On 2-Repeated Burst Codes

Authors

  • B. K. Dass Department of Mathematics University of Delhi Delhi - 110 007, India
  • Poonam Garg Department of Mathematics, Deen Dayal Upadhyaya College, (University of Delhi) Shivaji Marg, Karam Pura, New Delhi - 110 015, India

Abstract

There are several kinds of burst errors for which error detecting and error correcting codes have been constructed. In this paper, we consider a new kind of burst error which will be termed as ‘2-repeated burst error of length b(fixed)’. Linear codes capable of detecting such errors have been studied. Further, codes capable of detecting and simultaneously correcting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided.

References

Abramson, N.M. (1959), A class of systematic codes for non-independent errors, IRE Trans. on Information Theory, IT-5, No. 4, pp. 150{157.

Alexander, A.A., Gryb, R.M. and Nast, D.W. (1960), Capabilities of the telephone network for data transmission, Bell System Tech. J., Vol. 39, No. 3, pp. 431{476.

Berardi, L., Dass, B.K. and Verma, Rashmi (2009), On 2-repeated burst error detecting codes, Journal of Statistical Theory and Practice, Vol. 3, No. 2, pp. 381{391.

Bridwell, J.D. and Wolf, J.K. (1970), Burst distance and multiple-burst correction, Bell System Tech. J., Vol. 49, pp. 889{909.

Campopiano, C.N. (1962), Bounds on burst error correcting codes, IRE Trans., IT-8, pp. 257{259.

Chien, R.T. and Tang, D.T. (1965), On de nitions of a burst, IBM Journal of Research and Development, Vol. 9, No. 4, pp. 292{293.

Dass, B.K. (1980), On a burst-error correcting code, Journal of Information and Optimization Sciences, Vol. 1, No. 3, pp. 291{295.

Fire, P. (1959), A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Report RSL-E-2, Sylvania Reconnaissance Systems Laboratory, Mountain View, Calif.

Hamming, R.W. (1950), Error-detecting and error-correcting codes,

Bell System Technical Journal, Vol. 29, pp. 147{160.

Peterson, W.W. and Weldon, E.J., Jr. (1972), Error-Correcting Codes, 2nd edition, The MIT Press, Mass.

Reiger, S.H. (1960), Codes for the correction of clustered errors", IRE Trans. Inform. Theory, IT-6, pp. 16{21.

Stone, J.J. (1961), Multiple burst error correction, Information and Control, Vol. 4, pp. 324{331.

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Published

2009-12-11

Issue

Vol. 19 (2009)

Section

Volume 19-2009

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