Some voltage graph-based LDPC tailbiting codes with large girth

Abstract

The relation between the parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and the biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Algorithms for searching iteratively for LDPC block codes with large girth are presented and constructions based on Steiner Triple Systems and short QC block codes are introduced, leading to new QC regular LDPC block codes with girth up to 24.