Algebraic soft-decision decoding of Reed-Solomon codes

A polynomial-time soft-decision decoding algorithm for Reed-Solomon codes is developed. This list-decoding algorithm is algebraic in nature and builds upon the interpolation procedure proposed by Guruswami and Sudan(see ibid., vol.45, p.1757-67, Sept. 1999) for hard-decision decoding. Algebraic soft...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 49; no. 11; pp. 2809 - 2825
Main Authors: Koetter, R., Vardy, A.
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2003
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebra
Algorithm design and analysis
Algorithms
Asymptotic properties
Codes
Computer science
Constellation diagram
Decoding
Information theory
Interpolation
Maintenance
Modulation coding
Probabilistic methods
Probability theory
Reed-Solomon codes
Wireless communication
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:A polynomial-time soft-decision decoding algorithm for Reed-Solomon codes is developed. This list-decoding algorithm is algebraic in nature and builds upon the interpolation procedure proposed by Guruswami and Sudan(see ibid., vol.45, p.1757-67, Sept. 1999) for hard-decision decoding. Algebraic soft-decision decoding is achieved by means of converting the probabilistic reliability information into a set of interpolation points, along with their multiplicities. The proposed conversion procedure is shown to be asymptotically optimal for a certain probabilistic model. The resulting soft-decoding algorithm significantly outperforms both the Guruswami-Sudan decoding and the generalized minimum distance (GMD) decoding of Reed-Solomon codes, while maintaining a complexity that is polynomial in the length of the code. Asymptotic analysis for alarge number of interpolation points is presented, leading to a geo- metric characterization of the decoding regions of the proposed algorithm. It is then shown that the asymptotic performance can be approached as closely as desired with a list size that does not depend on the length of the code.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2003.819332