Lowering the error floor of LDPC codes using cyclic liftings

IEEE Transactions on Information Theory

Volumn 57, Issue 4, 2011, Pages 2213-2224

  Asvadi, Reza ^a   Banihashemi, Amir H ^b   Ahmadian Attari, Mahmoud ^a  

^a K N TOOSI UNIVERSITY OF TECHNOLOGY   (Iran)

^b CARLETON UNIVERSITY   (Canada)

Author keywords

Cyclic lifting; error floor; graph covering; graph lifting; low density parity check (LDPC) codes; trapping sets

Indexed keywords

CYCLIC LIFTING; ERROR FLOOR; GRAPH COVERING; GRAPH LIFTING; LOW-DENSITY PARITY-CHECK CODES; TRAPPING SETS;

CODING ERRORS; ERROR CORRECTION; FLOORS; GAUSSIAN NOISE (ELECTRONIC); ITERATIVE DECODING; WHITE NOISE;

CODES (SYMBOLS);

EID: 79952849807     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2110150     Document Type: Article

References (33)

1. L. Bazzi, T. J. Richardson, and R. L. Urbanke, Exact threshold and optimal codes for the binary-symmetric channel and Gallager's decoding algorithm A IEEE Trans. Inf. Theory, vol. 50, no. 9, pp. 2010-2021, Sep. 2004.
2. S. K. Chilappagari, M. Chertkov, M. G. Stepanov, and B. Vasic, Instanton- based techniques for analyzing and reduction of error floors of LDPC codes IEEE J. Sel. Areas Commun., vol. 27, no. 6, pp. 855-865, Aug. 2009.
3. S. K. Chilappagari, S. Sankaranarayanan, and B. Vasic, Error floors of LDPC codes on the binary symmetric channel in Proc. Int. Conf. Commun. (ICC 2006), Istanbul, Turkey, Jun. 2006, pp. 1089-1094. (Pubitemid 351575455)
4. C. A. Cole, S. G.Wilson, E. K. Hall, and T. R. Giallorenzi, A general method for finding low error rates of LDPC codes IEEE Trans. Inf. Theory, 2006.
5. C. Di, D. Proietti, I. E. Telatar, T. J. Richardson, and R. L. Urbanke, Finite-length analysis of low-density parity-check codes on the binary erasure channel IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1570-1579, Jun. 2002. (Pubitemid 34759861)
6. D. Divsalar, S. Dolinar, C. R. Jones, and K. Andrews, Capacity-approaching protograph codes IEEE J. Sel. Areas Commun., vol. 27, no. 6, pp. 876-888, Aug. 2009.
7. L. Dolecek, P. Lee, Z. Zhang, V. Anantharam, B. Nikolic, and M.Wainwright, Predicting error floors of structured LDPC codes: Deterministic bounds and estimates IEEE J. Sel. Areas Commun., vol. 27, no. 6, pp. 908-917, Aug. 2009.
8. 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.
9. R. G. Gallager, Low Density Parity Check Codes. Cambridge, MA: MIT Press, 1963.
10. J. L. Gross and T. W. Tucker, Topological Graph Theory. New York: Wiley, 1987.
11. Y. Han and W. E. Ryan, Low-floor decoders for LDPC codes IEEE Trans. Commun., vol. 57, no. 6, pp. 1663-1673, Jun. 2009.
12. M. Ivkovic, S. K. Chilappagari, and B. Vasic, Eliminating trapping sets in low-density parity-check codes by using Tanner graph covers IEEE Trans. Inf. Theory, vol. 54, no. 8, pp. 3763-3768, Aug. 2008.
13. X. Jiao, J. Mu, J. Song, and L. Zhou, Eliminating small stopping sets in irregular low-density parity-check codes IEEE Comm. Lett., vol. 13, no. 6, pp. 435-437, June 2009.
14. Y. Mao and A. H. Banihashemi, A heuristic search for good lowdensity parity-check codes at short block lengths in Proc. IEEE ICC 2001, Helsinki, Finland, Jun. 11-14, 2001.
15. D. J. C. Mackay, Encyclopedia of Sparse Graph Codes [Online]. Available: http://www.interference.phy.cam.ac.uk/mackay/codes/data.html
