Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes

IEEE Transactions on Information Theory

Volumn 56, Issue 1, 2010, Pages 181-201

  Dolecek, Lara ^a   Zhang, Zhengya ^b,c   Anantharam, Venkat ^c   Wainwright, Martin J ^c   Nikolić, Borivoje ^c  

^a Department of Electrical Engineering and Computer Science   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Absorbing set; Bit flipping; Error floor; Low density parity check (LDPC ) codes; Message passing decoding; Nearcodeword; Trapping set

Indexed keywords

ABSORBING SET; BIT FLIPPING; ERROR FLOOR; LOW-DENSITY PARITY-CHECK CODES; MESSAGE-PASSING DECODING;

CODING ERRORS; DECODING; FLOORS; MESSAGE PASSING; SIGNAL TO NOISE RATIO;

BIT ERROR RATE;

EID: 73849102493     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2034781     Document Type: Article

References (34)

1. Digital Video Broadcasting Standard, DVB-S2, 2006 [Online]. Available: http://pda.etsi.org/exchangefolder/en-302307v010102p.pdf, pp. 19-21.
2. 10 Gigabit Ethernet: IEEE Standard for Information Technology- Telecommunications and Information Exchange Between Systems- Local and Metropolitan Area Networks-Specific Requirements Part 3: Carrier Sense Multiple Access with Collision Detection (CSMA/CD) Access Method and Physical Layer Specifications, IEEE Std. 802.3an-2006, Sep. 2006 [Online]. Available: http://standards.ieee.org/getieee802/download/802.3an-2006.pdf, p. 3.
3. Mobile Wireless MAN 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 Layers for Combined Fixed and Mobile Operation in Licensed Bands and Corrigendum 1, IEEE Std. 802.16e-2005, Dec. 2005 [Online]. Available: http://standards.ieee.org/ getieee802/download/802.16e-2005.pdf, pp 626-630.
4. S. K. Chilappagari, S. Sankaranarayanan, and B. Vasic', "Error floors of LDPC codes on the binary symmetric channel," in Proc. IEEE Int. Conf. Communications, Istanbul, Turkey, Jun. 2006, pp. 1089-1094.
5. C. Di, D. Proietti, T. Richardson, E. Telatar, and R. 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.
6. I. Djurdjevic, J. Xu, K. Abdel-Ghaffar, and S. Lin, "A class of lowdensity parity-check codes constructed based on Reed-Solomon codes with two information symbols," IEEE Commun. Lett., vol. 7, no. 7, pp. 317-319, Jul. 2003.
7. L. Dolecek, P. Lee, Z. Zhang, V. Anantharam, B. Nikolic, and M. J. Wainwright, "Predicting error floors of structured LDPC codes: Deterministic bounds and estimates," IEEE J. Selected Areas Commun., vol. 27, no. 6, pp. 908-917, Aug. 2009.
8. L. Dolecek, Z. Zhang, M. J. Wainwright, V. Anantharam, and B. Nikolic, "Analysis of absorbing sets for array-based LDPC codes," in Proc. IEEE Int. Conf. Communications, Glasgow, Scotland, U.K., Jun. 2007, pp. 6261-6268.
9. L. Dolecek, Z. Zhang, M.Wainwright, V. Anantharam, and B. Nikolic, "Evaluation of the low frame error rate performance of LDPC codes using importance sampling," in Proc. IEEE Information Theory Workshop, Lake Tahoe, CA, Sep. 2007, pp. 202-207.
10. E. Eleftheriou and S. Ölçer, "Low density parity check codes for digital subscriber lines," in Proc. IEEE Int. Conf. Communications, New York, Apr./May 2002, pp. 1752-1757.
11. J. L. Fan, "Array-codes as low-density parity-check codes," in Proc. 2nd Int. Symp. Turbo Codes and Related Topics, Brest, France, Sep. 2000, pp. 543-546.
12. J. Feldman, M. J. Wainwright, and D. R. Karger, "Using linear programming to decode binary linear codes," IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 954-972, Mar. 2005.
13. G. D. Forney, "Codes on graphs: Normal realizations," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 520-548, Feb. 2001.
