- Research Article
Quasi-Cyclic LDPC Codes of Column-Weight Two Using a Search Algorithm
EURASIP Journal on Advances in Signal Processingvolume 2007, Article number: 045768 (2007)
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.
Gallager RG: Low-density parity-check codes. IRE Transactions on Information Theory 1962,8(1):21-28. 10.1109/TIT.1962.1057683
Song H, Liu J, Kumar BVKV: Low complexity LDPC codes for partial response channels. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '02), November 2002, Taipei, Taiwan 2: 1294–1299.
Song H, Liu J, Kumar BVKV: Large girth cycle codes for partial response channels. IEEE Transactions on Magnetics 2004,40(4, part 2):3084-3086. 10.1109/TMAG.2004.829197
Fossorier MPC: Quasi-cyclic low-density parity-check codes from circulant permutation matrices. IEEE Transactions on Information Theory 2004,50(8):1788-1793. 10.1109/TIT.2004.831841
O'Sullivan ME: Algebraic construction of sparse matrices with large girth. IEEE Transactions on Information Theory 2006,52(2):718-727.
Mao Y, Banihasherni AH: A heuristic search for good low-density parity-check codes at short block lengths. Proceedings of IEEE International Conference on Communications (ICC'01), June 2001, Helsinki, Finland 1: 41–44.
Zhang H, Moura JM: The design of structured regular LDPC codes with large girth. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '03), December 2003, San Francisco, Calif, USA 7: 4022–4027.
Malema G, Liebelt M: Low-complexity LDPC codes for magnetic recordings. Proceedings of International Enformatika Conference (IEC '05), August 2005, Prague, Czech Republic 5: 269–271.
Fujita H, Sakaniwa K: Some classes of quasi-cyclic LDPC codes: properties and efficient encoding method. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2005,E88-A(12):3627-3635. 10.1093/ietfec/e88-a.12.3627
Olçer S: Decoder architecture for array-code-based LDPC codes. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '03), December 2003, San Francisco, Calif, USA 4: 2046–2050.
Xu J, Chen L, Zeng L, Lan L, Lin S: Construction of low-density parity-check codes by superposition. IEEE Transactions on Communications 2005,53(2):243-251. 10.1109/TCOMM.2004.841966
Campello J, Modha DS, Rajagopalan S: Designing LDPC codes using bit-filling. Proceedings of IEEE International Conference on Communications (ICC '01), June 2001, Helsinki, Finland 1: 55–59.
Hu X-Y, Eleftheriou E, Arnold DM: Regular and irregular progressive edge-growth tanner graphs. IEEE Transactions on Information Theory 2005,51(1):386-398.
Kou Y, Lin S, Fossorier MPC: Low-density parity-check codes based on finite geometries: a rediscovery and new results. IEEE Transactions on Information Theory 2001,47(7):2711-2736. 10.1109/18.959255
Bresnan R: Novel code construction and decoding techniques for LDPC codes, M.Eng.Sc. thesis.
Meringer M: Fast generation of regular graphs and construction of cages. Journal of Graph Theory 1999,30(2):137-146. 10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G
Chen Y, Parhi KK: Overlapped message passing for quasi-cyclic low-density parity check codes. IEEE Transactions on Circuits and Systems 2004,51(6):1106-1113. 10.1109/TCSI.2004.826194
Thorpe J, Andrews K, Dolinar S: Methodologies for designing LDPC codes using protographs and circulants. Proceedings of IEEE International Symposium on Information Theory, June-July 2004, Chicago, Ill, USA 238–242.