Covering radius and writing on memories

  • Gérard D. Cohen
Invited Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 508)


We investigate and survey some connections between coding theory and the problem of writing on binary memories subject to constraints on transitions between states. More precisely, the existence of good covering codes is used for two purposes:
  • computing the capacity (maximum achievable rate) for some special classes of translation-invariant constraints

  • constructing error-correcting WOM- codes.

The talk is based mostly on two papers :
  • Writing on some binary memories with constraints(W*M's), presented at "Geometries, Codes and Cryptography, Udine, Italy, 19–23 June 1989,

  • Error-correcting WOM-codes, co-authored with G. ZEMOR, submitted to IEEE Trans. on Inform. Theory.


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  1. [1]
    R. AHLSWEDE, Z. ZHANG, Coding for write-efficient memories, Indorm. and Control, vol. 83, no1 (1989) 80–97.Google Scholar
  2. [2]
    L.BASSALYGO, S. GELFAND and M. PINSKER, Coding for channels with localized errors, Oberwolfach Tagungsbericht 21/1989, May 1989.Google Scholar
  3. [3]
    J.M. BORDEN, Coding for write-unidirectional memories. Preprint.Google Scholar
  4. [4]
    G. COHEN, P. FRANKL, Good coverings of Hamming spaces with spheres, Discrete Math. 56 (1985) 125–131.Google Scholar
  5. [5]
    G. COHEN, P. GODLEWSKI, F. MERKX, Linear block codes for write-once memories, IEEE Trans. Inform. Theory, IT-32, No5 (1986) 697–700.Google Scholar
  6. [6]
    G. COHEN, G. SIMONYI, Coding for write-unidirectional memories and conflict resolution, Discrete Applied Math. 24 (1989) 103–114.Google Scholar
  7. [7]
    G. COHEN, G. ZEMOR, Write-Isolated Memories, French-Israeli Conference on combinatorics and algorithms, Nov. 1988, Jerusalem, to appear in Discrete Math.Google Scholar
  8. [8]
    I. CSISZAR and J. KORNER, Information Theory, Academic Press.Google Scholar
  9. [9]
    M.R. FELLOWS, Encoding graphs in graphs, Ph. D. Dissertation, Univ-Calif. San Diego, Computer Science, 1985.Google Scholar
  10. [10]
    C. HEEGARD and A.A. EL GAMAL, On the capacity of Computer Memory with Defects, IEEE Trans. on Inform. Theory, vol. IT-29, no5, (1983) 731–739.Google Scholar
  11. [11]
    T. KLOVE, On Robinson's coding problem, IEEE Trans. on Inform. Theory, IT-29, no3 (1983) 450–454.Google Scholar
  12. [12]
    K.U. KOSCHNICK, Coding for Write-Undirectional Memories, Oberwolfach Tagungsbericht 21/1989, May 1989.Google Scholar
  13. [13]
    A.V. KUZNETSOV, Defective channels and defective memories, Oberwolfach Tagungsbericht 21/1989, May 1989.Google Scholar
  14. [14]
    A.V. KUZNETSOV and B.S. TSYBAKOV, Coding in memories with defective cells, Probl. Peredachi, Inform, vol. 10. no2 (1974) 52–60.Google Scholar
  15. [15]
    L. LOVASZ, On the ratio of optimal integral and fractional covers, Discrete Math. 13 (1975) 383–390.Google Scholar
  16. [16]
    F.J. MACWWILLIAMS and N.J.A. SLOANE, The Theory of Error-correcting Codes, North-Holland, New-York, 1977.Google Scholar
  17. [17]
    W. M.C.J. van OVERVELD, The four cases of WUM-codes over arbitrary alphabets, submitted to IEEE Trans. on Inform. TheoryGoogle Scholar
  18. [18]
    R.L. RIVEST, and A. SHAMIR, How to reuse a "write-once" memory, Inform. and Control 55 (1982) 1–19.Google Scholar
  19. [19]
    M.R. SCHROEDER, Number Theory in Science and Communication, Springer-Verlag Series in Information Sciences, 1984.Google Scholar
  20. [20]
    G. SIMONYI, On Write-Unidirectional Memory Codes, IEEE Trans. on Inform. Theory, vol. 35, no3 (1989) 663–669.Google Scholar
  21. [21]
    A. VINCK, personal communication.Google Scholar
  22. [22]
    H.S. WITSENHAUSEN and A.D. WYNER, On Storage Media with Aftereffects, Inform. and Control, 56 (1983), 199–211.Google Scholar
  23. [23]
    J.K. WOLF, A.D. WYNER, J. ZIV and J. KÖRNER, Coding for write-once memory, AT and T Bell Lab.-Tech. J. 63, No6 (1984) 1089–1112.Google Scholar
  24. [24]
    G. D. COHEN, M. G. KARPOVSKY, H. F. MATTSON Jr. and J. R. SHATZ, Covering radius — survey and recent results, IEEE Trans. on Inform. Theory 31 (1985) 328–343.Google Scholar
  25. [25]
    P. GODLEWSKI, WOM-codes construits à partir des codes de Hamming, Discrete Math. 65 (1987) 237–243.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Gérard D. Cohen
    • 1
  1. 1.ENSTParis cedex 13France

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