Subscribe
Issue No.05 - May (2013 vol.62)
pp: 984-989
Noha Elarief , Hewlett Packard, Corvallis
Bella Bose , Oregon State University, Corvallis
Samir Elmougy , King Saud University, Riyadh
ABSTRACT
The error detecting problem for limited magnitude errors over high radix channels is studied. In this error model, the error magnitude does not exceed a certain limited value and it is known beforehand. For asymmetric, unidirectional, and symmetric channels, both all and $(t)$ error detecting codes are studied. In all these cases, close-to-optimal codes are proposed.
INDEX TERMS
Vectors, Systematics, Ash, Measurement, Educational institutions, Error correction, Automatic repeat request, limited magnitude error, Vectors, Systematics, Ash, Measurement, Educational institutions, Error correction, Automatic repeat request, ARQ, Error detection, error correction, asymmetric errors, unidirectional errors
CITATION
Noha Elarief, Bella Bose, Samir Elmougy, "Limited Magnitude Error Detecting Codes over Z_{q}", IEEE Transactions on Computers, vol.62, no. 5, pp. 984-989, May 2013, doi:10.1109/TC.2012.51
REFERENCES
 [1] R. Ahlswede, H. Aydinian, L.H. Khachatrian, and L.M.G.M. Tolhuizen, "On Q-ary Codes Correcting All Unidirectional Errors of a Limited Magnitude," Proc. Ninth Int'l Workshop Algebraic and Comb Coding Theory, pp. 20-26, June 2004. [2] R. Ahlswede, H. Aydinian, and L.H. Khachatrian, "Unidirectional Error Control Codes and Related Combinatorial Problems," Proc. Eighth Int'l Workshop Algebraic and Combinatorial Coding Theory, pp. 6-9, Sept. 2002. [3] M. Blaum, Codes for Detecting and Correcting Unidirectional Errors. IEEE CS Press, 1993. [4] J.M. Borden, "Optimal Asymmetric Error Detecting Codes," Information and Control, vol. 53, pp. 66-73, Apr. 1982. [5] B. Bose and D. Pradhan, "Optimal Unidirectional Error Correcting/Detecting Codes," IEEE Trans. Computers, vol. 31, no. 6, pp. 564-568, June 1982. [6] B. Bose and D.J. Lin, "Systematic Unidirectional Error-Detecting Codes," IEEE Trans. Computers, vol. 34, no. 11, pp. 63-69, Nov. 1985. [7] B. Bose, S. Elmougy, and L.G. Tallini, "Systematic T-Unidirectional Error-Detecting Codes over $Z_m$ ," IEEE Trans. Computers, vol. 56, no. 7, pp. 876-880, July 2007. [8] Y. Cassuto, M. Schwartz, V. Bohossian, and J. Bruck, "Codes for Asymmetric Limited Magnitude Errors with Application to Multi-Level Flash Memories," IEEE Trans. Information Theory, vol. 56, no. 4, pp. 1582-1595, Apr. 2010. [9] N. Elarief and B. Bose, "Diversity Combining Arq over M-ary Unidirectional Channel," IEEE Trans. Computers, vol. 58, no. 8, pp. 1026-1034, Aug. 2009. [10] N. Elarief and B. Bose, "Optimal, Systematic Q-ary Codes Correcting All Asymmetric and Symmetric Errors of Limited Magnitude," IEEE Trans. Information Theory, vol. 56, no. 3, pp. 979-983, Mar. 2010. [11] B. Eitan, R. Kazerounian, A. Roy, G. Crisenza, P. Cappelletti, and A. Modelli, "Multilevel Flash Cells and Their Trade-Offs," Proc. Int'l Electron Devices Meeting, pp. 169-172, Dec. 1996. [12] R.W. Hamming, "Error Detecting and Error Correcting Codes," Bell System Technical J., vol. 29, no. 2, pp. 147-160, 1950. [13] A. Jiang, R. Mateesu, M. Schwartz, and J. Bruck, "Rank Modulation for Flash Memories," IEEE Trans. Information Theory, vol. 55, no. 6, pp. 2659-2673, June 2009. [14] I. Naydenova and T. Kløve, "Generalized Bose-Lin Codes, a Class of Codes Detecting Asymmetric Errors," IEEE Trans. Information Theory, vol. 53, no. 3, pp. 1188-1193, Mar. 2007. [15] T. Kløve, Codes for Error Detection. World Scientific, 2007. [16] T. Kløve and V. Korzhik, Error Detecting Codes: General Theory and Their Application in Feedback Communication Systems. Kluwer, 1995. [17] S. Lin, D. Costello, and M. Miller, "Automatic-Repeat-Request Error Control Schemes," IEEE Comm. Magazine, vol. 22, no. 12, pp. 5-17, Dec. 1984. [18] L. Tallini, "Bounds on the Capacity of Unidirectional Channels," IEEE Trans. Computers, vol. 54, no. 2, pp. 232-235, Feb. 2005.