Title :
Explicit Construction of Type-II QC LDPC Codes with Girth at least 6
Author_Institution :
RMIT Univ., Melbourne
Abstract :
Type-II quasi-cyclic (QC) LDPC codes are constructed from combinations of weight-0, weight-1 and weight-2 circulant matrices. The structure of cycles of length 2n are investigated, and necessary and sufficient conditions for a type-II QC LDPC parity check matrix H to have girth at least 2(n + 1) are given. An explicit construction of type-II codes which guarantees girth at least 6 is presented. A necessary and sufficient condition for a QC matrix with one or more rows of circulants, to be fullrank is derived.
Keywords :
cyclic codes; matrix algebra; parity check codes; circulant matrix; length cycles; parity check matrix; type-II quasicyclic LDPC codes; Encoding; Equations; Iterative algorithms; Iterative decoding; Mathematics; Parity check codes; Polynomials; Statistics; Sufficient conditions;
Conference_Titel :
Information Theory, 2007. ISIT 2007. IEEE International Symposium on
Conference_Location :
Nice
Print_ISBN :
978-1-4244-1397-3
DOI :
10.1109/ISIT.2007.4557574
