
11.1 General SP-Construction of NB LDPC Codes Using Binary Base Matrices
11.2 SP-Construction of NB QC-LDPC Codes
11.3 Construction of NB QC-SP-LDPC Codes Using q-ary CPM-Dispersion
11.4 CPM-D Construction of NB CPM-QC-SP-LDPC Codes Using Binary-to-Nonbinary Replacement
11.5 Algebraic Construction of NB QC-PTG-LDPC Codes
11.6 Construction of NB LDPC Codes from Reed-Solomon Codes
11.7 Construction of NB QC-SP-LDPC Codes based on RS Codes
11.8 Discussion and Remarks
12 Conclusion and Remarks
Appendices
A RC-Constrained Arrays of CPMs Constructed Based on Partial Geometries
A.1 RC-Constrained Arrays of CPMs Constructed Based on Two-Dimensional Euclidean Geometries over Finite Fields
A.2 RC-Constrained Arrays of CPMs Based on Partial Geometries Constructed from Prime Fields
B An Algorithm for Searching Compatible Masking and Base Matrices for the CPM-Dispersion Construction of QC-LDPC Codes
C Iterative Decoding Algorithm for NB LDPC Codes
C.1 Introduction
C.2 Algorithm Derivation
C.3 The NB LDPC Decoding Algorithm
References
Index
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