Browse > Article
http://dx.doi.org/10.1109/JCN.2015.000029

Construction of Block-LDPC Codes based on Quadratic Permutation Polynomials  

Guan, Wu (Institute of Microelectronics of Chinese Academy of Sciences)
Liang, Liping (Institute of Microelectronics of Chinese Academy of Sciences)
Publication Information
Abstract
A new block low-density parity-check (Block-LDPC) code based on quadratic permutation polynomials (QPPs) is proposed. The parity-check matrix of the Block-LDPC code is composed of a group of permutation submatrices that correspond to QPPs. The scheme provides a large range of implementable LDPC codes. Indeed, the most popular quasi-cyclic LDPC (QC-LDPC) codes are just a subset of this scheme. Simulation results indicate that the proposed scheme can offer similar error performance and implementation complexity as the popular QC-LDPC codes.
Keywords
Low-density parity-check (LDPC) codes; quadratic permutation polynomials (QPPs); quasi-cyclic (QC);
Citations & Related Records
연도 인용수 순위
  • Reference
1 D. J. C. Mackay, "Good error correcting codes based on very sparse matrices," IEEE Trans. Inf. Theory, vol. 45, no. 1, pp. 399-431, 1999.   DOI
2 A. A. Kh. Jabri and A. K. Al-Asmari, "Secure progressive transmission of compressed images," IEEE Trans. Consum. Electron., vol. 42, no. 3, pp. 504-512, 1996.   DOI
3 J. Chen, J. Zhou, and K. Wong, "A modified chaos-based joint compression and encryption scheme," IEEE Trans. Circuits Syst.-II: Express Briefs, vol. 58, no. 2, pp. 110-114, 2011.   DOI
4 S. Y. Chung, T. J. Richardson, and R. L. Urbanke, "Analysis of sumproduct decoding of low-density parity-check codes using a Gaussian approximation," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 657-670, Feb. 2001.   DOI
5 H. Xiao and A. H. Banihashemi, "Improved progressive-edge-growth (PEG) construction of irregular LDPC codes," in Proc. IEEE Globecom, 2004, pp. 489-492.
6 Y. Kou, S. Lin, and M. P. C. 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, 2001.   DOI
7 IEEE Std. 802.16e, IEEE standard for local and metropolitan area networks part 16: air interface for fixed and mobile broadband wireless access systems, amendment 2: physical and medium access control layer for combined fixed and mobile operation in licensed bands, IEEE, 2006.
8 A. Bennatan and D. Burshtein, "Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 549-583, 2006.   DOI
9 U. Wachsmann, R. F. H. Fischer, and J. B., "Multilevel codes: Theoretical concepts and practical design rules," IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 1361-1391, 1991.
10 G. Caire, G. Taricco, and E. Biglieri, "Bit interleaved coded modulation," IEEE Trans. Inf. Theory, vol. 44, no. 5, pp. 927-946, 1998.   DOI
11 W. Guan and H. Xiang, "Decoding and design of LDPC codes for high-order modulations," Wireless Pers. Commun., DOI: 10.1007/s11277-009-9830-0, 2009.   DOI
12 R. Lidl and H. Niederreiter, Finite Fields, 2nd edition, Cambridge University Press, 1997.
13 Z. Liu and D. A. Pados, "DPC codes from generalized polygons," IEEE Trans. Inf. Theory, vol. 51, pp. 3890-3898, Nov. 2005.   DOI
14 O. Y. Takashita, "A compact construction for LDPC codes using permutation polynomials," in Proc. ISIT, (Seattle, USA), July 2006, pp. 79-82.
15 T. Xiong and H. Zhao, "A compact construction for nonbinary LDPC codes using permutation polynomials," in Proc. WiCOM, (Shanghai, China), 2012.
16 R. L. Rivest, "Permutation polynomials modulo $2^w$," Finite Fields and their Appl., vol. 7, pp. 287-292, Feb, 2001.   DOI
17 J. Sun and O. Y. Takeshita, "Interleavers for turbo codes using permutation polynomials over integer rings," IEEE Trans. Inf. Theory, vol. 51, pp. 101-119, Jan. 2005.   DOI
18 J. Ryu and O. Y. Takeshita, "On quadratic inverses for quadratic permutation polynomials over integer rings," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1254-1260, Mar. 2006.   DOI
19 H. Zhao, P. Fan, and V. Tarokh, "On the equivalence of interleavers for Turbo codes using quadratic permutation polynomials over integer rings," IEEE Commun. Lett., vol. 14, no. 3, pp. 236-238, 2010.   DOI
20 R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory, vol. 27, no. 5, pp. 533-547, Sept. 1981.   DOI
21 M. P. C. Fossorier, "Quasi-cyclic low-density parity check codes from circulant permutation matrices," IEEE Trans. inf. Theory, vol. 50, pp. 1788-1793, 2004.   DOI
22 X. Tao, X. Zhou, D. Feng, and L. Zheng, "Circulant search algorithm for the construction of QC-LDPC codes," in Proc. IEEE IC-BNMT, 2011, pp. 188-191.
23 A. Ashikhmin, G. Kramer, and T. Brink, "Extrinsic information transfer functions: A model and two properties," in Proc. CISS, (Princeton, NJ), 2009, pp. 742-747.
24 J. Lin, J. Sha, Z. Wang, and L. Li, "Efficient decoder design for nonbinary quasicyclic LDPC codes," IEEE Trans. Circuits Syst.-I: Regular Papers, vol. 57, no. 5, pp. 1071-1082, May 2010.   DOI
25 H. Zhong and T. Zhang, "Block-LDPC: A practical LDPC coding system design approach," IEEE Trans. Circuits and Syst.-I: Regular Papers, vol. 52, no. 4, pp. 766-775, 2005.   DOI
26 Y. Lin, C. Chen, Y. Liao, and H. Chang, "Structured LDPC codes with low error floor based on PEG Tanner graphs," Proc. IEEE Int. Symp. Circuits Syst., (Seattle, WA), 2008, pp. 1846-1849.
27 R. Peng and R. Chen, "Application of nonbinary LDPC cycle codes to MIMO channels," IEEE Trans. Wireless Commun., vol. 7, no. 6, pp. 2020-2026, 2008.   DOI
28 ETSI EN 302 307, Second generation framing structure, channel coding and modulation system for broadcasting, interactive services, news gathering and other broadband satellite applications, ETSI, 2004.