Abstract
Algorithms for computation are a central part of digital signal processing and of decoders for error-control codes. When restricted to the study of their computational algorithms, there is not much to distinguish those two subjects. Only the arithmetic field is different; in one case the real or complex field, and a Galois field in the other. Even this distinction is hard to defend; signal processing problems may use Galois fields, and error-control codes in the real or complex field are now under study.
We will survey the state of modern fast algorithms for certain types of computations used in digital processing and error-control including tasks such as linear convolution, cyclic convolution, discrete Fourier transforms, and spectral estimation. In particular we will discuss the decoding of error-control codes as a problem in spectral estimation, and see how this viewpoint leads to the development of efficient decoder algorithms. The Winograd FFT, a fast Berlekamp-Massey algorithm, and a time-domain Reed-Solomon decoder will be described.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blahut, R. E., Theory and Practice of Error Control Codes, Addison-Wesley, 1983.
Wolf, J. K., “Redundancy, the Discrete Fourier Transform, and Impulse Noise Cancellation,” Proc Princeton Conf Inf Sci Syst, Princeton, NJ, 1982.
Marshall, T. G., Jr., “Real Number Transform and Convolutional Codes,” Proceedings of the 24th Midwest Symposium on Circuits and Systems, Ed S. Karne, Albuquerque, New Mexico, June 29–30, 1981.
Nussbaumer, H. J. Fast Fourier Transform and Convolution Algorithms, Springer Verlag, Berlin, 1981.
Winograd, S., “On Computing the Discrete Fourier Transform,” Math Comp Vol 32, pp 175–199, 1978.
Miller, R. L., T. K. Truong, and I. S. Reed, “Efficient ProgEam for Decoding the (255, 223) Reed-Solomon Code Over GF(2) with Both Errors and Erasures, Using Transform Decoding,” IEEE Proceedings, Volume 127, pp 136–142, 1980.
Blahut, R. E., “Efficient Decoder Algorithms Based on Spectral Techniques,” IEEE Abstracts of Papers - IEEE International Symposium on Information Theory, Santa Monica, California, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Martinus Nijhoff Publishers, Dordrecht
About this chapter
Cite this chapter
Blahut, R.E. (1985). Fast Algorithms for Signal Processing and Error Control. In: Skwirzynski, J.K. (eds) The Impact of Processing Techniques on Communications. NATO ASI Series, vol 91. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5113-6_8
Download citation
DOI: https://doi.org/10.1007/978-94-009-5113-6_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8760-5
Online ISBN: 978-94-009-5113-6
eBook Packages: Springer Book Archive