NDLI: On the Growth Rate of the Weight Distribution of Irregular Doubly Generalized LDPC Codes

Content Provider	IEEE Xplore Digital Library
Author	Flanagan, M.F. Paolini, E. Chiani, M. Fossorier, M.P.C.
Copyright Year	1963
Abstract	In this paper, the asymptotic growth rate of the weight distribution of irregular doubly generalized LDPC (D-GLDPC) codes is derived. The analysis yields a compact expression which accurately approximates the growth rate function for the case of small linear-weight codewords. This paper generalizes existing results for LDPC and generalized LDPC (GLDPC) codes. Ensembles with smallest check or variable node minimum distance greater than 2 are shown to have good growth-rate behavior, while for other ensembles a fundamental parameter is identified which discriminates between an asymptotically small and an asymptotically large expected number of small linear-weight codewords. Also, in the latter case it is shown that the growth rate depends only on the check and variable nodes with minimum distance 2. An important connection between this new result and the stability condition of D-GLDPC codes over the BEC is highlighted. Such a connection, previously observed for LDPC and GLDPC codes, is now extended to the case of D-GLDPC codes. Finally, it is shown that the analysis may be extended to include the growth rate of the stopping set size distribution of irregular D-GLDPC codes.
Sponsorship	IEEE Information Theory Society
Starting Page	3721
Ending Page	3737
Page Count	17
File Size	394030
File Format	PDF
ISSN	00189448
Volume Number	57
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Block codes Polynomials Stability analysis Asymptotic stability Iterative decoding Generators weight distribution Doubly generalized LDPC codes growth rate irregular code ensembles stopping set size distribution
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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