14. G. D. Forney, Jr., R. Koetter, F. R. Kschischang, and A. Reznick, "On the effective weights of pseudocodewords for codes defined on graphs with cycles," in Codes, Systems and Graphical Models. New York: Springer-Verlag, 2001, pp. 101-112.
15. R. Koetter and P. Vontobel, "Graph covers and iterative decoding of finite-length codes," in Proc. 3rd Int. Symp. Turbo Codes and Related Topics, Brest, France, Sep. 2003, pp. 75-82.
16. F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory, vol. 42, no. 2, pp. 498-519, Feb. 2001.
17. S. Laendner and O. Milenkovic, "Algorithmic and combinatorial analysis of trapping sets in structured LDPC codes," in Proc. Conf.Wireless Communications, Honolulu, HI, Jun. 2005, pp. 630-635.
18. D. MacKay and M. Postol, "Weaknesses of Margulis and Ramanujan- Margulis low-density parity-check codes," Electron. Notes in Theor. Comp. Sci., vol. 74, pp. 97-104, Oct. 2003.
19. O. Milenkovic, E. Soljanin, and P. Whiting, "Asymptotic spectra of trapping sets in regular and irregular LDPC code ensembles," IEEE Trans. Inf. Theory, vol. 53, no. 1, pp. 39-55, Jan. 2007.
20. T. Mittelholzer, "Efficient encoding and minimum distance bounds of Reed-Solomon-type array codes," in Proc. IEEE Int. Symp. Information Theory, Lausanne, Switzerland, Jul. 2002, p. 282.
21. A. Orlitsky, K. Viswanathan, and J. Zhang, "Stopping set distribution of LDPC code ensembles," IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 929-953, Mar. 2005.
22. W. W. Peterson and E. J. Weldon, Error Correcting Codes. Cambridge, MA: MIT Press, 1972.
23. T. Richardson, "Error-floors of LDPC codes," in Proc. 41st Annu. Allerton Conf. Communications, Control and Computing, Monticello, Ill., Oct. 2003, pp. 1426-1435.
24. M. Sipser and D. A. Spielman, "Expander codes," IEEE Trans. Inf. Theory, vol. 42, no. 6, pp. 1710-1722, Nov. 1996.
25. C. Schlegel and S. Zhang, "On the dynamics of the error floor behavior in (regular) LDPC codes," in Proc. IEEE Information Theory Workshop, Taormina, Italy, 2009, to be published.
26. Y. Y. Tai, L. Lan, L. Zeng, S. Lin, and K. Abdel-Ghaffar, "Algebraic construction of quasi-cyclic LDPC codes for the AWGN and erasure channels," IEEE Trans. Inf. Theory, vol. 54, no. 10, pp. 1765-1774, Oct. 2006.
27. R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory, vol. IT-27, no. 5, pp. 533-547, Sep. 1980.
28. R. M. Tanner, D. Sridhara, A. Sridharan, T. E. Fuja, and D. J. Costello, "LDPC block and convolutional codes based on circulant matrices," IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 2966-2984, Dec. 2004.
29. M. C. Valenti, S. Cheng, and R. I. Seshadri, "Turbo and LDPC codes for digital video broadcasting," in Turbo Code Applications: A Journey From a Paper to Realization. Amsterdam, The Netherlands: Springer, 2006, ch. 12.
30. B. Vasić and E. Kurtas, Coding and Signal Processing for Magnetic Recording Systems. Boca Raton, FL: CRC, 2005.
31. K. Yang and T. Helleseth, "On the minimum distance of array codes as LDPC codes," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3268-3271, Dec. 2003.
32. Z. Zhang, L. Dolecek, B. Nikolic, V. Anantharam, and M. J. Wainwright, "Investigation of error floors of structured low-density parity-check codes via hardware simulation," in Proc. IEEE Global Telecommunications Conference (GLOBECOM), San Francisco, CA, Oct./Nov. 2006, pp. 1-6.
33. Z. Zhang, L. Dolecek, B. Nikolic, V. Anantharam, and M.Wainwright, "Quantization effects in low-density parity-check decoders," in Proc. IEEE Int. Conf. Communications, Glasgow, Scotland, U.K., Jun. 2007, pp. 6231-6237.
34. Z. Zhang, L. Dolecek, B. Nikolic, V. Anantharam, and M. J. Wainwright, "Design of LDPC decoders for improved low error rate performance: Quantization and algorithm choices," IEEE Trans. Commun., to be published.