LDPC Code Designs, Constructions, and Unification

Written by leading experts, this self-contained text provides systematic coverage of LDPC codes and their construction techniques, unifying both algebraic- and graph-based approaches into a single theoretical framework (the superposition construction). An algebraic method for constructing protograph LDPC codes is described, and entirely new codes and techniques are presented. These include a new class of LDPC codes with doubly quasi-cyclic structure, as well as algebraic methods for constructing spatially and globally coupled LDPC codes. Authoritative, yet written using accessible language, this text is essential reading for electrical engineers, computer scientists and mathematicians working in communications and information theory.

1. Introduction; 2. Definitions, concepts, and fundamental characteristics of LDPC codes; 3. A review of PTG-based construction of LDPC codes; 4. An algebraic method for constructing QC-PTG-LDPC codes and code ensembles; 5. Superposition construction of LDPC codes; 6. Construction of base matrices and RC-constrained replacement sets for the SP-construction; 7. SP-construction of QC-LDPC codes using matrix dispersion and masking; 8. Doubly QC-LDPC codes; 9. SP-construction of spatially coupled QC-LDPC codes; 10. Globally coupled QC-LDPC codes; 11. SP-construction of nonbinary LDPC codes; 12. Conclusion and remarks.

Juane Li is a postdoctoral researcher in the Department of Electrical and Computer Engineering at the University of California, Davis. Her current research interests are channel coding for communications and storage systems, and hardware implementation of encoders and decoders for LDPC codes.
Shu Lin is an Adjunct Professor in the Department of Electrical and Computer Engineering at the University of California, Davis, and an IEEE Life Fellow. He is the co-author of Channel Codes: Classical and Modern (Cambridge, 2009) and Error Control Coding: Fundamentals and Applications (2nd edition, 2004).
Khaled Abdel-Ghaffar is Professor of Electrical and Computer Engineering at the University of California, Davis. He has held research positions at the IBM Almaden Research Center, Delft University of Technology, and the University of Bergen.
William E. Ryan is an IEEE Fellow and currently works for Zeta Associates, USA. He was previously a professor at New Mexico State University and the University of Arizona. He is the co-author of Channel Codes: Classical and Modern (Cambridge, 2009).
Daniel J. Costello, Jr, is the Leonard Bettex Professor Emeritus of Electrical Engineering at the University of Notre Dame, and an IEEE Fellow. He is the co-author of the textbook Error Control Coding: Fundamentals and Applications (2nd edition, 2004).