16. T. Richardson, Error floors of LDPC codes in Proc. 41st Ann. Allerton Conf. Commun., Contr. Comput., Monticello, IL, Oct. 2003, pp. 1426-1435.
17. T. Richardson and R. Urbanke, The capacity of low-density parity-check codes under message-passing decoding IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 599-618, Feb. 2001. (Pubitemid 32318092)
18. T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge, U.K.: Cambridge Univ. Press, 2008.
19. R. Smarandache, A. E. Pusane, P. O. Vontobel, and D. J. Costello, Jr., Pseudocodeword performance analysis for LDPC convolutional codes IEEE Trans. Inf. Theory, vol. 55, no. 6, pp. 2577-2598, Jun. 2009.
20. R. Smarandache and P. O. Vontobel, Quasi-cyclic LDPC codes: Influence of proto- and Tanner-graph structure on minimum Hamming distance upper bounds IEEE Trans. Inf. Theory Jan. 2009 [Online]. Available:
21. M. Stepanov and M. Chertkov, Instanton analysis of low-density parity-check codes in the error floor regime in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Seattle, WA, Jul. 2006, pp. 9-14.
22. R. M. Tanner, A recursive approach to low complexity codes IEEE Trans. Inf. Theory, vol. 27, pp. 533-547, Sep. 1981. (Pubitemid 12446960)
23. R. M. Tanner, D. Sridhara, and T. Fuja, A class of group-structured LDPC codes in Proc. ISCTA 2001, Ambleside, U.K., 2001.
24. J. Thorpe, LDPC codes constructed from protographs IPN Progr. Rep., pp. 42-154, Aug. 2003, JPL.
25. T. Tian, C. R. Jones, J. D. Villasenor, and R. D. Wesel, Selective avoidance of cycles in irregular LDPC code construction IEEE Trans. Commun., vol. 52, no. 8, pp. 1242-1247, Aug. 2004.
26. D. Vukobratovic and V. Senk, Evaluation and design of irregular LDPC codes using ACE spectrum IEEE Trans. Commun., vol. 57, no. 8, pp. 2272-2278, Aug. 2009.
27. C.-C. Wang, Code annealing and suppressing effect of the cyclically lifted LDPC code ensembles in Proc. IEEE Inf. Theory Workshop 2006, Chengdu, China, Oct. 2006, pp. 86-90.
28. C.-C. Wang, S. R. Kulkarni, and H. V. Poor, Finding all small errorprone substructures in LDPC codes IEEE Trans. Inf. Theory, vol. 55, no. 5, pp. 1976-1999, May 2009.
29. H. Xiao and A. H. Banihashemi, Improved progressive-edge-growth wth (PEG) construction of irregular LDPC codes IEEE Commun. Lett., vol. 8, no. 12, pp. 715-717, Dec. 2004. (Pubitemid 40085293)
30. H. Xiao and A. H. Banihashemi, Hard-decision performance of LDPC codes on binary symmetric channels with small crossover probabilities in Proc. 23rd Biennial Symp. Commun., Kingston, Ontario, Canada, May 29-Jun. 1 2006, Queen's Univ..
31. H. Xiao and A. H. Banihashemi, Estimation of bit and frame error rates of finite-length low-density parity-check codes on binary symmetric channels IEEE Trans. Commun., vol. 55, no. 12, pp. 2234-2239, , Dec. 2007.
32. H. Xiao and A. H. Banihashemi, Error rate estimation of finite-length low-density parity-check codes decoded by soft-decision iterative algorithms in Proc. 2008 IEEE ISIT, Jul. 2008, pp. 439-443.
33. H. Xiao and A. H. Banihashemi, Error rate estimation of low-density parity-check codes on binary symmetric channels using cycle enumeration IEEE Trans. Commun., vol. 57, no. 6, pp. 1550-1555, Jun. 2009.