Hierarchical and High-Girth QC LDPC Codes
| Autor: | Jonathan S. Yedidia, Yige Wang, Stark C. Draper |
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| Rok vydání: | 2013 |
| Předmět: |
FOS: Computer and information sciences
Discrete mathematics Hierarchy (mathematics) Computer science Computer Science - Information Theory Information Theory (cs.IT) Structure (category theory) Degrees of freedom (statistics) Girth (graph theory) Library and Information Sciences Computer Science Applications Parity-check matrix Low-density parity-check code Circulant matrix Information Systems |
| Zdroj: | IEEE Transactions on Information Theory. 59:4553-4583 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2013.2253512 |
| Popis: | We present a general approach to designing capacity-approaching high-girth low-density parity-check (LDPC) codes that are friendly to hardware implementation. Our methodology starts by defining a new class of "hierarchical" quasi-cyclic (HQC) LDPC codes that generalizes the structure of quasi-cyclic (QC) LDPC codes. Whereas the parity check matrices of QC LDPC codes are composed of circulant sub-matrices, those of HQC LDPC codes are composed of a hierarchy of circulant sub-matrices that are in turn constructed from circulant sub-matrices, and so on, through some number of levels. We show how to map any class of codes defined using a protograph into a family of HQC LDPC codes. Next, we present a girth-maximizing algorithm that optimizes the degrees of freedom within the family of codes to yield a high-girth HQC LDPC code. Finally, we discuss how certain characteristics of a code protograph will lead to inevitable short cycles, and show that these short cycles can be eliminated using a "squashing" procedure that results in a high-girth QC LDPC code, although not a hierarchical one. We illustrate our approach with designed examples of girth-10 QC LDPC codes obtained from protographs of one-sided spatially-coupled codes. Comment: Submitted to IEEE Transactions on Information THeory |
| Databáze: | OpenAIRE |
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