This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Failure-Detecting Arithmetic Convolutional Codes and an Iterative Correcting Strategy
November 2003 (vol. 52 no. 11)
pp. 1434-1442

Abstract—Errors due to failures in data processing algorithms may be detected and even corrected by employing systematic convolutional codes defined over the fixed-point arithmetic structures supporting the computations. A new class of arithmetic convolutional codes using symbols from the finite ring associated with normal signed arithmetic is based on binary burst-correcting codes and a code's performance in the larger context exceeds that of an underlying basis code. When failures satisfy the usual guard band requirements for the binary code, error correction is possible using an iterative feedback decoder processing syndromes that are defined over the integers modulo a power of two. A class of high rate burst-correcting codes is discussed in more detail and their properties guarantee the detection of the onset of errors. The corrector also contains failure error-detecting capabilities.

[1] K.H. Huang and J.A. Abraham, Algorithm-Based Fault Tolerance for Matrix Operations IEEE Trans. Computers, vol. 33, no. 12, pp. 518-528, Dec. 1984.
[2] V.S.S. Nair and J.A. Abraham, "Real-Number Codes for Fault-Tolerant Matrix Operations on Processor Arrays," IEEE Trans. on Computers, Vol. 39, No. 4, Apr. 1990, pp. 426-435.
[3] G.R. Redinbo, “Generalized Algorithm-Based Fault Tolerance: Error Correction via Kalman Estimation,” IEEE Trans. Computers, vol. 47, no. 6, pp. 639-655, June 1998.
[4] W.B. Pennebaker and J.L. Mitchell, JPEG Still Image Data Compression Standard. Van Nostrand Reinhold, 1993.
[5] G.L. Feng, T.R.N. Rao, and M.S. Kolluru, "Error Correcting Codes Over$Z_{2^m}$for Algorithm-Based Fault Tolerance," IEEE Trans. Computers, vol. 43, no. 3, pp. 370-374, Mar. 1994.
[6] D.A. Patterson and J.L. Hennessy, Computer Organization and Design, 2d ed., Morgan Kaufmann, San Mateo, Calif., 1998.
[7] I. Niven, H.S. Zuckerman, and H.L. Montgomery, An Introduction to the Theory of Numbers, fifth ed. New York: John Wiley&Sons, 1991.
[8] C.H. Roth Jr., Fundamentals of Logic Design, fourth ed. New York: West Publishing, 1992.
[9] N. Jacobson, Basic Algebra I, second ed. New York: W.H. Freeman and Company, 1985.
[10] G.D. Forney Jr., The Viterbi Algorithm Proc. IEEE, vol. 61, pp. 268-278, 1973.
[11] S. Lin and D.J. Costello Jr., Error Control Coding Fundamentals and Applications. Englewood Cliffs, N.J.: Prentice-Hall, 1983.
[12] E.R. Berlekamp, A Class of Convolution Codes Information and Control, vol. 6, pp. 1-13, 1962.
[13] J.L. Massey, Implementation of Burst-Correcting Convolutional Codes IEEE Trans. Information Theory, vol. 11, pp. 416-422, July 1965.

Index Terms:
Algorithm-based fault tolerance, convolutional codes over integers, iterative decoding, free modules, fixed-point arithmetic, burst-correcting codes, syndrome decoding, real number codes.
Citation:
G. Robert Redinbo, "Failure-Detecting Arithmetic Convolutional Codes and an Iterative Correcting Strategy," IEEE Transactions on Computers, vol. 52, no. 11, pp. 1434-1442, Nov. 2003, doi:10.1109/TC.2003.1244941
Usage of this product signifies your acceptance of the Terms of Use.