Abstract
This paper presents a comparison of different algebraic methods for decoding Reed-Solomon (RS) codes. Three kinds of decoding algorithms have been studied, two of them are «time domain» algorithms, while the third employs a transform decoding method. We achieve with this development, measurements that will permit the selection of the method with optimal decoding in the case of one future microprogramming implementation. Optimal decoding implies that the faster algorithm is the best one. It can be concluded that acceptable RS decoders can be constructed with microprocessors only for low speed transmission rates.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
R.F. Rice, "Channel coding and data compression system considerations for efficient communication of planetary imaging data", Tech. Memo. 33-695, Jet Propulsion Laboratory, Pasadena, CA, June 1974.
A. Hauptschein, "Practical, high performance concatenated coded spread spectrum channel for JTIDS", in Proc. Nat. Telecommun. Conf. 1977, p. 35: 4–1 to 4–8.
K.Y. Liu and J. Lee, "An experimental study of the concatenated Reed-Solomon/Viterbi channel coding system performance and its impact on space communications", in Proc.Nat. Telecommun. Conf., 1981.
K.Y. Liu and K.T. Woo, "The effects on receiver tracking phase error on the performance of concatenated Reed-Solomon/Viterbi channel coding system", in Proc. Nat.Telecommun. Conf., 1980, pp. 51.5.1–51.5.5.
Odenwalder et al, "Hybrid coding system study", submited to NASA Ames Research Center Linkabit Co. San Diego, CA, Final Rep., Contract NAS-2-6722, Sept. 1972.
W.W. Peterson and E.J. Weldon, Jr, Error-Correcting Codes, Cambridge MA: MIT Press, 1972.
R.L. Miller, T.K. Truong and I. S. Reed, "Efficient program for decoding the (255,223) Reed-Solomon code over GF(28) with both errors and erasures, using transform decoding", IEEE Proc. Vol. 127, Pt. E, No.4, July 1980.
I.S. Reed, T.K. Truong and R.L. Miller, "Simplified algorithm for correcting both errors and erasures of Reed-Solomon codes", IEE Proc., Vol. 126, No.10, October 1979.
E. Lenormand, "Réalisation d'un codeur-décodeur (31,15) de Reed-Solomon", Revue Technique Thomson-CSF, Vol.12,No.3,September 1980.
R.E. Blahut, "Transform techniques for error control codes", IBM J. Res. Develop., Vol.23, No.3, May 1979.
I.S. Reed, T.K. Truong and R.L. Miller, "Decoding of B.C.H. and R. S. codes with errors and erasures using continued fractions", Electronics Letters, Vol.15, No.17, 16th August 1979.
F. Mac Williams and N. Sloane, The Theory of Error-Correcting Codes, Amsterdam: North-Holland Publishing Co., 1977.
In-Shek Hsu, I.S. Reed, T.K. Truong, Ke Wang, Chiunn-Shyong Yeh and L.J. Deutsch, "The VLSI implementation of a Reed-Solomon encoder using Berlekamp's bit-serial multiplier algorithm", IEEE Trans. on Computers,Vol.C-33, No.10, October 1984.
Kuang Yung Liu, "Architecture for VLSI design of Reed-Solomon decoders", IEEE Trans. on Computers, Vol.C-33, No.2, February 1984.
F.J. García Ugalde, "Les performances des codes de Reed-Solomon sur un canal discret sans memoire", X Colloque sur le Traitement du Signal et ses Applications, Nice du 20 au 24 Mai 1985, pp.619–624.
E.R. Berlekamp, Algebraic Coding Theory, New York, McGraw-Hill, 1968.
J.L. Massey, "Shift-register synthesis and BCH decoding", IEEE Trans. on Inform. Theory, Vol.IT-15, pp.122–127, Jan. 1969.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
García-Ugalde, F.J. (1988). Coding and decoding algorithms of Reed-Solomon codes executed on a M68000 microprocessor. In: Cohen, G., Godlewski, P. (eds) Coding Theory and Applications. Coding Theory 1986. Lecture Notes in Computer Science, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19368-5_20
Download citation
DOI: https://doi.org/10.1007/3-540-19368-5_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19368-5
Online ISBN: 978-3-540-39243-9
eBook Packages: Springer Book Archive