CFP last date
20 December 2024
Reseach Article

Eigen Decomposition of Reed Muller Transform using KRONECKER Method

by Jyotsna Singh, Shikha Garg
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 1 - Number 10
Year of Publication: 2010
Authors: Jyotsna Singh, Shikha Garg
10.5120/231-382

Jyotsna Singh, Shikha Garg . Eigen Decomposition of Reed Muller Transform using KRONECKER Method. International Journal of Computer Applications. 1, 10 ( February 2010), 1-4. DOI=10.5120/231-382

@article{ 10.5120/231-382,
author = { Jyotsna Singh, Shikha Garg },
title = { Eigen Decomposition of Reed Muller Transform using KRONECKER Method },
journal = { International Journal of Computer Applications },
issue_date = { February 2010 },
volume = { 1 },
number = { 10 },
month = { February },
year = { 2010 },
issn = { 0975-8887 },
pages = { 1-4 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume1/number10/231-382/ },
doi = { 10.5120/231-382 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T19:45:39.592715+05:30
%A Jyotsna Singh
%A Shikha Garg
%T Eigen Decomposition of Reed Muller Transform using KRONECKER Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 1
%N 10
%P 1-4
%D 2010
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Spectral methods have been applied to many areas of digital system design. Reed-Muller Transform (RMT) is a spectral transform which is self inverse in nature. In this paper, eigen-decomposition of Reed-Muller Transform using Kronecker Product method is introduced. The properties of eigenvectors and eigenvalues of RMT are also illustrated.

References
  1. I. S. Reed, " A Class of Multiple-Error-Correcting Codes and the Decoding Scheme," IEEE Trans. Inf. Theory, vol. IT-4, pp. 38-49, 1954.
  2. D.E. Muller, " Application of Boolean Algebra to Switching Circuit Design and to Error Detection," IRE Trans. Electronic Computers, vol. 3, pp. 6-12, 1954.
  3. T. Damarla and M. G. Karpovsky, " Reed-Muller spectral techniques for fault detection," IEEE Trans. Comput., vol. 38, no. 6, pp. 788-797, June 1989.
  4. B. J. Falkowski and B. T. Olejnicka, " Multiple-valued and spectral approach to lossless compression of binary, gray scale and color biomedical images," in Proc. 32nd IEEE Int. Symp. Multiple- Valued Logic, Boston, Massachusetts, May 2002, pp.136-142.
  5. T. Sasao, "Logic Synthesis with EXOR Logic Gates", Logic Synthesis and optimization, ed. Kluwer Academic, 1993.
  6. Sasao, T., "Logic Synthesis and Optimization," Ed., Boston: Kluwer, 1993.
  7. T. Sasao and J.T. Butler, "The eigenfunction of the Reed-Muller transformation," RM-2007, Oslo, Norway, May 16, 2007.
  8. C. C. Tseng., " Eigenvector and Fractionalization of Discrete Hadamard Transform," In Proceedings of IEEE International Symposium on Circuits and Systems, New Orleans, LA, May 2007, pp.2307-2310.
  9. Graham, A., "Kronecker products and matrix calculus with applications," Ellis Horwood Limited and John Wiley and Sons, 1981.
  10. C.H. Chang and B. J. Falkowski, " Flexible optimization of fixed polarity Reed-Muller expansions for multiple output incompletely specified Boolean functions," Proc. Asia South Pacific Design Automation Conference, Makuhari, Japan, pp.335-340, Aug 1995.
  11. Kamran Iravani, Marek A. Perkowski, " Image Compression based on Reed Muller Transorm" in Proc. Int. Conf. on Computational Intelligence and Multimedia Applications, 1998, pp. 81-95.
  12. Whitney J. Townsend, Mitchell A Thornton, Rolf Drechsler, D. Michael Miller, " ComputingWalsh, Arithmetic, and Reed-Muller Spectral Decision Diagrams using Graph Transformations", GLSVLSI'02, April 18-19, 2002, New York, USA.
Index Terms

Computer Science
Information Sciences

Keywords

eigenvalue eigenvector Kronecker Product Reed Muller Transform