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Location and Simultaneous Correction of Burst/Solid Burst Errors

Year 2014, Volume 2, 2014, 1 - 14, 26.05.2016

Abstract

This paper proposes a class of error locating codes that locates burst/solid bursts of length s or less as well as corrects burst/solid bursts of length b(< s) or less. Lower and upper bounds on parity check digits for such codes are obtained. Examples of such codes are also provided. Further, comparisons between the bounds of these codes with other types of codes: (a) codes that correct all bursts/solid bursts of length s or less, and (b) codes that detect solid bursts of length s or less as well as correct solid bursts of length b(< s) or less, are also provided.

References

  • J. Arlat and W.C. Carter, Implementation and Evaluation of a (b, k)-Adjacent ErrorCorrecting/Detecting Scheme for Supercomputer Systems, IBM J. Res. Develop., vol. 28, No. 2, 159-169 (1984).
  • P.K. Das, Codes Detecting and Correcting Solid Burst Errors, Bulletin of Electrical Engineering and Informatics, vol. 1, No. 3, 225-232 (2012).
  • P.K. Das, Codes Detecting and Locating Solid Burst Errors, Romanian Journal of Mathematics and Computer Science, vol. 2, No. 2, 1-10 (2012).
  • P.K. Das, Blockwise Solid Burst Error Correcting Codes, International Journal on Information Theory, vol. 1, No. 1, 11-17 (2012).
  • P.K. Das, Codes correcting and simultaneously detecting solid burst errors, Computer Engineering and Application Journal, vol. 2, No. 1, 143-150 (2013).
  • P.K. Das, Difference Equations and SBEC Optimal Codes, Journal of Mathematics and Computer Science, vol. 7, No. 4, 258-265 (2013).
  • B.K. Dass, Burst error locating linear codes. J. Inf. and Optimization Sciences, vol. 3, No. 1, 77-80 (1982).
  • B.K. Dass and S. Madan, Repeated Burst Error Locating Linear Codes, Discrete Mathematics, Algorithms and Applications, vol. 2, No. 2, 181-188 (2010).
  • P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Report RSL-E-2, Sylvania Reconnaissance Systems Laboratory, Mountain View, Calif, (1959).
  • E. Fujiwara and M. Kitakami, A Class of Error Locating Codes for Byte-Organized Memory System, IEEE Trans. Inform. Theory, IT-40, 1857-1865 (1994).
  • D.W. Jensen, Block code to efficiently correct adjacent data and/or check bit errors, Patent number: US6604222 B1, Date of Patent Aug. 5, (www.google.com/patents/US6604222), (2003).
  • M. Kitakami and E. Fujiwara, A Class of Error Locating Codes- SEC-Se/bEL Codes, IEICE Trans. Fundamentals, E78-A, No. 9, 1-6 (1995).
  • W.W. Peterson and E.J. Weldon(Jr.), Error-Correcting Codes, 2nd edition, The MIT Press, Mass, 1972.
  • G.E. Sacks, Multiple error correction by means of parity-checks, IRE Trans. Inform. Theory, IT-4, 145-147 (1958).
  • A.G. Schillinger, A class of solid burst error correcting codes, Polytechnic Institute of Brooklyn, N.Y., Research Rept. PIBMRI, April, 1223-64 (1964).
  • B.D. Sharma and B.K. Dass, Adjacent error correcting binary perfect codes, J. Cybernetics, vol. 7, 9-13 (1977).
  • S.G.S. Shiva and C.L. Sheng, Multiple solid burst-error- correcting binary codes, IEEE Trans. Inform. Theory, IT-15, 188-189 (1969).
  • J. Wolf and B. Elspas, Error-locating codes a new concept in error control, IEEE Transactions on Information Theory, vol. 9, No. 2, 113-117 (1963).

