Title :
On the growth rate of the weight distribution of irregular doubly-generalized LDPC codes
Author :
Flanagan, Mark F. ; Paolini, Enrico ; Chiani, Marco ; Fossorier, Marc P C
Author_Institution :
Inst. fur Math., Univ. of Zurich, Zurich
Abstract :
In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC and generalized LDPC (GLDPC) codes. Assuming that there exist check and variable nodes with minimum distance 2, it is shown that the growth rate depends only on these nodes. 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.
Keywords :
parity check codes; doubly-generalized LDPC codes; low density parity check codes; weight distribution; Asymptotic stability; Bipartite graph; Block codes; Channel capacity; Communication channels; Equations; Iterative decoding; Parity check codes;
Conference_Titel :
Communication, Control, and Computing, 2008 46th Annual Allerton Conference on
Conference_Location :
Urbana-Champaign, IL
Print_ISBN :
978-1-4244-2925-7
Electronic_ISBN :
978-1-4244-2926-4
DOI :
10.1109/ALLERTON.2008.4797656
