Codes for asymmetric limited-magnitude errors with application to multilevel flash memories

IEEE Transactions on Information Theory

Volumn 56, Issue 4, 2010, Pages 1582-1595

  Cassuto, Yuval ^a   Schwartz, Moshe ^b   Bohossian, Vasken ^c   Bruck, Jehoshua ^c  

^a SAN JOSE RESEARCH CENTER   (United States)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^c California Institute of Technology   (United States)

Author keywords

Asymmetric limited magnitude errors; Error correcting codes; Flash memory codes; Q ary codes; Systematic codes

Indexed keywords

ERROR CORRECTING CODE; ERROR-CORRECTING CODES; MAGNITUDE ERROR; Q-ARY CODES; SYSTEMATIC CODE;

ARTIFICIAL INTELLIGENCE; BLOCK CODES; ERRORS; INFORMATION THEORY; SYSTEMATIC ERRORS;

FLASH MEMORY;

EID: 77950222707     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2040971     Document Type: Article

References (16)

1. R. Ahlswede, H. Aydinian, and L. Khachatrian, "Unidirectional error control codes and related combinatorial problems," in Proc. Eighth Int. Workshop Algebr. Combin. Coding Theory (ACCT-8), St. Petersburg, Russia, 2002, pp. 6-9 [Online]. Available: http://arxiv.org/abs/cs/ 0607132
2. S. Al-Bassam and B. Bose, "Asymmetric/unidirectional error correcting and detecting codes," IEEE Trans. Comput., vol.43, pp. 590-597, 1994.
3. A. Bandyopadhyay, G. Serrano, and P. Hasler, "Programming analog computational memory elements to 0.2% accuracy over 3.5 decades using a predictive method," in Proc. IEEE Int. Symp. Circuits Syst., 2005, pp. 2148-2151.
4. J. Borden, "Bounds and constructions for error correcting/detecting codes on the Z-channel," in Proc. IEEE Int. Symp. Inf. Theory, 1981, pp. 94-95.
5. B. Eitan and A. Roy, "Binary and multilevel flash cells," in Flash Memories, P. Cappelletti, C. Golla, P. Olivo, and E. Zanoni, Eds. New York: Kluwer, 1999, pp. 91-152.
6. N. Elarief and B. Bose, "Optimal, systematic q-ary codes correcting all asymmetric errors of limited magnitude," in Proc. IEEE Int. Symp. Inf. Theory, Seoul, Korea, Jun. 2009, pp. 2704-2707.
7. S. Gregori, A. Cabrini, O. Khouri, and G. Torelli, "On-chip error correcting techniques for new-generation flash memories," Proc. IEEE, vol.91, pp. 602-616, 2003.
8. W. Huffman and V. Pless, Fundamentals of Error-Correcting Codes. Cambridge, U.K.: Cambridge university press, 2003.
9. H. Kaneko and E. Fujiwara, "A class of M-ary asymmetric symbol error correcting codes for data entry devices," IEEE Trans. Comput., vol.53, pp. 159-167, 2004.
10. T. Kløve, Error Correcting Codes for the Asymmetric Channel Dept. Mathematics, University of Bergen, Norway, 1981, 18-09-07-81.
11. J. Leech and N. Sloane, "Sphere packing and error-correcting codes," Canadian J. Math., vol.23, no.4, pp. 718-745, 1971.
12. F. MacWilliams and N. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.
13. R. McEliece, "Comments on 'A class of codes for asymmetric channels and a problem from the additive theory of numbers'," IEEE Trans. Inf. Theory, vol.19, no.1, pp. 137-137, Jan. 1973.
14. S. Stein, "Packings of by certain error spheres," IEEE Trans. Inf. Theory, vol.30, no.2, pp. 356-363, Mar. 1984.
15. R. Varshamov, "A class of codes for asymmetric channels and a problem from the additive theory of numbers," IEEE Trans. Inf. Theory, vol.19, no.1, pp. 92-95, Jan. 1973.
16. J. K. Wolf, "An introduction to tensor product codes and applications to digital storage systems," in Proc. IEEE Inf. Theory Workshop, Chengdu, China, 2006, pp. 6-10.