 | LDPC code designs, constructions, and unification / J.Li et al. - Cambridge: Cambridge university press, 2017. - ix, 247 p.: ill., tab. - Bibliogr.: p.237-243. - Ind.: p.244-247. - ISBN 978-1-107-17568-6
Шифр: (И/З 81-L43) 02
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Preface ...................................................... viii
1 Introduction ................................................. 1
2 Definitions, Concepts, and Fundamental Characteristics of
LDPC Codes ................................................... 6
2.1 Matrices and Matrix Dispersions of Finite Field
Elements ................................................ 6
2.2 Fundamental Stractural Properties and Performance
Characteristics of LDPC Codes ........................... 8
2.3 Discussion and Remarks ................................. 14
3 A Review of PTG-Based Construction of LDPC Codes ............ 16
3.1 PTG-LDPC Code Construction ............................. 16
3.2 Conclusion and Remarks ................................. 20
4 An Algebraic Method for Constructing QC-PTG-LDPC Codes
and Code Ensembles .......................................... 21
4.1 Construction of QC-PTG-LDPC Codes by Decomposing
Base Matrices .......................................... 21
4.2 Construction of RC-Constrained PTG Parity-Check
Matrices ............................................... 26
4.3 Examples ............................................... 28
4.4 Construction of the Ensemble of PTG-LDPC Codes from
an Algebraic Point of View ............................. 38
4.5 Discussion and Remarks ................................. 40
5 Superposition Construction of LDPC Codes .................... 41
5.1 SP-Construction of LDPC Codes and Its Graphical
Interpretation ......................................... 41
5.2 Ensembles of SP-LDPC Codes ............................. 43
5.3 Constraints on the Construction of SP-LDPC Codes
Free of Cycles of Length 4 ............................. 44
5.4 SP-Construction of QC-LDPC Codes ....................... 48
5.5 SP-Base Matrices over Nonnegative Integers ............. 49
5.6 Discussion and Remarks ................................. 50
6 Construction of Base Matrices and RC-Constrained
Replacement Sets for SP-Construction ........................ 51
6.1 RC-Constrained Base Matrices ........................... 51
6.2 Construction of RC-Constrained Replacement Sets
Based on Hamming Codes ................................. 53
6.3 Construction of RC-Constrained Replacement Sets
Based on m-dimensional Euclidean Geometry EG(m, 2)
over GF(2) ............................................. 59
6.4 Construction of RC-Constrained Replacement Sets
Based on RC-Constrained Arrays of CPMs ................. 62
6.5 Discussion and Remarks ................................. 69
7 SP-Construction of QC-LDPC Codes Using Matrix Dispersion
and Masking ................................................. 72
7.1 A Deterministic SP-Construction of QC-LDPC Codes ....... 72
7.2 Conditions on Girth of CPM-QC-SP-LDPC Codes ............ 73
7.3 A Finite Field Construction of 2 × 2 SM-Constrained
SP-Base Matrices and Their Associated CPM-QC-SP-LDPC
Codes .................................................. 74
7.4 Masking ................................................ 77
7.5 Design of Masking Matrices ............................. 84
7.6 Construction of CPM-QC-SP-LDPC Codes for Correcting
Bursts of Erasures by Masking .......................... 92
7.7 Discussion and Remarks ................................. 95
8 Doubly QC-LDPC Codes ........................................ 98
8.1 Base Matrices with Cyclic Structure .................... 98
8.2 CPM-D-SP-Construction of Doubly QC-LDPC Codes ......... 100
8.3 Masking and Variations ................................ 104
8.4 SP-Construction of CPM-QC-SP-LDPC Codes ............... 108
8.5 Discussion and Remarks ................................ 108
9 SP-Construction of Spatially Coupled QC-LDPC Codes ......... 111
9.1 Base Matrices and Their Structural Properties ......... 112
9.2 Type-1 QC-SC-LDPC Codes ............................... 114
9.3 Type-2 QC-SC-LDPC Codes ............................... 120
9.4 Terminated and Tailbiting CPM-QC-SC-LDPC Codes ........ 123
9.5 A More General Construction of Type-1
CPM-QC-SC-LDPC Codes .................................. 129
9.6 A More General Construction of Type-2
CPM-QC-SC-LDPC Codes .................................. 134
9.7 Discussion and Remarks ................................ 135
10 Globally Coupled QC-LDPC Codes ............................. 138
10.1 Construction of CN-Based QC-GC-LDPC Codes: Method-1 ... 138
10.2 A Local/Global Two-Phase Decoding of CN-Based
CPM-QC-GC-LDPC Codes .................................. 146
10.3 Construction of CN-Based GC-LDPC Codes: Method-2 ...... 149
10.4 CPM-Dispersion Construction of CN-Based Product
QC-GC-LDPC Codes ...................................... 154
10.5 Discussion and Remarks ................................ 162
11 SP-Construction of Nonbinary LDPC Codes .................... 166
11.1 General SP-Construction of NB LDPC Codes Using
Binary Base Matrices .................................. 166
11.2 SP-Construction ofNB QC-LDPC Codes .................... 167
11.3 Construction of NB QC-SP-LDPC Codes Using q-ary
CPM-Dispersion ........................................ 173
11.4 CPM-D Construction of NB CPM-QC-SP-LDPC Codes Using
Binary-to-Nonbinary Replacement ....................... 175
11.5 Algebraic Construction of NB QC-PTG-LDPC Codes ........ 182
11.6 Construction of NB LDPC Codes from Reed-Solomon
Codes ................................................. 193
11.7 Construction of NB QC-SP-LDPC Codes based on RS
Codes ................................................. 197
11.8 Discussion and Remarks ................................ 205
12 Conclusion and Remarks ..................................... 209
Appendices ................................................. 215
A RC-Constrained Arrays of CPMs Constructed Based on
Partial Geometries ......................................... 217
A.1 RC-Constrained Arrays of CPMs Constructed Based on
Two-Dimensional Euclidean Geometries over Finite
Fields ................................................ 218
A.2 RC-Constrained Arrays of CPMs Based on Partial
Geometries Constructed from Prime Fields .............. 223
В An Algorithm for Searching Compatible Masking and Base
Matrices for the CPM-Dispersion Construction of QC-LDPC
Codes ...................................................... 225
С Iterative Decoding Algorithm for NB LDPC Codes ............. 228
C.l Introduction .......................................... 228
C.2 Algorithm Derivation .................................. 229
C.3 The NB LDPC Decoding Algorithm ........................ 235
References .................................................... 237
Index ......................................................... 244
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