Probabilistic analysis of linear programming decoding

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 07-09-January-2007, Issue , 2007, Pages 385-394

  Daskalakis, Constantinos ^a   Dimakis, Alexandros G ^a   Karp, Richard M ^a   Wainwright, Martin J ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CODES (SYMBOLS); DECODING; FORWARD ERROR CORRECTION; SATELLITE COMMUNICATION SYSTEMS;

BIPARTITE GRAPHS; CORRECTABLE ERRORS; EXPANSION COEFFICIENTS; HIGH PROBABILITY; LINEAR PROGRAMMING DECODING; LOW-DENSITY PARITY-CHECK (LDPC) CODES; NON-ASYMPTOTIC; PROBABILISTIC ANALYSIS;

LINEAR PROGRAMMING;

EID: 84969277873     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. A. Barg and G. Zémor. Error exponents of expander codes under linear-complexity decoding. SIAM Journal on Discrete Math, 17(3):426-445, 2004.
2. E. Berlekamp, R. McEliece, and H. van Tilborg. On the inherent intractability of certain coding problems. IEEE Trans. Info. Theory, pages 384-386, 1978.
3. D. Bienstock. Potential Function Methods for Approximately Solving Linear Programming Problems. Kluwer Academic, Boston, 2002.
4. S.Y. Chung, T. Richardson, and R. Urbanke. Analysis of sum-product decoding of low-density parity check codes using a Gaussian approximation. IEEE Trans. Info. Theory, 47:657-670, February 2001.
5. C. Daskalakis, A. G. Dimakis, R. M. Karp, and M. J. Wainwright. Probabilistic analysis of linear programming decoding. In Technical Report 718, Department of Statistics, UC Berkeley, October 2006.
6. A. G. Dimakis and M. J. Wainwright. Guessing Facets: Improved LP decoding and Polytope Structure. In International Symposium on Information Theory, Seattle, Washington, July 2006.
7. J. Feldman and D. Karger. Decoding turbo-like codes in polynomial time with provably good error-correcting performing via linear programming. In FOCS, July 2002.
8. J. Feldman, D. R. Karger, and M. J. Wainwright. Linear programming-based decoding of turbo-like codes and its relation to iterative approaches. In Proc. 40th Annual Allerton Conf. on Communication, Control, and Computing, October 2002.
9. J. Feldman, T. Malkin, R. A. Servedio, C. Stein, and M. J. Wainwright. LP decoding corrects a constant fraction of errors. Technical Report CORC Technical Report TR-2003-08, Operations Research, Columbia University, December 2003.
10. J. Feldman, T. Malkin, R. A. Servedio, C. Stein, and M. J. Wainwright. LP decoding corrects a constant fraction of errors. In Proc. IEEE International Symposium on Information Theory, 2004.
11. J. Feldman and C. Stein. LP decoding achieves capacity. In Symposium on Discrete Algorithms (SODA '05), January 2005.
12. J. Feldman, M. J. Wainwright, and D. R. Karger. Using linear programming to decode binary linear codes. IEEE Transactions on Information Theory, 51:954-972, March 2005.
13. R. G. Gallager. Low-density parity check codes. MIT Press, Cambridge, MA, 1963.
14. N. Halabi and G. Even. Improved bounds on the word error probability of RA(2) codes with linear-programming-based decoding. IEEE Trans. Info. Theory, 51:265-280, January 2005.
15. W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58:13-30, 1963.
16. R. Koetter and P. O. Vontobel. Graph-covers and iterative decoding of finite length codes. In Proc. 3rd International Symp. on Turbo Codes, September 2003.
17. F.R. Kschischang, B.J. Frey, and H.-A. Loeliger. Factor graphs and the sum-product algorithm. IEEE Trans. Info. Theory, 47(2):498-519, February 2001.
18. M. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. Spielman. Improved low-density parity check codes using irregular graphs. IEEE Trans. Info. Theory, 47:585-598, February 2001.
19. D. MacKay. Good error correcting codes based on very sparse matrices. IEEE Trans. Info. Theory, 45(2):399-431, 1999.
20. T. Richardson and R. Urbanke. The capacity of low-density parity check codes under message-passing decoding. IEEE Trans. Info. Theory, 47:599-618, February 2001.
21. Michael Sipser and Daniel A. Spielman. Expander codes. In IEEE Symposium on Foundations of Computer Science, pages 566-576, 1994.
22. P. O. Vontobel and R. Koetter. Bounds on the threshold of linear programming decoding. In Information Theory Workshop, March 2006.
23. P.O. Vontobel and R. Koetter. "Towards low-complexity linear-programming decoding". In Proc. of the 4th Int. Symp. on Turbo Codes and Related Topics, Munich, Germany, April 2006.
24. M. J. Wainwright, T. S. Jaakkola, and A. S. Willsky. Exact MAP estimates via agreement on (hyper)trees: Linear programming and message-passing. IEEE Trans. Information Theory, 51(11):3697-3717, November 2005.