Design of Multiple-Edge Protographs for QC LDPC Codes Avoiding Short Inevitable Cycles

There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them focus on protographs with single edges and little research has been done for the construction of QC LDPC codes lifted from protographs with multiple...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on information theory 2013-07, Vol.59 (7), p.4598-4614
Main Authors: PARK, Hosung, HONG, Seokbeom, NO, Jong-Seon, SHIN, Dong-Joon
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Applied sciences
Coding, codes
Design theory
Exact sciences and technology
girth
Hamming distance
Indexes
inevitable cycle
Information theory
Information, signal and communications theory
Iterative decoding
minimum Hamming distance
multiple-edge protograph
Polynomials
quasi-cyclic (QC) low-density parity-check (LDPC) codes
Signal and communications theory
Telecommunications and information theory
Upper bound
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them focus on protographs with single edges and little research has been done for the construction of QC LDPC codes lifted from protographs with multiple (i.e., parallel) edges. Compared to single-edge protographs, multiple-edge protographs have benefits such that QC LDPC codes lifted from them can potentially have larger minimum Hamming distance. In this paper, all subgraph patterns of multiple-edge protographs, which prevent QC LDPC codes from having large girth by inducing inevitable cycles, are fully investigated based on a graph-theoretic approach. By using combinatorial designs, a systematic construction method of multiple-edge protographs is proposed for regular QC LDPC codes with girth at least 12 and another method is proposed for regular QC LDPC codes with girth at least 14. Moreover, a construction algorithm of QC LDPC codes based on certain liftings of multiple-edge protographs is proposed and it is shown that the resulting QC LDPC codes have larger upper bounds on the minimum Hamming distance than those lifted from single-edge protographs. Simulation results are provided to compare the performance of the proposed QC LDPC codes with progressive edge-growth (PEG) LDPC codes and with PEG QC LDPC codes.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2250574