Short quasi-cyclic LDPC codes from convolutional codes

Abstract

We search for good regular quasi-cyclic (QC) LDPC codes with J = 2 ones in each column. In order to simplify the search, QC LDPC codes are represented in the form of tail-biting (TB) convolutional codes. A modified BEAST algorithm is used for finding the free distance (minimum distance) and the girth of both parent convolutional and block LDPC codes. Representations of known bipartite graphs and LDPC based on finite geometries in the form of TB convolutional codes are found. This approach is further generalized for J = 3 QC LDPC codes. Examples of good short LDPC codes with large girth and minimum distance are given. For example, we present a rate 2=5 J = 3 QC LDPC (225, 92)- code with girth 8 and minimum distance 24.