Codes correcting and simultaneously detecting solid burst errors

P.K. Das

doi:10.18495/comengapp.v2i1.15

[1] Argyrides CA, Reviriego P, Pradhan DK, Maestro JA. Matrix-Based Codes for Adjacent Error Correction. IEEE Transactions on Nuclear Science.2010; 57(4): 2106-2111.
[2] Arlat J, Carter WC. Implementation and Evaluation of a (b,k)-Adjacent Error-Correcting/Detecting Scheme for Supercomputer Systems. IBM J. RES. DEVELOP.1984; 28(2): 159-169.
[3] Bossen DC. b-Adjacent Error Correction. IBM Journal of Research and Development. 1970; 14(4): 402-408.[4] Das PK. Codes Detecting and Correcting Solid Burst Errors. Bulletin of Electrical Engineering and Informatics.2012; 1(3): 225-232.
[5] Das PK. Codes Detecting and Locating Solid Burst Errors. Romanian Journal of Mathematics and Computer Science. 2012; 2 (2): 1-10.
[6] Das PK. Blockwise Solid Burst Error Correcting Codes. International Journal on Information Theory. 2012; 1(1): 11-17.
[7] Dass BK, Verma R. Repeated burst error detecting linear codes. Ratio Mathematica —J. Appl. Math. 2009; 19:25-30.
[8] Etzion T. Optimal codes for correcting single errors and detecting adjacent errors. IEEE Trans. Inform. Theory. 1992; 38: 1357–1360.
[9] Hamming RW. Error-detecting and error-correcting codes. BellSystem Technical Journal. 1950; 29: 147-160.
[10] Jensen DW. Block code to efficiently correct adjacent data and/or check bit errors. Patent no: US 6604222 B1. Date of Patent Aug 5(www.google.com/patents/US6604222). 2003.
[11] Katti RS. Comments on A Systematic (16, 8) Code for Correcting Double Errors and Detecting Triple Adjacent Errors. IEEE Trans. on Computers. 1995; 44(12): 1472-1473.
[12] Kitakami M, Jiang S, Fujiwara E. Metrics of error locating codes. Proc. of 1997 Int. Symp. Infom. Theory. 1997; 264.
[13] Peterson WW, Weldon EJ(Jr). Error-Correcting Codes, 2nd edition, The MIT Press, Mass, 1972.
[14] Ray-Chaudhuri DK, Singhi NM, Sanyal S, Subramanian PS.Theory and Design of t-Unidirectional Error-Correctingand d-Unidirectional Error-Detecting Code. IEEE Trans. on Computer.1994; 43(10): 1221-1226.
[15] Sacks GE. Multiple error correction by means of parity-checks. IRE Trans. Inform. Theory IT. 1958; 4: 45-147.
[16] Schillinger AG. A class of solid burst error correcting codes. Polytechnic Institute of Brooklyn. N.Y., Research Rept. PIBMRI. April 1964; 1223-64.
[17] Sharma BD, Dass BK. Adjacent error correcting binary perfect codes. J. Cybernetics. 1977; 7: 9-13.
[18] Shiva SGS, Sheng CL. Multiple solid burst-error-correcting binary codes.IEEE Trans. Inform. Theory, IT-15. 1969; 188-189.

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Affiliations

P.K. Das
Department of Mathematics Shivaji College University of Delhi

Content Top

Codes correcting and simultaneously detecting solid burst errors

P.K. Das

Vol 2 No 1 (2013)

DOI 10.18495/comengapp.v2i1.15

Submitted: Oct 13, 2013

Published: Feb 25, 2013

Abstract

Detecting and correcting errors is one of the main tasks in coding theory. The bounds are important in terms of error-detecting and -correcting capabilities of the codes. Solid Burst error is common in several communication channels. This paper obtains lower and upper bounds on the number of parity-check digits required for linear codes capable of correcting any solid burst error of length b or less and simultaneously detecting any solid burst error of length s(>b) or less. Illustration of such a code is also provided.Keywords: Parity check matrix, Syndromes, Solid burst errors, Standard arrayDOI:Â 10.18495/comengapp.21.143150Â Â