This Article 
 Bibliographic References 
 Add to: 
Systematic Wavelet Subcodes for Data Protection
June 2011 (vol. 60 no. 6)
pp. 904-909
G. Robert Redinbo, University of California, Davis, Davis
Real number data processing failures are detected by comparing parity values associated with a wavelet code which is most efficient in systematic form. Any rate k/n wavelet code, a form of real number convolutional code, is manipulated into a systematic wavelet subcode, with slightly reduced rate (k-1)/n, staying within the original algebraic structure.

[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] I. Koren and C.M. Krishna, Fault-Tolerant Systems. Elsevier, 2007.
[4] D.P. Siewiorek and R.S. Swarz, Reliable Computer Systems Design and Evaluation, second ed. Digital Press, 1992.
[5] G.R. Redinbo, "Wavelet Codes for Algorithm-Based Fault Tolerance Applications," IEEE Trans. Dependable and Secure Computing, vol. 7, no. 3, pp. 315-328, July-Sept. 2010.
[6] Z. Cvetkovic and M. Vetterli, "Oversampled Filter Banks," IEEE Trans. Signal Processing, vol. 46, no. 5, pp. 1245-1255, May 1998.
[7] 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.
[8] R. Johannesson and K.S. Zigangirov, Fundamentals of Convolutional Coding, Chapter 2. IEEE Press, 1999.
[9] Y.J. Chen and K.S. Amaratunga, "M-Channel Lifting Factorization of Perfect Reconstruction Filter Banks and Reversible M-Band Wavelet Transforms," IEEE Trans. Circuits and Systems- II Analog and Digital Signal Processing, vol. 50, no. 12, pp. 963-976, Dec. 2003.
[10] F.R. Gantmacher, The Theory of Matrices, vol. 1, Chapter VI. Chelsea Publishing Company, 1960.
[11] I. Gohberg, P. Lancaster, and L. Rodman, Matrix Polynomials, Chapter S1. Academic Press, 1992.
[12] D.G. Daut, J W. Modestino, and L.D. Wismer, "New Short Constraint Length Convolutional Code Construction for Selected Rational Rates," IEEE Trans. Information Theory, vol. IT-28, no. 5, pp. 794-800, Sept. 1982.
[13] R.J. McEliece, "The Algebraic Theory of Convolutional Codes," Handbook of Coding Theory, Chapter 12, V.S. Pless and W.C. Huffman, eds., pp. 1065-1138, Elsevier Science B.V., 1998.

Index Terms:
Real number convolutional code, wavelet code design, wavelet subcode, polyphase system matrix, algorithm-based fault tolerance (ABFT), error detection only, polynomial matrix manipulation, modified Smith normal form.
G. Robert Redinbo, "Systematic Wavelet Subcodes for Data Protection," IEEE Transactions on Computers, vol. 60, no. 6, pp. 904-909, June 2011, doi:10.1109/TC.2010.251
Usage of this product signifies your acceptance of the Terms of Use.