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http://dx.doi.org/10.1109/JCN.2014.000044

Optimized Geometric LDPC Codes with Quasi-Cyclic Structure  

Jiang, Xueqin (College of Information Sciences and Technology Donghua University)
Lee, Moon Ho (Division of Electronic and Information Engineering in Chonbuk National University)
Gao, Shangce (College of Information Sciences and Technology Donghua University)
Wu, Yun (College of Information Sciences and Technology Donghua University)
Publication Information
Journal of Communications and Networks / v.16, no.3, 2014 , pp. 249-257 More about this Journal
Abstract
This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by these methods have quasi-cyclic (QC) structure and large girth. By decomposing hyperplanes in Euclidean geometry, the proposed irregular LDPC codes have flexible column/row weights. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting in the extrinsic information transfer (EXIT) charts. Simulation results show that the proposed codes perform very well with an iterative decoding over the AWGN channel.
Keywords
Column decomposing; Euclidean geometry; EXIT chart; Galois fields; irregular; low-density parity-check (LDPC); parallel bundles; regular; $p_i$ ${\mu}$-flats;
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  • Reference
1 R. G. Gallager, "Low density parity check codes," IEEE Trans. Inf. Theory, vol. IT-8, no. 1, pp. 21-28, Jan. 1962.
2 D. J. C. MacKay and R. M. Neal, "Near Shannon limit performance of low density parity check codes," IEEE Electron. Lett., vol. 32, no. 18, pp. 1645-1646, Aug. 1996.   DOI
3 S. Lin and D. J. Costello, Jr., Error Control Coding: Fundamentals Appl., 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2004.
4 T. Richardson, A. Shokrollahi, and R. Urbanke, "Design of capacityapproaching irregular low-density parity-check codes," IEEE Trans. Inf. Theory, vol. 47, pp. 619-637, Feb. 2001.   DOI
5 S. ten Brink, G. Kramer, and A. Ashikmin, "Detection and decoding of multi-antenna signals with low-density parity-check codes," IEEE Trans. Commun., vol. 52, no. 4, pp. 670-678, Apr. 2004.   DOI
6 Y. Kou, S. Lin, and M. Fossorier, "Low-density parity-check codes based on finite geometries: A rediscovery and new results," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2711-2736, Nov. 2001.   DOI
7 H. Tang, J. Xu, S. Lin, and K. Abdel-Ghaffar, "Codes on finite geometries," IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 572-596, Feb. 2005.   DOI
8 L. Zeng, L. Lan, Y. Y. Tai, B. Zhou, S. Lin and K. Abdel-Ghaffar, "Construction of nonbinary cyclic, quasi-cyclic and regular LDPC codes: A finite geometry approach," IEEE Trans. Inf. Theory, vol. 56, no. 3, pp. 378-387, Feb. 2008.
9 Y. Liu, X.Wang and J. Ma, "Design of quasi-cyclic LDPC codes based on Euclidean geometries," in Proc. ANIA, Bradford, United Kingdom, May 26-29, 2009, pp. 207-211.
10 Q. Huang, S. Lin, and K. Abdel-Ghaffar, "Cyclic and quasi-cyclic LDPC codes on row and column constrained parity-check matrices and their trapping sets," IEEE Trans. Inf. Theory, vol. 58, no. 5, pp. 2648-2671, May 2012.   DOI
11 X. Jiang, Y. yan, and M. Lee, "Construction of mutiple-rate quasi-cyclic LDPC codes via the hyperplane decomposing," J. Commun. Netw., vol. 12, no. 3, June 2011.
12 S. Myung, K. Yang, and J. Kim, "Quasi-cyclic LDPC codes for fast encoding," IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2894-2901, Aug. 2005.   DOI
13 M. P. C. Fossorier, "Quasi-cyclic low-density parity-check codes from circulant permutation matrices," IEEE Trans. Inf. Theory, vol. 50, no. 8, pp, 1788-1793, Aug. 2004.   DOI
14 X. Jiang and M. Lee "Large girth bon-binary LDPC codes based on Euclidean Geometries and finite fields," IEEE Signal Process. Lett., vol. 16, no. 6, June 2009.
15 X. Jiang and M. Lee, "Large girth quasi-cyclic LDPC codes based on the Chinese remainder theorem," IEEE Commun. Lett., vol. 13, no. 5, pp. 342-344, May 2009.   DOI
16 S. Myung, K. Yang and Y. Kim, "Lifting methods for quasi-cyclic LDPC codes," IEEE Commun. Lett., vol. 10, no. 6, pp. 489-452, June 2006.   DOI
17 J. Lu and J. M. F. Moura, "Partition-and-shift LDPC codes," IEEE Trans. Magn., vol. 41, no. 10, pp. 2977-2979, Oct. 2005.   DOI
18 L. Lan, L. Zeng, Y. Y. Tai, L. Chen, S. Lin, and K. Abdel-Ghaffar, "Construction of qasi-cyclic LDPC codes for AWGN and binary erasure channels: A finite field approach," Trans. Inf. Theory, vol. 53, no. 7, July 2007.
19 M. Tuechler and J. Hagenauer, "EXIT charts and irregular codes," in Proc. Conf. Inform. Sci. Syst., Princeton, NJ, Mar. 2002, pp. 748-753.
20 S. ten Brink, "Convergence behavior of iteratively decoded parallel concatenated codes," IEEE Trans. Commun., vol. 49, pp. 1727-1737, Oct. 2001.   DOI
21 C. Di, T. J. Richardson and R. L. Urbanke, "Weight distribution of lowdensity parity-check codes," IEEE Trans. Inf. Theory, vol. 52, no. 11, pp. 4839-4855, Nov. 2006.   DOI
22 W. Weng, A. Ramamoorthy, and R. Wesel, "Lowering the error floors of irregular high-rate LDPC codes by graph conditioning," in Proc. VTC, Los Angeles, CA, Sept. 2004.