Array codes correcting a two-dimensional cluster of errors

IEEE Transactions on Information Theory

Volumn 44, Issue 5, 1998, Pages 2025-2031

  Breitbach, Markus ^a,b   Bossert, Martin ^a,b   Zyablov, Viktor ^a,b   Sidorenko, Vladimir ^a,b  

^a UNIVERSITY OF ULM   (Germany)

^b INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

Author keywords

Array codes, generalized singleton bound, hamming bound, two dimensional cluster correcting codes

Indexed keywords

ALGORITHMS; DECODING; ERROR CORRECTION; REDUNDANCY;

ARRAY CODES;

CODES (SYMBOLS);

EID: 0032163457     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.705587     Document Type: Article

References (23)

1. E. N. Gilbert, "Capacity of a burst-noise channel," Bell Syst. Tech. J., vol. 39, pp. 1253-1265, Sept. 1960.
2. M. Bossert and V. Sidorenko, "Singleton type bounds for blot correcting codes," IEEE Trans. Inform. Theory, vol. 42, pp. 1021-1023, May 1996.
3. E. L. Blokh and V. V. Zyablov, "Cascaded iterative codes and their application for correction of bursts of errors," in Transmission of Discrete Information Over Channels with Clustered Errors. Moscow, USSR: Nauka, 1972, pp. 5-8, in Russian.
4. M. Kasahara, Y. Sugiyama, S. Hirasawa, and T. Namekawa, "New classes of binary codes constructed on the basis of concatenated codes and product codes," IEEE Trans. Inform. Theory, vol. IT-22, pp. 462-468, July 1976.
5. M. Bossert, M. Breitbach, V. V. Zyablov, and V. Sidorenko, "Codes, correcting a set of clusters of errors or erasures," Probl. Pered. Inform., no. 4, Oct.-Dec. 1997, in Russian.
6. M. Breitbach, M. Bossert, V. V. Zyablov, and V. Sidorenko, "Array codes correcting likely burst error patterns," Europ. Trans. Telecom., submitted for publication.
7. M. Breitbach, "On the correction of two-dimensional clusters of errors," Ph.D. dissertation, Universität Ulm, Fakultät Ingenieurwissenschaften, Düsseldorf, VDI-Verlag, 1997.
8. R. M. Roth and G. Seroussi, "Reduced-redundancy product codes," in Proc. IEEE Int. Workshop Information Theory (Haifa, Israel, June 1996), p. 78.
9. _, "Array codes with progressive redundancy," in Proc. IEEE Int. Symp. Information Theory (Ulm, Germany, June 29-July 4, 1997), p. 296.
10. T. Garde, J. Justesen, and V. Zyablov, "Generalized concatenated codes with very high rate," preprint.
11. E. M. Gabidulin and V. V. Zanin, "Codes that correct two-dimensional burst errors," in Workshop on Information Protection (Moscow, Russia, Dec. 6-9, 1993).
12. E. M. Gabidulin, "Matrix codes correcting array errors of size 2x2," in Int. Symp. Communications Theory and Applications (Charlotte Mason College, Ambleside, U.K., July 11-16, 1993).
13. V. Sidorenko, "Tilings of the plane and codes for translational combinatorial metrics," in Proc. IEEE Int. Symp. Information Theory (Trondheim, Norway, June 1994), p. 107.
14. M. Bossert, M. Breitbach, and V. Sidorenko, "Blot-correcting codes in radio channels," in Proc. ITG-Fachtagung "Mobile Kommunika-tion" (Neu-Ulm, Germany, Sept. 1995), ITG-Fachbericht, no. 135, pp. 501-508.
15. C. de Almeida and R. Palazzo, "Two-dimensional interleaving using the set partitioning technique," in Proc. IEEE Int. Symp. Information Theory (Trondheim, Norway, 1994), p. 505.
16. M. Blaum and J. Brück, "Correcting two-dimensional clusters by interleaving of symbols," in Proc. IEEE Int. Symp. Information Theory (Trondheim, Norway, 1994), p. 504.
17. H. Imai, "Two-dimensional fire codes," IEEE Trans. Inform. Theory, vol. IT-19, pp. 796-806, 1973;
18. also K. A. S. Abdel-Ghaffar, R. J. McEliece, and H. C. A. van Tilborg, "Two-dimensional burst identification codes and their use in burst correction," IEEE Trans. Inform. Theory, vol. 34, pp. 494-504, May 1988.
19. K. A. S. Abdel-Ghaffar, R. J. McEliece, and H. C. A. van Tilborg, "Two-dimensional burst identification codes and their use in burst correction," IEEE Trans. Inform. Theory, vol. 34, pp. 494-504, May 1988.
20. M. Blaum and P. G. Farrell, "A family of cluster-correcting array codes," IBM Res. Rep. RJ 9836, June 1994.
21. R. E. Blahut, Theory and Practice of Error Control Codes. Reading, MA: Addison-Wesley, 1984.
22. F. J. Mac Williams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.
23. W. W. Peterson and E. J. Weldon, Error Correcting Codes, 2nd ed. Cambridge, MA: MIT Press, 1972.