Algebraic soft-decision decoding of {R}eed-{S}olomon codes

  • Koetter R
  • Vardy A
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Abstract

A polynomial-time soft-decision decoding algorithm for Reed-Solomon<br />codes is developed. This list-decoding algorithm is algebraic in<br />nature and builds upon the interpolation procedure proposed by Guruswami<br />and Sudan(see ibid., vol.45, p.1757-67, Sept. 1999) for hard-decision<br />decoding. Algebraic soft-decision decoding is achieved by means of<br />converting the probabilistic reliability information into a set of<br />interpolation points, along with their multiplicities. The proposed<br />conversion procedure is shown to be asymptotically optimal for a<br />certain probabilistic model. The resulting soft-decoding algorithm<br />significantly outperforms both the Guruswami-Sudan decoding and the<br />generalized minimum distance (GMD) decoding of Reed-Solomon codes,<br />while maintaining a complexity that is polynomial in the length of<br />the code. Asymptotic analysis for alarge number of interpolation<br />points is presented, leading to a geo- metric characterization of<br />the decoding regions of the proposed algorithm. It is then shown<br />that the asymptotic performance can be approached as closely as desired<br />with a list size that does not depend on the length of the code.

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Koetter, R., & Vardy, A. (2003). Algebraic soft-decision decoding of {R}eed-{S}olomon codes. Information Theory, IEEE Transactions On, 49(11), 2809–2825. https://doi.org/10.1109/TIT.2003.819332

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