On the minimal pseudo-codewords of codes from finite geometries

IEEE International Symposium on Information Theory - Proceedings

Volumn 2005-January, Issue , 2005, Pages

  Vontobel, Pascal O ^a   Smarandache, Roxana ^b   Kiyavash, Negar ^c   Teutsch, Jason ^d   Vukobratovic, Dejan ^e  

^a University of Wisconsin Madison   (United States)

^b SAN DIEGO STATE UNIVERSITY   (United States)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^d INDIANA UNIVERSITY   (United States)

^e UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; LINEAR PROGRAMMING; MAXIMUM LIKELIHOOD;

EUCLIDEAN PLANES; FINITE GEOMETRY; HAMMING WEIGHTS; LINEAR PROGRAMMING DECODING; LP DECODING; MAXIMUM-LIKELIHOOD DECODING; NUMERICAL RESULTS; PSEUDO WEIGHTS;

ITERATIVE DECODING;

EID: 33744482594     PISSN: 21578095     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2005.1523484     Document Type: Conference Paper

References (18)

1. R. Koetter and P. O. Vontobel, "Graph covers and iterative decoding of fi nitelength codes," in Proc. 3rd Intern. Conf. on Turbo Codes and Related Topics, (Brest, France), pp. 75-82, Sept. 1-5 2003.
2. P. O. Vontobel and R. Koetter, "On the relationship between linear programming decoding and min-sum algorithm decoding," in Proc. Intern. Symp. on Inform. Theory and its Applications (ISITA), (Parma, Italy), pp. 991-996, Oct. 10-13 2004.
3. R. Lucas, M. Fossorier, Y. Kou, and S. Lin, "Iterative decoding of one-step majority logic decodable codes based on belief propagation," IEEE Trans. on Comm., vol. COMM-48, pp. 931-937, June 2000.
4. Y. Kou, S. Lin, and M. P. C. Fossorier, "Low-density parity-check codes based on fi nite geometries: A rediscovery and new results," IEEE Trans. on Inform. Theory, vol. IT-47, pp. 2711-2736, Nov. 2001.
5. L. M. Batten, Combinatorics of Finite Geometries. Cambridge: Cambridge University Press, second ed., 1997.
6. J. Feldman, Decoding Error-Correcting Codes via Linear Programming. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, 2003. Available online under http://www.columbia.edu/-jf2189/pubs.html.
7. J. Feldman, M. J. Wainwright, and D. R. Karger, "Using linear programming to decode binary linear codes," IEEE Trans. on Inform. Theory, vol. IT-51, no. 3, pp. 954-972, 2005.
8. T. Y. Hwang, "Decoding linear block codes for minimizing word error rate," IEEE Trans. on Inform. Theory, vol. 25, no. 6, pp. 733-737, 1979.
9. E. Agrell, "Voronoǐ regions for binary linear block codes," IEEE Trans. on Inform. Theory, vol. 42, no. 1, pp. 310-316, 1996.
10. A. Ashikhmin and A. Barg, "Minimal vectors in linear codes," IEEE Trans. on Inform. Theory, vol. 44, no. 5, pp. 2010-2017, 1998.
11. Y. Borissov, N. Manev, and S. Nikova, "On the non-minimal codewords in the binary Reed-Muller code," in Proc. IEEE Intern. Symp. on Inform. Theory, (Washington, D.C., USA), p. 39, June 24-29 2001.
12. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, UK: Cambridge University Press, 2004.
13. G. D. Forney, Jr., R. Koetter, F. R. Kschischang, and A. Reznik, "On the effective weights of pseudocodewords for codes defi ned on graphs with cycles," in Codes, Systems, and Graphical Models (Minneapolis, MN, 1999) (B. Marcus and J. Rosenthal, eds.), vol. 123 of IMA Vol. Math. Appl., pp. 101-112, Springer Verlag, New York, Inc., 2001.
14. P. O. Vontobel and R. Koetter, "Lower bounds on the minimum pseudo-weight of linear codes," in Proc. IEEE Intern. Symp. on Inform. Theory, (Chicago, IL, USA), p. 70, June 27-July 2 2004.
15. N. Kashyap and A. Vardy, "Stopping sets in codes from designs," in Proc. IEEE Intern. Symp. on Inform. Theory, (Pacifi co Yokohama, Japan), p. 122, June 29 -July 4 2003.
16. D. J. C. MacKay and M. C. Davey, "Evaluation of Gallager codes for short block length and high rate applications," in Codes, Systems, and Graphical Models (Minneapolis, MN, 1999) (B. Marcus and J. Rosenthal, eds.), pp. 113-130, Springer Verlag, New York, Inc., 2001.
17. G. E. Séguin, "A lower bound on the error probability for signals in white Gaussian noise," IEEE Trans. on Inform. Theory, vol. 44, no. 7, pp. 3168-3175, 1998.
18. D. Avis, "lrs: A revised implementation of the reverse search vertex enumeration algorithm," in Polytopes - Combinatorics and Computation (G. Kalai and G. M. Ziegler, eds.), pp. 177-198, Birkhäuser-Verlag, 2000. Programs are available online under http://cgm.cs.mcgill.ca/-avis/C/lrs.html