Abstract
Error correction codes defined over real-number field have been studied and recognized as useful in many applications. However, most real-number codes in literature are quite suspect in their numerical stability. In this paper, we introduce a class of real-number codes based on random generator matrices over real-number fields. Codes over complex-number field are also discussed. Experiment results demonstrate our codes are numerically much more stable than existing codes in literature.
This research was supported in part by the Los Alamos National Laboratory under Contract No. 03891-001-99 49 and the Applied Mathematical Sciences Research Program of the Office of Mathematical, Information, and Computational Sciences, U.S. Department of Energy under contract DE-AC05-00OR22725 with UT-Battelle, LLC.
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Keywords
- Condition Number
- Discrete Cosine Transform
- Discrete Fourier Transform
- Random Matrix
- Error Correction Code
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References
Azais, J.M., Wschebor, M.: Upper and lower bounds for the tails of the distribution of the condition number of a gaussian matrix. Submitted for publication (2003)
Boley, D.L., Brent, R.P., Golub, G.H., Luk, F.T.: Algorithmic Fault Tolerance Using the Lanczos Method. SIAM Journal on Matrix Analysis and Applications 13, 312–332 (1992)
Edelman, A.: Eigenvalues and Condition Numbers of Random Matrices, Ph.D. thesis, Dept. of Math., M.I.T (1989)
Edelman, A.: On the distribution of a scaled condition number. Mathematics of Computation 58, 185–190 (1992)
Ferreira, P.: Stability issues in error control coding in complex field, interpolation, and frame bounds. IEEE Signal Processing Letters 7(3), 57–59 (2000)
Ferreira, P., Vieira, J.: Stable DFT codes and frames. IEEE Signal Processing Letters 10(2), 50–53 (2003)
Golub, G.H., Van Loan, C.F.: Matrix Computations, 2nd edn. The John Hopkins University Press (1989)
Hadjicostis, C.N., Verghese, G.C.: Coding approaches to fault tolerance in linear dynamic systems. Submitted to IEEE Transactions on Information Theory
Henkel, W.: Multiple error correction with analog codes. In: Proceedings of AAECC, pp. 239–249. Springer, Heidelberg (1989)
Huang, H., Abraham, J.A.: Algorithm-based fault tolerance for matrix operations. IEEE Transactions on Computers C-39, 300–304 (1984)
Luk, F.T., Park, H.: An analysis of algorithm-based fault tolerance techniques. Journal of Parallel and Distributed Computing 5, 1434–1438 (1988)
Marvasti, F., Hasan, M., Echhart, M., Talebi, S.: Efficient algorithms for burst error recovery using FFT and other transform kernels. IEEE Transactions on Signal Processing 47(4), 1065–1075 (1999)
Nair, S.S., Abraham, J.A.: Real-number codes for fault-tolerant matrix operations on processor arrays. IEEE Transactions on Computers C-39, 300–304 (1990)
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Chen, Z., Dongarra, J. (2005). Numerically Stable Real Number Codes Based on Random Matrices. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428831_15
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DOI: https://doi.org/10.1007/11428831_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26032-5
Online ISBN: 978-3-540-32111-8
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