Very large girth column-weight two quasi-cyclic LDPC codes

Abstract

In this paper a modified bit-filling algorithm is used for constructing column-weight two quasi-cyclic low-density parity-check codes with large girths. Code rows are divided into groups. A column is connected to two rows from different groups, which are apart by at least a specified minimum length. Rows that meet the minimum length are searched sequentially. Group rows are connected to consecutive columns resulting in a cyclic structure in the code matrix. Larger codes can be obtained by using larger row groups. Compared to other methods, the algorithm provides an easy and fast way to construct codes of a wide range of rates, girths and lengths. Constructed codes show good bit error rate performance. They are also easily implementable in hardware compared to those obtained using the original bit filling algorithm.