Performance analysis of a decoding algorithm for algebraic-geometry codes

The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt (see ibid., vol. 41, p. 1762-8, Nov. 1995) corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm...

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Published in:IEEE transactions on information theory Vol. 45; no. 5; pp. 1712 - 1717
Main Authors: Jensen, H.E., Nielsen, R.R., Hoholdt, T.
Format: Journal Article
Language:English
Published: New York IEEE 01.07.1999
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebraic-geometric codes
Algorithms
Computer science
Errors
ISSN:0018-9448, 1557-9654
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Abstract The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt (see ibid., vol. 41, p. 1762-8, Nov. 1995) corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm for heavier error patterns. It turns out that in the typical case, where the error points are "independent", one can prove that the algorithm always fails, that is gives a wrong or no answer, except for high rates where it does much better than expected. This explains the simulation results presented by O'Sullivan at the IEEE Int. Symp. Information Theory, Ulm, Germany (1997). We also show that for dependent errors the algorithm almost always corrects these.
AbstractList The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt corrects all error patterns of weight less than half the Feng-Rao minimum distance.
The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt (see ibid., vol. 41, p. 1762-8, Nov. 1995) corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm for heavier error patterns. It turns out that in the typical case, where the error points are "independent", one can prove that the algorithm always fails, that is gives a wrong or no answer, except for high rates where it does much better than expected. This explains the simulation results presented by O'Sullivan at the IEEE Int. Symp. Information Theory, Ulm, Germany (1997). We also show that for dependent errors the algorithm almost always corrects these
The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt (see ibid., vol. 41, p. 1762-8, Nov. 1995) corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm for heavier error patterns. It turns out that in the typical case, where the error points are "independent", one can prove that the algorithm always fails, that is gives a wrong or no answer, except for high rates where it does much better than expected. This explains the simulation results presented by O'Sullivan at the IEEE Int. Symp. Information Theory, Ulm, Germany (1997). We also show that for dependent errors the algorithm almost always corrects these.
Author Nielsen, R.R.
Jensen, H.E.
Hoholdt, T.
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Cites_doi 10.1109/18.476248
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ref4
shokrollahi (ref3) 1997
o sullivan (ref1) 1997
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  article-title: decoding hermitian codes beyond $(d_{\min}-1)/2$
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  doi: 10.1006/jcom.1997.0439
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  publication-title: Decoding algebraic-geometric codes beyond the error-correction bound
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Snippet The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt (see ibid., vol. 41, p. 1762-8, Nov. 1995) corrects...
The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt corrects all error patterns of weight less than half...
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SubjectTerms Algebraic-geometric codes
Algorithms
Computer science
Errors
Title Performance analysis of a decoding algorithm for algebraic-geometry codes
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