Two-dimensional cluster-correcting codes

IEEE Transactions on Information Theory

Volumn 51, Issue 6, 2005, Pages 2121-2132

  Schwartz, Moshe ^a,b   Etzion, Tuvi ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Burst correcting codes; Cluster correcting codes; Two dimensional codes

Indexed keywords

ERROR CORRECTION; MATHEMATICAL MODELS; MATRIX ALGEBRA; RANDOM PROCESSES; SET THEORY;

BURST ERROR CORRECTING CODES; CLUSTER CORRECTING CODES; TWO DIMENSIONAL CODES;

CODES (SYMBOLS);

EID: 20544473125     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.847726     Document Type: Article

References (26)

1. 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. Inf. Theory, vol. 34, no. 3, pp. 494-504, May 1988.
2. K. A. S. Abdel-Ghaffar, R. J. McEliece, A. M. Odlyzko, and H. C. A. van Tilborg, "On the existence of optimum cyclic burst-correcting codes," IEEE Trans. Inf. Theory, vol. IT-32, no. 6, pp. 768-775, Nov. 1986.
3. M. Blaum, J. Bruck, and P. G. Farrell, "Two-Dimensional Interleaving Schemes With Repetitions," IBM, Tech. Rep. RJ 10047 (90543), 1996.
4. M. Blaum and P. G. Farrell, "Array codes for cluster-error correction," Electron. Lett., vol. 30, no. 21, pp. 1752-1753, Oct. 1994.
5. M. Blaum and J. Bruck, "MDS array codes for correcting criss-cross errors," IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1068-1077, May 2000.
6. M. Blaum, J. Bruck, and A. Vardy, "Interleaving schemes for multidimensional cluster errors," IEEE Trans. Inf. Theory, vol. 44, no. 2, pp. 730-743, Mar. 1998.
7. M. Bossert and V. Sidorenko, "Singleton-type bounds for blot-correcting codes," IEEE Trans. Inf. Theory, vol. 42, no. 3, pp. 1021-1023, May 1996.
8. M. Breitbach, M. Bossert, V. Zyablov, and V. Sidorenko, "Array codes correcting a two-dimensional cluster of errors," IEEE Trans. Inf. Theory, vol. 44, no. 5, pp. 2025-2031, Sep. 1998.
9. T. Etzion, "Constructions for perfect 2-burst-correcting codes," IEEE Trans. Inf. Theory, vol. 47, no. 6, pp. 2553-2555, Sep. 2001.
10. T. Etzion and A. Vardy, "Two-dimensional interleaving schemes with repetitions: Constructions and bounds," IEEE Trans. Inf. Theory, vol. 48, no. 2, pp. 428-457, Feb. 2002.
11. P. G. Farrell, "Array codes for correcting cluster-error patterns," in Proc. IEE Conf. Electrical Signal Processing, York, U.K., Jul. 1982.
12. E. M. Gabidulin, "Theory of codes with maximum rank distance," Probl. Pered. Inform., vol. 21, pp. 3-16, 1985.
13. C. Gu, J. Hong, I. McMichael, R. Saxena, and F. Mok, "Cross-talk limited storage capacity of volume holographic memory," J. Opt. Soc. Amer., vol. 9A, pp. 1978-1987, 1992.
14. J. F. Heanie, M. C. Bashaw, and L. Hesselink, "Volume holographic storage anal retrieval of digital data," Sci. Mag., vol. 265, pp. 749-752, 1994.
15. H. Imai, "Two-dimensional Fire codes," IEEE Trans. Inf. Theory, vol. IT-19, no. 6, pp. 796-806, Nov. 1973.
16. H. Imai, "A theory of two-dimensional cyclic codes," Inf. Control, vol. 34, pp. 1-21, 1977.
17. A. Jiang, M. Cook, and J. Bruck, "Optimal t-interleaving on tori," in Proc. IEEE Int. Symp. Information Theory (ISIT2004), Chicago, IL, Jun./Jul. 2004, p. 22.
18. Y. Merksamer and T. Etzion, "On the optimality of coloring with a lattice," SIAM J. Discr. Math., to be published.
19. M. A. Neifeld and M. McDonald, "Error correction for increasing the usable capacity of photorefractive memories," Opt. Lett., vol. 19, pp. 1483-1483, 1994.
20. S. H. Reiger, "Codes for the correction of 'clustered' errors," IRE Trans. Inf. Theory, vol. IT-6, no. 1, pp. 16-21, Mar. 1960.
21. R. M. Roth, "Maximum-rank arrays codes and their application to crisscross error correction," IEEE Trans. Inf. Theory, vol. 37, no. 2, pp. 328-336, Mar. 1991.
22. R. M. Roth, "Probabilistic crisscross error correction," IEEE Trans. Inf. Theory, vol. 43, no. 5, pp. 1425-1438, Sep. 1997.
23. R. M. Roth, private communication, 2003.
24. M. Schwartz and T. Etzion, "Optimal 2-dimensional 3-dispersion lattices," in Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, 2003, vol. 2643, pp. 216-225.
25. N. J. A. Sloane. The on-line encyclopedia of integer sequences. Sequence A093424, A093426, and A093427. [Online]. Available: http://www.research. att.com/~njas/sequences/
26. W. Weeks and R. E. Blahut, "The capacity and coding gain of certain checkerboard codes," IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 1193-1203, May 1998.