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}
}
  • R. Blahut
  • Published 1 May 1979
  • Computer Science
  • IBM J. Res. Dev.
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… 

Codes For Error Correction Based Upon Interpolation Of Real-number Sequences

  • T. Marshall
  • Computer Science
    Nineteeth Asilomar Conference on Circuits, Systems and Computers, 1985.
  • 1985
It will be shown that correction of burst errors in coded signals can be accomplished by error-trapping structures, and the complete coding system is conveniently realizable by general-purpose, programmable, digital signal or image processors.

Extended-BCH codes using fourier transform over a finite field

It is shown that when the code is constructed by this method, the fast Fourier transform algorithm can be applied to a wider range of code lengths than before in syndrome-calculation.

On Blahut's Decoding Algorithms for Two-Dimensional BCH Codes

It is shown that Blahut's decoding algorithms have optimal error-correcting capability and improved decoding algorithms are presented, which have less computational complexity.

Developments in Error Control Coding Techniques and some Results on Concatenated Codes

An attempt to present an overview of the error control coding techniques by suitably classifying them and drawing a qualitative comparison between them in order to provide a design tool to the researcher.

A transform approach to Goppa codes

It is shown how the class of Goppa codes can be easily decoded in the context of this transformation by using the Berlekamp-Massey decoding algorithm.

Generalized minimum distance decoding with arbitrary error, erasure tradeoff

A means of expressing their error-correcting capabilities by a unified function, the Generalized Decoding Radius is introduced, which considers the decoding radius of GMD decoding, i.e., the maximum number of errors that are correctable with guarantee.

The application of Walsh transform for forward error correction

  • F. MarvastiM. HungM. Nakhai
  • Computer Science
    1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)
  • 1999
A novel class of forward error correcting codes constructed using the discrete Walsh transform are presented, defined on the field of real numbers, and compared to those of the well-known BCH and RS codes.

A Reed-Solomon code simulator and periodicity algorithm

The periodicity algorithm is introduced and its validity is verified by exhaustive computer simulations and it is concluded that the periodicity algorithms is the optimal solution for both decoding time and memory space.

Fast Transform for Decoding Both Errors and Erasures of Reed-Solomon Codes Over GF for

The complexity of the transform-domain decoder for correcting both errors and era- sures of the Reed-Solomon codes of block length over GF for is reduced substantially from the pre- vious time- domain decoder.

Fast Transform for Decoding Both Errors and Erasures of Reed – Solomon Codes Over GF ( 2 m ) for 8 m 10

In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2 1 points over GF(2 ), where
...

References

SHOWING 1-10 OF 24 REFERENCES

Shift-register synthesis and BCH decoding

  • J. Massey
  • Computer Science
    IEEE 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

Cyclic product codes

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

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

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

  • E. Berlekamp
  • Computer Science
    McGraw-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

Further results on cyclic product codes

The algebraic structure of cyclic product codes can be applied to establish the exact minimum distance of certain subclasses of BCH codes.

Error Free Coding

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.

Polynomial codes

A class of cyclic codes is introduced by a polynomial approach that is an extension of the Mattson-Solomon method and of the Muller method and some subclasses are shown to be majority-logic decodable.

On decoding BCH codes

  • G. Forney
  • Computer Science
    IEEE 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

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.