Advertisement

Abstract

This contribution is concerned with codes formed by generalising (or iterating) one or more component codes into arrays in (conceptually) two or more dimensions (which need not be orthogonal). Array codes can be used for multiple randan-error detection and correction, for burst-error detection and correction, and for detecting and correcting clusters or patches of errors. They are particularly useful when the data to be protected is presented in a rectangular format, such as punched card, magnetic or paper tape, graphs, maps, or pictures. Many of the array codes which will be mentioned are well known, but seme new codes and decoding techniques11–14 will also be described. The motivation for studying array codes is that they are relatively simple to decode, and also, at least in some cases, have relatively high efficiencies (data rates).

Keywords

Parity Check Magnetic Tape Information Digit Product Code Burst Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Goldberg, M., Easily decoded error-correcting codes and techniques for their generation, Ph.D. Thesis, University of London, 1971.Google Scholar
  2. 2.
    Goldberg, M., Augmentation techniques for a class of product codes, IEEE Trans, IT-19, 666, 1973.zbMATHGoogle Scholar
  3. 3.
    N.E. Head, A high-speed data transmission system, CEC Jour., 30 No. 3, 129, 1963.Google Scholar
  4. 4.
    N.J.A. Sloane, A simple description of an error-correcting code for high-density magnetic tape; BSTJ, 55 No. 2, 157, Feb. 1976.MathSciNetGoogle Scholar
  5. 5.
    D.T. Brown & F.F. Sellers, Error correction for IBM 800-bit-per-inch magnetic tape, IBM Jour Res Dev, 384, July 1970.Google Scholar
  6. 6.
    C.D. Mathers, Digital video recording — seme experiments in error protection, BBC Res. kept Rep. 1976/1, Jan. 1976.Google Scholar
  7. 7.
    P. Calingaert, Two-dimensional parity checking, Jour Assoc Comp Mach, 8 No. 2, 186, 1961.CrossRefzbMATHGoogle Scholar
  8. 8.
    H.O. Burton & E.J. Weldon, Cyclic product codes; IEEE Trans, IT-11, 433, July 1965.MathSciNetzbMATHGoogle Scholar
  9. 9.
    P. Elias, Error-free coding, IRE Trans, IT-4, 29, Sept. 1954.MathSciNetGoogle Scholar
  10. 10.
    A.B. Cooper, Algebraic codes constructed frcm other algebraic codes: A short survey and sane recent results; Proc. NATO ASI on Canm. Systs and Randan Proc. Theory, Ed. J. Skwirzymski, pub. Sijthoff & Noordhoff, 1978.Google Scholar
  11. 11.
    G. Riley, Error control for data multiplex systems; Ph.D. Thesis, Univ. of Kent at Canterbury, 1975.Google Scholar
  12. 12.
    R.J.G. Smith, Easily decoded error-correcting codes, Ph.D. Thesis, 1978.Google Scholar
  13. 13.
    R.J.G. Smith, Easily decoded efficient self-orthogonal block codes, Elec Letters, 13 No. 7, 173, 31st March 1977.CrossRefGoogle Scholar
  14. 14.
    T. Meshkati, Two-diniensional-burst-error-correcting codes, Postgrad. Dip. Dissertation, Univ. of Kent at Canterbury (in preparation).Google Scholar
  15. 15.
    R. Rowland, Error-detecting capabilities of two-coordinate parity codes; Electronic Eng., 16, Jan. 1968.Google Scholar
  16. 16.
    P.G. Farrell, E. Munday & N. Kalligeros, Digital carmunications using soft-decision detection techniques; AGARD Symp. on Digital Corns. in Avionics, Munich, June 1978 (Conf. Preprint No. 239).Google Scholar
  17. 17.
    J.L. Massey, Threshold decoding; MIT Press, 1963.Google Scholar
  18. 18.
    M. Kasahara, et al, New class of binary codes constructed on the basis of concatenated codes and product codes; IEEE Trans, IT-22, 462, 1976.MathSciNetzbMATHGoogle Scholar
  19. 19.
    R.L. Townsend & E.J. Weldon, Self-orthogonal quasi-cyclic codes; IEEE Trane, IT-13, 183, 1967.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1979

Authors and Affiliations

  • P. G. Farrell
    • 1
  1. 1.The Electronics LaboratoriesThe University of Kent at CanterburyCanterbury, KentEngland

Personalised recommendations