Abstract
The frequency transformation methods like fast fourier transform algorithms can be competently used in realization of discrete fourier transforms over Galois field, which have broad applications in network security and digital communication in error correcting codes. The cyclotomic fast fourier transform (CFFT) is a type of fast fourier transform algorithm over finite fields This method utilizes the benefit of cyclic decomposition. The cyclotomic breakdown of input data is used to reduce the number of operations which can be equally exploited to get a set by set treatment of the input sequence. Common subexpression elimination (CSE) is an useful optimization process to solve the multiple constant multiplication problems. In this paper, common subexpression elimination algorithm for cyclotomic fast fourier transform over fixed field 23 is designed. Using CSE algorithm, we reduce the additive complexities of cyclotomic fast fourier transform. The design of CSE is to spot regular patterns that are present in expressions more than once and replace them with a single variable. Using above method every regular pattern calculates only once, thus minimizing the area of CFFT architecture required in VLSI implementation.
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References
S. V. Fedorenko and P. V. Trifonov: A method for Fast Computation of the Fast Fourier Transform over a Finite Field. Problems of Information Transmission, 39(3):231–238, July−September 2003.
Ali AL GHOUWAYEL, Yves LOUET, Amor NAFKHA and Jacques PALICOT: On the FPGA Implementation of the Fourier Transform over Finite Fields GF (2m). SUPELEC-IETR Avenue de la Boulaie CS 4760135576 CESSON-SEVIGNE Cedex, FRANCE-2007.
Truong, T.-K., Jeng, J.-H., and Reed, I.S.: Fast Algorithm for Computing the Roots of Error Locator Polynomials up to Degree 11 in Reed–Solomon Decoders. IEEE Trans. Commun., vol. 49, no. 5, pp. 779–783, 2001.
N. Chen, and Z. Y. Yan: Cyclotomic FFTs With Reduced Additive Complexities Based on a Novel Common Subexpression Elimination Algorithm. IEEE Tranc. Signal Processing, Vol. 57, no.3, pp. 1010–1020, Mar.2009.
M. M. Wong, and M. L. D. Wong: A new common subexpression elimination algorithm with application in composite field AES S-box. Tenth Int. Conf. Information Sciences Signal Processing and their Applications (ISSPA 2010), pp. 452–455, May 2010.
R. Blahut: Theory and Practice of Error Control Codes. Reading, Massachusetts: Addison-Wesley, 1983.
Ning Wu, Xiaoqiang Zhang, Yunfei Ye, and Lidong Lan: Improving Common subexpression Elimination Algorithm with A New Gate-Level Delay Computing Method. Proceedings of the World Congress on Engineering and Computer Science, Vol II 23–25 October, San Francisco, USA, 2013.
Acknowledgments
The authors would like to show gratitude Prof. P. Trifonov and Ali AL GHOUWAYEL for providing details of CFFTs. They are thankful to Ning Wu, Xiaoqiang Zhang, Yunfei Ye and Lidong Lan for providing details of common subexpression elimination algorithm.
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Tejaswini Deshmukh, Prashant Deshmukh, Pravin Dakhole (2017). Design of Common Subexpression Elimination Algorithm for Cyclotomic Fast Fourier Transform Over GF (23). In: Satapathy, S., Bhateja, V., Joshi, A. (eds) Proceedings of the International Conference on Data Engineering and Communication Technology. Advances in Intelligent Systems and Computing, vol 468. Springer, Singapore. https://doi.org/10.1007/978-981-10-1675-2_55
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DOI: https://doi.org/10.1007/978-981-10-1675-2_55
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