Year 2014, Volume 2, 2014, 1 - 14, 26.05.2016

Abstract

References

  • J. Arlat and W.C. Carter, Implementation and Evaluation of a (b, k)-Adjacent ErrorCorrecting/Detecting Scheme for Supercomputer Systems, IBM J. Res. Develop., vol. 28, No. 2, 159-169 (1984).
  • P.K. Das, Codes Detecting and Correcting Solid Burst Errors, Bulletin of Electrical Engineering and Informatics, vol. 1, No. 3, 225-232 (2012).
  • P.K. Das, Codes Detecting and Locating Solid Burst Errors, Romanian Journal of Mathematics and Computer Science, vol. 2, No. 2, 1-10 (2012).
  • P.K. Das, Blockwise Solid Burst Error Correcting Codes, International Journal on Information Theory, vol. 1, No. 1, 11-17 (2012).
  • P.K. Das, Codes correcting and simultaneously detecting solid burst errors, Computer Engineering and Application Journal, vol. 2, No. 1, 143-150 (2013).
  • P.K. Das, Difference Equations and SBEC Optimal Codes, Journal of Mathematics and Computer Science, vol. 7, No. 4, 258-265 (2013).
  • B.K. Dass, Burst error locating linear codes. J. Inf. and Optimization Sciences, vol. 3, No. 1, 77-80 (1982).
  • B.K. Dass and S. Madan, Repeated Burst Error Locating Linear Codes, Discrete Mathematics, Algorithms and Applications, vol. 2, No. 2, 181-188 (2010).
  • P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Report RSL-E-2, Sylvania Reconnaissance Systems Laboratory, Mountain View, Calif, (1959).
  • E. Fujiwara and M. Kitakami, A Class of Error Locating Codes for Byte-Organized Memory System, IEEE Trans. Inform. Theory, IT-40, 1857-1865 (1994).
  • D.W. Jensen, Block code to efficiently correct adjacent data and/or check bit errors, Patent number: US6604222 B1, Date of Patent Aug. 5, (www.google.com/patents/US6604222), (2003).
  • M. Kitakami and E. Fujiwara, A Class of Error Locating Codes- SEC-Se/bEL Codes, IEICE Trans. Fundamentals, E78-A, No. 9, 1-6 (1995).
  • W.W. Peterson and E.J. Weldon(Jr.), Error-Correcting Codes, 2nd edition, The MIT Press, Mass, 1972.
  • G.E. Sacks, Multiple error correction by means of parity-checks, IRE Trans. Inform. Theory, IT-4, 145-147 (1958).
  • A.G. Schillinger, A class of solid burst error correcting codes, Polytechnic Institute of Brooklyn, N.Y., Research Rept. PIBMRI, April, 1223-64 (1964).
  • B.D. Sharma and B.K. Dass, Adjacent error correcting binary perfect codes, J. Cybernetics, vol. 7, 9-13 (1977).
  • S.G.S. Shiva and C.L. Sheng, Multiple solid burst-error- correcting binary codes, IEEE Trans. Inform. Theory, IT-15, 188-189 (1969).
  • J. Wolf and B. Elspas, Error-locating codes a new concept in error control, IEEE Transactions on Information Theory, vol. 9, No. 2, 113-117 (1963).
There are 18 citations in total.

Details

Other ID JA22TD72NT
Authors

Pankaj Kumar Das This is me

Publication Date May 26, 2016
Published in Issue Year 2014 Volume 2, 2014

Cite

APA Das, P. K. (2016). Location and Simultaneous Correction of Burst/Solid Burst Errors. Turkish Journal of Mathematics and Computer Science, 2(1), 1-14. https://izlik.org/JA99SM59DT
AMA 1.Das PK. Location and Simultaneous Correction of Burst/Solid Burst Errors. TJMCS. 2016;2(1):1-14. https://izlik.org/JA99SM59DT
Chicago Das, Pankaj Kumar. 2016. “Location and Simultaneous Correction of Burst Solid Burst Errors”. Turkish Journal of Mathematics and Computer Science 2 (1): 1-14. https://izlik.org/JA99SM59DT.
EndNote Das PK (May 1, 2016) Location and Simultaneous Correction of Burst/Solid Burst Errors. Turkish Journal of Mathematics and Computer Science 2 1 1–14.
IEEE [1]P. K. Das, “Location and Simultaneous Correction of Burst/Solid Burst Errors”, TJMCS, vol. 2, no. 1, pp. 1–14, May 2016, [Online]. Available: https://izlik.org/JA99SM59DT
ISNAD Das, Pankaj Kumar. “Location and Simultaneous Correction of Burst Solid Burst Errors”. Turkish Journal of Mathematics and Computer Science 2/1 (May 1, 2016): 1-14. https://izlik.org/JA99SM59DT.
JAMA 1.Das PK. Location and Simultaneous Correction of Burst/Solid Burst Errors. TJMCS. 2016;2:1–14.
MLA Das, Pankaj Kumar. “Location and Simultaneous Correction of Burst Solid Burst Errors”. Turkish Journal of Mathematics and Computer Science, vol. 2, no. 1, May 2016, pp. 1-14, https://izlik.org/JA99SM59DT.
Vancouver 1.Das PK. Location and Simultaneous Correction of Burst/Solid Burst Errors. TJMCS [Internet]. 2016 May 1;2(1):1-14. Available from: https://izlik.org/JA99SM59DT