Abstract
With the end goal of implementing optimal Reed-Solomon error control decoders on FPGAs, we characterize the FPGA performance of several finite field multiplier designs reported in the literature. We discover that finite field multipliers optimized for VLSI implementation are not optimized for FPGA implementation. Based on this observation, we discuss the relative merits of each multiplier design and show why each does not perform well on FPGAs. We then suggest how to improve the performance of many finite field multiplier designs.
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References
Politano, J.L., Deprey, D.: A30 mbits/s (255,223) Reed-Solomon decoder. In: Charpin, P., Cohen, G. (eds.) EUROCODE 1990. LNCS, vol. 514, pp. 385–391. Springer, Heidelberg (1991)
Wicker, S.B.: Error Control Systems for Digital Communication and Storage. Prentice Hall, Englewood Cliffs (1995)
Lin, S., Costello, D.J.: Error Control Coding: Fundamentals and Applications. Prentice-Hall, Englemwood Cliffs (1983)
Mastrovito, E.D.: VLSI Architectures for Computations in Galois Fields. PhD thesis, Linköping University, Dept. Electr. Eng., Linköping, Sweden (1991)
C. A. Wang, T. K. Truong, H. M. Shao, L. J. Deutsch, J. K. Omura, and I. S. Reed. VLSI architectures for computing multiplications and inverses in GF(2m). IEEE Transactions on Computers, 34(8):709–717, Aug 1985.
Massey, J.L., Omura, J.K.: Computational method and apparatus for finite field arithmetic. U. S. Patent Application (1981)
Hasan, M.A., Bhargava, V.K.: Bit-serial systolic divider and multiplier for finite fields GF(2m). IEEE Transactions on Computers 41(8), 972–980 (1992)
Paar, C., Rosner, M.: Comparison of arithmetic architectures for Reed-Solomon decoders in reconfigurable hardware. IEEE Transactions on Computers 41(8), 219–224 (1997)
Morii, M., Kasahara, M., Whiting, D.: Efficient bit-serial multiplication and the discrete-time Wiener-Hopf equation over finite fields. IEEE Transactions on Information Theory 35(6), 1177–1183 (1989)
Berlekamp, E.: Bit-serial Reed-Solomon encoders. IEEE Transactions on Information Theory IT-28(6), 869–874 (1982)
Hutchings, B., Bellows, P., Hawkins, J., Hemmert, S., Nelson, B., Rytting, M.: A C AD suite for high-performance FPGAde sign. In: Pocek, K., Arnold, J. (eds.) IEEE Symposium on Field-Programmable Custom Computing Machines (FCCM 1999). pp. TBA. IEEE Computer Society, Los Alamitos (1999)
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Ahlquist, G.C., Nelson, B., Rice, M. (1999). Optimal Finite Field Multipliers for FPGAs. In: Lysaght, P., Irvine, J., Hartenstein, R. (eds) Field Programmable Logic and Applications. FPL 1999. Lecture Notes in Computer Science, vol 1673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48302-1_6
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DOI: https://doi.org/10.1007/978-3-540-48302-1_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66457-4
Online ISBN: 978-3-540-48302-1
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