Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

A COMPLEXITY-REDUCED INTERPOLATION ALGORITHM FOR SOFT-DECISION DECODING OF REED-SOLOMON CODES

  • Lee, Kwankyu (Department of Mathematics, Chosun University)
  • Received : 2013.04.26
  • Accepted : 2013.07.08
  • Published : 2013.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Soon after Lee and O'Sullivan proposed a new interpolation algorithm for algebraic soft-decision decoding of Reed-Solomon codes, there have been some attempts to apply a coordinate transformation technique to the new algorithm, with a remarkable complexity reducing effect. In this paper, a conceptually simple way of applying the transformation technique to the interpolation algorithm is proposed.

Keywords

References

  1. Venkatesan Guruswami and Mahdu Sudan, Improved decoding of Reed-Solomon and algebraic-geometry codes, IEEE Trans. Inf. Theory 45 (1999), no. 6, 1757-1767. https://doi.org/10.1109/18.782097
  2. Sunghyu Han, Notes on MDS self-dual codes, J. Appl. Math. Inform. 30 (2012), no. 5-6, 821-827. https://doi.org/10.14317/JAMI.2012.30.5_6.821
  3. Sunghyu Han and Jon-Lark Kim, Computational results of duadic double circulant codes, J. Appl. Math. Comput. 40 (2012), no. 1-2, 33-43. https://doi.org/10.1007/s12190-012-0543-2
  4. R. Koetter and A. Vardy, A complexity reducing transformation in algebraic list decoding of Reed-Solomon codes, Proc. IEEE Symp. Information Theory Workshop (Paris, France), April 2003, pp. 10-13.
  5. Ralf Koetter, On algebraic decoding of algebraic-geometric and cyclic codes, Ph.D. Thesis, University of Linkoping, Sweden, 1996.
  6. Ralf Koetter and Alexander Vardy, Algebraic soft-decision decoding of Reed-Solomon codes, IEEE Trans. Inf. Theory 49 (2003), no. 11, 2809-2825. https://doi.org/10.1109/TIT.2003.819332
  7. Kwankyu Lee and M. E. O'Sullivan, List decoding of Reed-Solomon codes from a Grobner basis perspective, J. Symbolic Comput. 43 (2008), no. 9, 645-658. https://doi.org/10.1016/j.jsc.2008.01.002
  8. Kwankyu Lee and M. E. O'Sullivan, List decoding of Hermitian codes using Grobner bases, Journal of Symbolic Computation (2009), no. 44, 1662-1675.
  9. Kwankyu Lee and Michael E. O'Sullivan, An interpolation algorithm using Grobner bases for soft-decision decoding of Reed-Solomon codes, Proc. IEEE Symp. Information Theory (Seattle, WA.), July 2006, pp. 2032-2036.
  10. Jun Ma and Alexander Vardy, A complexity reducing transformation for the Lee- O'Sullivan interpolation algorithm, Personal communication, February 2007.
  11. Madhu Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound, J. Complexity 13 (1997), no. 1, 180-193. https://doi.org/10.1006/jcom.1997.0439
  12. Xinmiao Zhang and Jiangli Zhu, Low-complexity interpolation architecture for soft- decision Reed-Solomon decoding, Personal communication, January 2007.