This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Wavelet Codes for Algorithm-Based Fault Tolerance Applications
July-September 2010 (vol. 7 no. 3)
pp. 315-328
G. Robert Redinbo, University of California, Davis, Davis
Algorithm-based fault tolerance (ABFT) methods, which use real number parity values computed in two separate comparable ways to detect computer-induced errors in numerical processing operations, can employ wavelet codes for establishing the necessary redundancy. Wavelet codes, one form of real number convolutional codes, determine the required parity values in a continuous fashion and can be intertwined naturally with normal data processing. Such codes are the transform coefficients associated with an analysis uniform filter bank which employs downsampling, while parity-checking operations are performed by a syndrome synthesis filter bank that includes upsampling. The data processing operations are merged effectively with the parity generating function to provide one set of parity values. Good wavelet codes can be designed starting from standard convolutional codes over finite fields by relating the field elements with the integers in the real number space. ABFT techniques are most efficient when employing a systematic form and methods for developing systematic codes are detailed. Bounds on the ABFT overhead computations are given and ABFT protection methods for processing that contains feedback are outlined. Analyzing syndromes' variances guide the selection of thresholds for syndrome comparisons. Simulations demonstrate the detection and miss probabilities for some high-rate wavelet codes.

[1] K.H. Huang and J.A. Abraham, "Algorithm-Based Fault Tolerance for Matrix Operations," IEEE Trans. Computers, vol. 33, no. 6, 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. Computers, vol. 39, no. 4, pp. 426-435, Apr. 1990.
[3] D.P. Siewiorek and R.S. Swarz, Reliable Computer Systems, second ed. Digital Press, 1992.
[4] P.P. Vaidyanathan, "Orthonormal and Biorthonormal Filter Banks as Convolvers, and Convolutional Coding Gain," IEEE Trans. Signal Processing, vol. 41, no. 6, pp. 2110-2130, June 1993.
[5] F. Labeau, L. Vandendorpe, and B. Macq, "Oversampled Filter Banks as Error Correcting Codes," Proc. Fifth Int'l Symp. Wireless Personal Multimedia Communications, pp. 1265-1269, Oct. 2002.
[6] F. Labeau, J.C. Chiang, M. Kieffer, P. Duhamel, L. Vanderendorpe, and B. Macq, "Oversampled Filter Banks as Error Correcting Codes: Theory and Impulse Noise Correction," IEEE Trans. Signal Processing, vol. 53, no. 12, pp. 4619-4630, Dec. 2005.
[7] G. Strang and T. Nguyen, Wavelets and Filter Banks. Wellesley-Cambridge Press, 1997.
[8] P.P. Vaidyanathan, Multirate Systems and Filter Banks. Prentice-Hall, 1993.
[9] H. Bolcskei, F. Hlawatsch, and H.G. Feichtinger, "Frame-Theoretic Analysis of Oversampled Filter Banks," IEEE Trans. Signal Processing, vol. 46, no. 5, pp. 3256-3268, Dec. 1998.
[10] N.K. Bose, Digital Filters Theory and Applications. Elsevier Science Publishing, 1985.
[11] R. Johannesson and K.S. Zigangirov, Fundamentals of Convolutional Coding. IEEE Press, 1999.
[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, no. 3, pp. 416-422, July 1965.
[14] S. Lin and D.J. CostelloJr., Error Control Coding Fundamentals and Applications, Section 14.2. Prentice-Hall, 1983.
[15] O. Christensen, An Introduction to Frames and Riesz Bases. Birkauser, 2003.
[16] S. Mallat, A Wavelet Tour of Signal Processing, second ed. Academic Press, 1999.
[17] T.R.N. Rao and E. Fujiwara, Error-Control Coding for Computer Systems. Prentice-Hall, 1989.

Index Terms:
Algorithm-based fault tolerance (ABFT), wavelet codes, real number coding, failure error detection, systematic wavelet structures, recursive processing.
Citation:
G. Robert Redinbo, "Wavelet Codes for Algorithm-Based Fault Tolerance Applications," IEEE Transactions on Dependable and Secure Computing, vol. 7, no. 3, pp. 315-328, July-Sept. 2010, doi:10.1109/TDSC.2009.14
Usage of this product signifies your acceptance of the Terms of Use.