Woven graph codes: Asymptotic performances and examples

IEEE Transactions on Information Theory

Volumn 56, Issue 1, 2010, Pages 121-129

  Bocharova, Irina E ^a   Johannesson, Rolf ^b   Kudryashov, Boris D ^a   Zyablov, Viktor V ^c  

^a ITMO UNIVERSITY   (Russian Federation)

^b LUND UNIVERSITY   (Sweden)

^c INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

Author keywords

Convolutional codes; Girth; Graph codes; Graphs; Hypergraphs; Low density parity check (LDPC) codes; Tailbiting (TB) codes; Woven codes

Indexed keywords

GRAPH CODES; HYPER GRAPH; HYPERGRAPHS; LOW-DENSITY PARITY-CHECK CODES; TAIL-BITING;

CONVOLUTION; GRAPH THEORY; TERBIUM ALLOYS; WEAVING;

CONVOLUTIONAL CODES;

EID: 73849093577     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2034787     Document Type: Article

References (20)

1. R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.
2. C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo codes," in Proc. IEEE Int. Conf. Communications (ICC), Geneva, Switzerland, 1993, pp. 1064-1070.
3. A. Barg and G. Zémor, "Distance properties of expander codes," IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 78-90, Jan. 2006.
4. X.-Y. Hu and M. F. Fossorier, "On the computation of the minimum distance of low-density parity-check codes," in Proc. IEEE Int. Conf. Communications (ICC'04), Paris, France, Jun. 2004, pp. 767-771.
5. G. Schmidt, V. V. Zyablov, and M. Bossert, "On expander codes based on hypergraphs," in Proc. IEEE Int. Symp. Information Theory (ISIT 2003), Yokohama, Japan, Jun./Jul. 2003, p. 88.
6. S. Hoory and Y. Bilu, "The codes from hypergraphs," Europ. J. Combinatorics, vol. 25, no. 3, pp. 339-354, Apr. 2004.
7. M. Lentmaier and K. Sh. Zigangirov, "On generalized low-density parity-check codes based on Hamming component codes," IEEE Commun. Lett., vol. 3, no. 8, pp. 248-250, Aug. 1999.
8. N. Miladinovic and M. P. C. Fossorier, "Generalized LDPC codes and generalized stopping sets," IEEE Trans. Commun., vol. 56, no. 2, pp. 201-212, Feb. 2008.
9. M. Sipser and D. A. Spielman, "Expander codes," IEEE Trans. Inf. Theory, vol. 42, no. 6, pp. 1710-1722, Nov. 1996.
10. Z. Wei, M. Lentmaier, D. J. Costello, and K. Sh. Zigangirov, "Braided convolutional codes," in Proc. IEEE Int. Symp. Information Theory (ISIT'05), Adelaide, Australia, Sep. 2005, pp. 592-596.
11. A. Barg, A. Mazumdar, and G. Zémor, "Weight distribution and decoding of codes on hypergraphs," Adv. Math. Commun., vol. 2, no. 4, pp. 433-450, 2008.
12. G. Solomon and H. C. A. van Tilborg, "A connection between block and convolutional codes," SIAM J. Appl. Math., vol. 37, pp. 358-369, 1979.
13. J. H. Ma and J. K. Wolf, "On tail-biting convolutional codes," IEEE Trans. Commun., vol. COM-34, no. 2, pp. 104-111, Feb. 1986.
14. I. E. Bocharova, B. D. Kudryasov, R. Johannesson, and P. Stahl, "Tailbiting codes: Bounds and search results," IEEE Trans. Inf. Theory, vol. 48, no. 1, pp. 137-148, Jan. 2002.
15. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications. New York: North Holland, 1976, p. 236 and 244.
16. F. Harary, Graph Theory. Reading, MA: Addison-Wesley, 1994, p. 173.
17. R. Johannesson and K. Sh. Zigangirov, Fundamentals of Convolutional Coding. Piscataway, NJ: IEEE Press, 1999.
18. M. Bossert, C. Medina, and V. Sidorenko, "Encoding and distance estimation of product convolutional codes," in Proc. IEEE Int. Symp. Information Theory (ISIT'05), Adelaide, Australia, Sep. 2005, pp. 1063-1067.
19. S. Höst, R. Johannesson, and V. V. Zyablov, "Woven convolutional codes I: Encoder properties," IEEE Trans. Inf. Theory, vol. 48, no. 1, pp. 149-161, Jan. 2002.
20. I. E. Bocharova, M. Handlery, R. Johannesson, and B. D. Kudryashov, "A BEAST for prowling in trees," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1295-1302, Jun. 2004.