Skip to content


  • Research Article
  • Open Access

Quasi-Cyclic LDPC Codes of Column-Weight Two Using a Search Algorithm

EURASIP Journal on Advances in Signal Processing20072007:045768

  • Received: 16 February 2006
  • Accepted: 6 February 2007
  • Published:


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.


  • Information Technology
  • Rate Performance
  • Search Algorithm
  • Quantum Information
  • Equal Size


Authors’ Affiliations

School of Electrical and Electronic Engineering, The University of Adelaide, North Terrace, Adelaide, SA, 5005, Australia


  1. Gallager RG: Low-density parity-check codes. IRE Transactions on Information Theory 1962,8(1):21-28. 10.1109/TIT.1962.1057683MathSciNetView ArticleMATHGoogle Scholar
  2. 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.Google Scholar
  3. 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.2004.829197View ArticleGoogle Scholar
  4. 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.2004.831841MathSciNetView ArticleMATHGoogle Scholar
  5. O'Sullivan ME: Algebraic construction of sparse matrices with large girth. IEEE Transactions on Information Theory 2006,52(2):718-727.MathSciNetView ArticleMATHGoogle Scholar
  6. 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.Google Scholar
  7. 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.View ArticleGoogle Scholar
  8. 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.Google Scholar
  9. 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.12.3627View ArticleGoogle Scholar
  10. 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.View ArticleGoogle Scholar
  11. 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.2004.841966View ArticleGoogle Scholar
  12. 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.Google Scholar
  13. 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.MathSciNetView ArticleMATHGoogle Scholar
  14. 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. 10.1109/18.959255MathSciNetView ArticleMATHGoogle Scholar
  15. Bresnan R: Novel code construction and decoding techniques for LDPC codes, M.Eng.Sc. thesis.Google Scholar
  16. 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-GMathSciNetView ArticleMATHGoogle Scholar
  17. 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.2004.826194MathSciNetView ArticleGoogle Scholar
  18. 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.Google Scholar


© G. Malema and M. Liebelt. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.