Analysis of connections between pseudocodewords

IEEE Transactions on Information Theory

Volumn 55, Issue 9, 2009, Pages 4099-4107

  Axvig, Nathan ^a   Dreher, Deanna ^a   Morrison, Katherine ^a   Psota, Eric ^a   Pérez, Lance C ^a   Walker, Judy L ^a  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

Graph cover decoding; Iterative message passing decoding; Linear programming decoding; Low density parity check (LDPC) codes; Pseudocodewords

Indexed keywords

GRAPH COVER DECODING; ITERATIVE MESSAGE-PASSING DECODING; LINEAR PROGRAMMING DECODING; LOW-DENSITY PARITY-CHECK (LDPC) CODES; PSEUDOCODEWORDS;

COMMUNICATION CHANNELS (INFORMATION THEORY); DYNAMIC PROGRAMMING; GRAPH THEORY; LINEAR PROGRAMMING; LINEARIZATION; MESSAGE PASSING; OPTIMIZATION;

ITERATIVE DECODING;

EID: 69449090759     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2025529     Document Type: Article

References (17)

1. C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding," in Proc. 1993 IEEE Int. Conf. Communications, Geneva, Switzerland, 1993, pp. 1064-1070.
2. R. G. Gallager, Low-Density Parity Check Codes. Cambridge, MA: MIT Press, 1963.
3. D. J. C. MacKay and R. M. Neal, "Near Shannon limit performance of low-density parity check codes," IEE Electron. Lett., vol. 32, no. 18, pp. 1645-1646, Aug. 1996.
4. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., vol. 27, pp. 379-423, 623-656, Jul., Oct. 1948.
5. G. D. Forney, Jr., R. Koetter, F. R. Kschischang, and A. Reznik, "On the effective weights of pseudocodewords for codes defined on graphs with cycles," in Codes, Systems, and Graphical Models, ser. IMA Vol. Math. Appl. New York/Minneapolis, NY/MN: Springer, 1999, 2001, vol. 123, pp. 101-112.
6. D. Changyan, D. Proetti, 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.
7. C. Kelley, D. Sridhara, J. Xu, and J. Rosenthal, "Pseudocodeword weights and stopping sets," in Proc. 2004 IEEE Int. Symp. Information Theory, Chicago, IL, Jun./Jul. 2004, p. 150.
8. N. Wiberg, "Codes and Decoding on General Graphs," Ph.D. dissertation, Linköping Univ., Linköping, Sweden, 1996.
9. T. Richardson, A. Shokrollahi, and R. Urbanke, "Design of capacity-approaching irregular low-density parity check codes," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 619-637, Feb. 2001.
10. T. Richardson and R. Urbanke, "The capacity of low-density parity check codes under message-passing decoding," IEEE Trans. Inf. Theory, 47, no. 2, pp. 599-618, Feb. 2001.
11. P. Vontobel and R. Koetter, "Graph-cover decoding and finite-length analysis of message-passing iterative decoding of LDPC codes," IEEE Trans. Inf. Theory, to be published.
12. J. Feldman, "Decoding Error-Correcting Codes via Linear Programming," Ph.D. dissertation, MIT, Cambridge, MA, 2003.
13. N. Axvig, K. Morrison, E. Psota, D. Dreher, L. C. Pérez, and J. L. Walker, Towards a Universal Theory of Decoding and Pseudocodewords University of Nebraska-Lincoln, SGER Tech. Rep. 0801, Mar. 2008 [Online]. Available: http://www.math.unl.edu/~jwalker7/papers/ SGER_tech_report.pdf
14. R. Koetter, W.-C. W. Li, P. O. Vontobel, and J. L.Walker, "Characterizations of pseudo-codewords of LDPC codes," Adv. Math. vol. 213, pp. 205-229, 2007.
15. C. Kelley and D. Sridhara, "Pseudocodewords of Tanner graphs," IEEE Trans. Inf. Theory, vol. 53, no. 11, pp. 4013-4038, Nov. 2007.
16. N. Axvig, E. Price, E. Psota, D. Turk, L. Pérez, and J. Walker, "A universal theory of pseudocodewords," in Proc. 45th Ann. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Sept. 2007, pp. 336-343.
17. J. L. Gross and T. W. Tucker, Topological Graph Theory. Mineola, NY: Dover, 2001, reprint of the 1987 original Wiley, New York; MR0898434 (88h:05034) with a new preface and supplementary bibliography.