Tree-based construction of LDPC codes having good pseudocodeword weights

IEEE Transactions on Information Theory

Volumn 53, Issue 4, 2007, Pages 1460-1478

  Kelley, Christine A ^a,b,c,d   Sridhara, Deepak ^b,e   Rosenthal, Joachim ^b  

^a UNIVERSITY OF NOTRE DAME   (United States)

^b UNIVERSITY OF ZURICH   (Switzerland)

^c FIELDS INSTITUTE   (Canada)

^d OHIO STATE UNIVERSITY   (United States)

^e SEAGATE TECHNOLOGY   (United States)

Author keywords

Iterative decoding; Low density parity check (LDPC) codes; Min sum iterative decoding; P ary pseudoweight; Pseudocodewords

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; ITERATIVE DECODING; TREES (MATHEMATICS);

LOW-DENSITY PARITY-CHECK CODES; PSEUDOCODEWORDS;

CODES (SYMBOLS);

EID: 34147129057     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.892774     Document Type: Article

References (26)

1. N. L. Biggs, "Construction for cubic graphs of large girths," Electron. J. Comb., vol. 5, 1998.
2. R. C. Bose, "On the application of the properties of Galois fields to the problem of construction of Hyper-Graceo-Latin squares," Sankhyā, pp. 323-338, 1938.
3. M. C. Davey, "Error-correction using low-density parity-check codes," Ph.D. dissertation, Cambridge Univ., Cambridge, U.K., 1999.
4. M. C. Davey and D. J. C. MacKay, "Low density parity check codes over GF(q)," IEEE Commun. Lett., vol. 2, no. 6, pp. 159-166, Jun. 1998.
5. C. Di, D. Proietti, I. E. Teletar, T. Richardson, and R. Urbanke, "Finite-length analysis of low-density parity-check codes on the binary erasure channel," IEEE Trans. Inf. Theory, vol. 48, no. 2, pp. 1570-1579, Feb. 2002.
6. G. D. Forney Jr., R. Koetter, F. Kschischang, and A. Reznik, "On the effective weights of pseudocodewords for codes defined on graphs with cycles," in Codes, Systems and Graphical Models, B. Marcus and J. Rosenthal, Eds. New York: Springer-Verlag, 2001, IMA, vol. 123, pp. 101-112.
7. J. Han and P. H. Siegel, "Improved upper bounds on stopping redundancy," IEEE Trans. Inf. Theory vol. 53, no. 1, pp. 90-107, Jan. 2007 [Online]. Available: http://arxiv.org/abs/cs/0511056
8. N. Kashyap and A. Vardy, "Stopping sets in codes from designs," in Proc. IEEE Int/Symp. Information Theory, Yokohama, Japan, Jun./Jul. 2003, p. 122.
9. C. A. Kelley and D. Sridhara, "Pseudocodewords of Tanner graphs," IEEE Trans. Inf. Theory, submitted for publication.
10. C. A. Kelley, D. Sridhara, J. Xu, and J. Rosenthal, "Pseudocodeword weights and stopping sets," in Proc. IEEE Int. Symp. Information Theory, Chicago, IL, Jun./Jul. 2004, p. 150.
11. R. Koetter and P. O. Vontobel, "Graph-covers and iterative decoding of finite length codes," in Proc. IEEE Int. Symp. Turbo Codes and Applications, Brest, France, Sep. 2003, pp. 75-82.
12. 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, Nov. 2001.
13. MAGMA Software, [Online]. Available: http://magma.maths.usyd.edu.
14. R. L. Graham and F. J. MacWilliams, "On the number of information symbols in difference-set cyclic codes," Bell Labs Tech. J., vol. 45, pp. 1057-1070, 1966.
15. H. van Maldeghem, Generalized Polygons. Basel, Switzerland: Birkhäuser, 1998.
16. F. S. Roberts, Applied Combinatorics. Englewood Cliffs, NJ: Prentice-Hall, 1984.
17. L. Rudolph, "A class of majority logic decodable codes," IEEE Trans. Inf. Theory, vol. IT-13, no. 2, pp. 305-307, Apr. 1967.
18. D. Sridhara and T. E. Fuja, "LDPC codes over rings for PSK-modulation," IEEE Trans. Inf. Theory, vol. 51, no. 9, pp. 3209-3220, Sep. 2005.
19. H. Tang, J. Xu, S. Lin, and K. A. S. Abdel Ghaffar, "Codes on finite geometries," IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 572-596, Feb. 2005.
20. R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory, vol. IT-27, no. 5, pp. 533-547, Sep. 1981.
21. J. H. van Lint and R. M. Wilson, A Course in Combinatorics, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 2001.
22. J. Rosenthal and P. O. Vontobel, "Constructions of LDPC codes using Ramanujan graphs and ideas from Margulis," in Proc. 38th Allerton Conf. Communication, Control, and Computing, Monticello, IL, 2000, pp. 248-257.
23. M. Schwartz and A. Vardy, "On the stopping distance and the stopping redundancy of codes," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 922-932, Mar. 2006.
24. R. M. Tanner, D. Sridhara, A. Sridharan, D. J. Costello Jr., and T. E. Fula, "LDPC block and convolutional codes based on circulant matrices," IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 2966-2984, Dec. 2004.
25. P. O. Vontobel and R. M. Tanner, "Construction of codes based on finite generalized quadrangles for iterative decoding," in Proc. IEEE Int. Symp. Information Theory, Washington, DC, Jun. 2001, p. 223.
26. N. Wiberg, "Codes and decoding on general graphs," Ph.D. dissertation, Linköping Univ., Linköping, Sweden, 1996.