Problems of Information Transmission

, Volume 50, Issue 4, pp 303–312 | Cite as

Successive cancellation decoding of Reed-Solomon codes

Coding Theory

Abstract

A novel soft-decision decoding algorithm for Reed-Solomon codes over GF(2m) is proposed, which is based on representing them as polar codes with dynamic frozen symbols and applying the successive cancellation method. A further performance improvement is obtained by exploiting multiple permutations of codewords which are taken from the automorphism group of Reed-Muller codes. It is also shown that the proposed algorithm can be simplified in the case of decoding a binary image of the Reed-Solomon code.

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References

  1. 1.
    Koetter, R. and Vardy, A., Algebraic Soft-Decision Decoding of Reed-Solomon Codes, IEEE Trans. Inform. Theory, 2003, vol. 49, no. 11, pp. 2809–2825.CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    El-Khamy, M. and McEliece, R., Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes, IEEE J. Select. Areas Commun., 2006, vol. 24, no. 3, pp. 481–490.CrossRefGoogle Scholar
  3. 3.
    Vardy, A. and Beery, Y., Bit-Level Soft-Decision Decoding of Reed-Solomon Codes, IEEE Trans. Commun., 1991, vol. 39, no. 3, pp. 440–444.CrossRefMATHGoogle Scholar
  4. 4.
    Bellorado, J., Kavčić, A., Marrow, M., and Ping, L., Low-Complexity Soft-Decoding Algorithms for Reed-Solomon Codes—Part II: Soft-Input Soft-Output Iterative Decoding, IEEE Trans. Inform. Theory, 2010, vol. 56, no. 3, pp. 960–967.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Arikan, E., Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels, IEEE Trans. Inform. Theory, 2009, vol. 55, no. 7, pp. 3051–3073.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Tal, I. and Vardy, A., List Decoding of Polar Codes, in Proc. 2011 IEEE Int. Sympos. on Information Theory (ISIT’2011), St. Petersburg, Russia, July 31–August 5, 2011, pp. 1–5.Google Scholar
  7. 7.
    Chen, K., Niu, K., and Lin, J., Improved Successive Cancellation Decoding of Polar Codes, IEEE Trans. Commun., 2013, vol. 61, no. 8, pp. 3100–3107.CrossRefGoogle Scholar
  8. 8.
    Trifonov, P. and Miloslavskaya, V., Polar Codes with Dynamic Frozen Symbols and Their Decoding by Directed Search, in Proc. 2013 IEEE Information Theory Workshop (ITW’2013), Sevilla, Spain, Sept. 9–13, 2013, pp. 1–5.Google Scholar
  9. 9.
    Kolesnik, V.D. and Mironchikov, E.T., Cyclic Reed-Muller Codes and Their Decoding, Probl. Peredachi Inf., 1968, vol. 4, no. 4, pp. 20–25 [Probl. Inf. Trans. (Engl. Transl.), 1968, vol. 4, no. 4, pp. 15–19].MATHMathSciNetGoogle Scholar
  10. 10.
    Kasami, T., Lin, S., and Peterson, W., New Generalizations of the Reed-Muller Codes. I: Primitive Codes, IEEE Trans. Inform. Theory, 1968, vol. 14, no. 2, pp. 189–199.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Declercq, D. and Fossorier, M.P., Decoding Algorithms for Nonbinary LDPC Codes over GF(q), IEEE Trans. Commun., 2007, vol. 55, no. 4, pp. 633–643.CrossRefGoogle Scholar
  12. 12.
    Tal, I. and Vardy, A., How to Construct Polar Codes, IEEE Trans. Inform. Theory, 2013, vol. 59, no. 10, pp. 6562–6582.CrossRefMathSciNetGoogle Scholar
  13. 13.
    Chung, S.-Y., Richardson, T.J., and Urbanke, R.L., Analysis of Sum-Product Decoding of Low-Density Parity-Check Codes Using a Gaussian Approximation, IEEE Trans. Inform. Theory, 2001, vol. 47, no. 2, pp. 657–670.CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Trifonov, P., Efficient Design and Decoding of Polar Codes, IEEE Trans. Commun., 2012, vol. 60, no. 11, pp. 3221–3227.CrossRefGoogle Scholar
  15. 15.
    Abbe, E. and Telatar, E., Polar Codes for the m-User Multiple Access Channel, IEEE Trans. Inform. Theory, 2012, vol. 58, no. 8, pp. 5437–5448.CrossRefMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2014

Authors and Affiliations

  1. 1.St. Petersburg State Polytechnical UniversitySt. PetersburgRussia

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