NDLI: On the Girth of Quasi-Cyclic Protograph LDPC Codes

Content Provider	IEEE Xplore Digital Library
Author	Karimi, M. Banihashemi, A.H.
Copyright Year	1963
Abstract	In this paper, we study the relationships between the girth of the Tanner graph of a quasi-cyclic (QC) protograph low-density parity-check (LDPC) code, the lifting degree, and the size and the structure of the base graph. As a result, for a given base graph, we derive a lower bound on the lifting degree as a necessary condition for the lifted graph to have a certain girth. This also provides an upper bound on the girth of the family of graphs lifted from a given base graph with a given lifting degree. The upper bounds derived here, which are applicable to both regular and irregular base graphs with no parallel edges, are in some cases more general and in some other cases tighter than the existing bounds. The results presented in this work can be used to design cyclic liftings with relatively small degree and relatively large girth. As an example, we present new QC protograph LDPC code constructions with girth 8 using fully connected base graphs. These constructions provide upper bounds on the lifting degree required for achieving girth 8 using fully connected base graphs.
Sponsorship	IEEE Information Theory Society
Starting Page	4542
Ending Page	4552
Page Count	11
File Size	1772819
File Format	PDF
ISSN	00189448
Volume Number	59
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Parity check codes Upper bound Bipartite graph upper bounds on girth Cyclic lifting girth lifting low-density parity-check (LDPC) codes protograph protograph LDPC codes quasi-cyclic LDPC codes
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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