Open AccessRecursive method for generating column weight 3 low‐density parity‐check codes based on three‐partite graphs
Author(s) -
Esmaeili Morteza,
Ahmadi Mahnaz,
Aaron Gulliver T.
Publication year - 2014
Publication title -
iet communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.355
H-Index - 62
eISSN - 1751-8636
pISSN - 1751-8628
DOI - 10.1049/iet-com.2014.0235
Subject(s) - combinatorics , low density parity check code , mathematics , bipartite graph , discrete mathematics , vertex (graph theory) , parity check matrix , binary number , decoding methods , algorithm , graph , arithmetic
In this study, a method is presented to construct column weight 3 (CW3) low‐density parity‐check (LDPC) codes using three‐partite graphs. Let G b be a bipartite graph and N g be the set of all minimum length cycles in G b . Using G b and N g , a three‐partite graph denoted G ( G b , N g ), or simply G t , is formed. Let T be the set of length 3 cycles in G t and T a be the set of three element subsets of vertices in G t such that each of these subsets form a subgraph with no edges in G t and has precisely one element in each section of G t . Furthermore, let H be the binary matrix in which the set of rows represent the set of vertices of G t , the columns represent the elements of V := T ∪ T a , and h ij = 1 if and only if the i th vertex of G t belongs to the j th three element set in V . Then H is a CW3 binary matrix. Using the Tanner graph representing H , a recursive construction for CW3 LDPC codes is provided. Applying a simple restriction on T and T a , codes free of length 4 cycles are generated. Euclidean and finite geometry codes are used as the base codes for generating new CW3 LDPC codes. Results are presented which show that these new codes perform well in an additive white Gaussian noise (AWGN) channel with the iterative sum‐product decoding algorithm.