Transform Techniques for Error Control Codes
@article{Blahut1979TransformTF, title={Transform Techniques for Error Control Codes}, author={Richard E. Blahut}, journal={IBM J. Res. Dev.}, year={1979}, volume={23}, pages={299-315} }
By using the theory of finite field Fourier transforms, the subject of error control codes is described in a language familiar to the field of signal processing. The many important uses of spectral techniques in error control are summarized. Many classes of linear codes are given a spectral interpretation and some new codes are describe. Several alternative encoder/ decoder schemes are described by frequency domain reasoning. In particular, an errors-and-erasures decoder for a BCH code is…
201 Citations
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References
SHOWING 1-10 OF 24 REFERENCES
Shift-register synthesis and BCH decoding
- Computer ScienceIEEE Trans. Inf. Theory
- 1969
It is shown in this paper that the iterative algorithm introduced by Berlekamp for decoding BCH codes actually provides a general solution to the problem of synthesizing the shortest linear feedback…
On decoding of Reed-Solomon codes
- Computer ScienceIEEE Trans. Inf. Theory
- 1971
It is shown how nonsystematic Reed-Solomon (RS) codes encoded by means of the Chinese remainder theorem can be decoded using the Berlekamp algorithm. The Chien search and calculation of error values…
Cyclic product codes
- Computer ScienceIEEE Trans. Inf. Theory
- 1965
A new class of cyclic codes, cyclic product codes, is characterized and is shown to be capable of unambiguous correction of both bursts and random errors and to be a compromise between random and burst-error-correcting codes.
Algebraic generalization of BCH-Goppa-Helgert codes
- Computer ScienceIEEE Trans. Inf. Theory
- 1975
Based on the Mattsom-Solomon polynomial, a class of algebraic linear error-correcting codes is proposed, which includes the Bose-Chaudhuri-Hocquenghen (BCH), Goppa codes, and Srivastava codes as subclasses, and it is shown that this class of codes asymptotically approaches the Varshamov-Gilbert bound.
A new approach to error-correcting codes
- Computer ScienceIEEE Trans. Inf. Theory
- 1977
A correspondence between linear (n,k,d) codes and algorithms for computing a system of k bilinear forms is established, holding promise of a better understanding of the structure of existing codes as well as for methods of constructing new codes with prescribed rate and distance.
Algebraic coding theory
- Computer ScienceMcGraw-Hill series in systems science
- 1968
This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering…
Error Free Coding
- Computer Science
- 1973
Preliminary results of several sets of data from the ERTS-l data frame and the ERIM· airoraft data frame showed that an error· free reconstruction of the data can be achieved with four bits per picture element or less.
On decoding BCH codes
- Computer ScienceIEEE Trans. Inf. Theory
- 1965
The Gorenstein-Zierler decoding algorithm for BCH codes is extended, modified, and analyzed and it is shown how to correct erasures as well as errors, and improved procedures for finding error and erasure values are exhibited.
A New Treatment of Bose-Chaudhuri Codes
- Mathematics, Computer Science
- 1961
The (12, 23) Golay code is proved very simply to have $d = 7$; and a (24, 47) code is shown to have £d\leqq 9$, thus improving by 4 the usual lower bound $d_0 = 5$ for that code.