IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Fast generation of regular graphs and construction of cages
Journal of Graph Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Quasicyclic low-density parity-check codes from circulant permutation matrices
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
Algebraic construction of sparse matrices with large girth
IEEE Transactions on Information Theory
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This article introduces a search algorithm for constructing quasi-cyclic LDPC codes of column-weight two. To obtain a submatrix structure, rows are divided into groups of equal sizes. Rows in a group are connected in their numerical order to obtain a cyclic structure. Two rows forming a column must be at a specified distance from each other to obtain a given girth. The search for rows satisfying the distance is done sequentially or randomly. Using the proposed algorithm regular and irregular column-weight-two codes are obtained over a wide range of girths, rates, and lengths. The algorithm, which has a complexity linear with respect to the number of rows, provides an easy and fast way to construct quasi-cyclic LDPC codes. Constructed codes show good bit-error rate performance with randomly shifted codes performing better than sequentially shifted ones.