ERROR CORRECTING CODE USING LATIN SQUARE

Abdul-Waheed.Abdul-Jabbar, Makarim; Makki Sagheer, Ali

doi:10.37652/juaps.2008.15649

Document Type : Research Paper

Authors

College of Computer, University of Anbar

10.37652/juaps.2008.15649

Abstract

ABSTRACT:Digital data stored in computers or transmitted over computer networks are constantly subject to error due to the physical medium in which they are stored or transmitted. Error-correction codes are means of introducing redundancy in the data so that even if part of it is corrupted or completely lost, the original data can be recovered. Error correcting codes are used in modern technology to protect information from errors. Burst error correcting codes are needed in virtually uncountable applications. Such codes will be called complete burst error correcting codes. There are quite a few constructions for complete burst error correcting codes. This paper presents an error correcting code based on the concept and the theory of the Latin Squares, where it employ the characteristics of the orthogonal Latin Squares to correct the errors. That is not complete burst error correcting codes, since it can correct most burst pattern of length i „T n, but not all of them. However, if the number of uncorrectable patterns is sufficiently small, this code can be used in practice as a burst error correcting code.

Keywords

Main Subjects

Computer

References

[1] B. A. Anderson, Sequencings and Starters, Pacific J. Math . 64 ( 1976) 17-24.

[2] E. R. Berlekamp, Algebraic Coding Theory, MC Graw – Hill

[3] N. Cal and R. W. Yeung, Network Error Correction, Part II: Lower Bounds, Communications In Information And Systems, Vol. 6, No. 1, pp. 37-54, 2006, International Press, 003.

[4] M. Grassl, Classical Information Theory and Classical Error Correction, Lectures on Quantum Information, WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim ISBN: 978-3-527-40527-5, 2007.

[5] R. W. Hamming. Error-detecting and error-correcting codes. Bell System Technical Journal, 29(2):147–160, 1950.

[6] G. Held, Data communication networking devices: operations, utilization and LAN and WAN internetworking, forth edition, John Wiley & Sons Ltd, 2001.

[7] J. Higham , A Product Theorem For Row – Complete Latin Squares, J. Combi. Des 5 311-318, 1997.

[8] M. Y. Hsiao, D. C. Bossen and R. T. Chien, Orthogonal Latin Square Codes, 1969.

[9] D. R. Irvin, Embedded a Secondary Communication Channel Transparently within a Cyclic Redundancy Check (CRC), 2001.

[10] J. Isbell, Sequencing Certain Dihedral Group, Discrete Math. 85(1990) 323-328.

[11] P. Li, Sequencing the Dihedral Groups D4K, Discrete Math. 157 271-276, 1997.

[12] A. D. Keed Well, Complete Mapping and Sequencing of Finite Group, The CRC Handbook of combinatorial Designs ( Eds. C.J.Colbourn and J.H. Dinitz ) CRC, Press 246-253, 1996.

[13] A. Nayak, Error-Correction Codes, UW Math 135, July 29, 2005.

[14] R. Friedlander, Sequences in Group with Distinct Partial Products , Aequations math. 14 (1976) 59-66.

[15] M. A. Ollis, Sequenceable Groups and Related Topics, 2002

[16] V. Pless, Introduction to the Theory of Error–Correcting Code, Wiley, New York, 1982.

[17] D. Raphaeli, A Simple and Efficient Burst Error Correcting Code Based on an Array Code, Senior Member IEEE

[18] J. Rotman, An Introduction To The Theory Of Groups, 4th Edition, Springer-Verlag, 1994.

[19] N. Ruskus, Finite Mathematics, March 6, 2002.

[20] R. W. Yeung and N. Cal, Network Error Correction, Part I: Basic Concepts And Upper Bounds, Communications In Information And Systems, Vol. 6, No. 1, pp. 19-36, 2006, International Press, 002.

Journal of University of Anbar for Pure Science

ERROR CORRECTING CODE USING LATIN SQUARE

References

References

Volume 2, Issue 3
December 2008
Page 81-91

ERROR CORRECTING CODE USING LATIN SQUARE

References

References

Volume 2, Issue 3December 2008Page 81-91

Volume 2, Issue 3
December 2008
Page 81-91