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On Integer Programming Problems Related to Soft-Decision Iterative Decoding Algorithms

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1719))

Abstract

We consider sufficient conditions for ruling out some useless iteration steps or all subsequent iteration steps without degradation of error performance in soft-decision iterative decoding algorithms for binary block codes used over the AWGN channel using BPSK signaling. Then the derivation of such sufficient conditions and the selection of centers of search regions in iterative steps are formulated uniformly as a type of integer programming problems. Several techniques for reducing such an integer programming problem to a set of subprograms with smaller computational complexities are presented.

The paper is partially based on reference [14].

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References

  1. D. J. Taipale and M. B. Pursley, “An Improvement to Generalized Minimum-Distance Decoding,” IEEE Trans. Inform. Theory, vol. 37, pp. 167–172, Jan. 1991.

    Article  MATH  MathSciNet  Google Scholar 

  2. T. Kaneko, T. Nishijima, H. Inazumi, and S. Hirasawa, “An Efficient Maximum-Likelihood-Decoding Algorithm for Linear Block Codes with Algebraic Decoder,” IEEE Trans. Inform. Theory, vol. 40, pp. 320–327, Mar. 1994.

    Article  MATH  Google Scholar 

  3. T. Kasami, T. Takata, T. Koumoto, T. Fujiwara, H. Yamamoto and S. Lin, “The Least Stringent Sufficient Condition on Optimality of Suboptimal Decoded Codewords,” Technical Report of IEICE, Japan, IT94-82, Jan. 1995.

    Google Scholar 

  4. T. Kasami, T. Koumoto, T. Takata and S. Lin, “The Effectiveness of the Least Stringent Sufficient Condition on the Optimality of Decoded Codewords,” Proc. of the 3rd Int. Symp. on Commu. Theory & Appl., pp. 324–333, Ambleside, UK, July 1995.

    Google Scholar 

  5. Y. Tang, T. Kasami and T. Fujiwara, “An Optimality Testing Algorithm for a Decoded Codeword of Binary Block Codes and Its Computational Complexity,” to appear in Proc. of the 13th Int. Symp. AAECC, Honolulu, HI, USA, Nov. 1999.

    Google Scholar 

  6. T. Koumoto, T. Takata, T. Kasami and S. Lin, “A Low-Weight Trellis Based Iterative Soft-Decision Decoding Algorithm for Binary Linear Block Codes,” IEEE Trans. Inform. Theory, vol. 45, pp. 731–741, Mar. 1999.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. P. C. Fossorier and S. Lin, “Soft-Decision Decoding of Linear Block Codes Based on Ordered Statistics, ” IEEE Trans. Inform. Theory, vol. 41. pp. 1379–1396, Sept. 1995.

    Article  MATH  Google Scholar 

  8. D. Gazelle and J. Snyders, “Reliability-Based Code-Search Algorithms for Maximum-Likelihood Decoding of Block Codes,” IEEE Trans. Inform. Theory, vol. 43. pp. 239–249, Jan. 1995.

    Article  MathSciNet  Google Scholar 

  9. C. X. Chen, “Sufficient Conditions for the Optimality of a Codeword in Soft-Decision Decoding of Binary Linear Block Codes,” Master Thesis, Univ. of Hawaii, Oct. 1998.

    Google Scholar 

  10. M. P. C. Fossorier, T. Koumoto, T. Takata, T. Kasami and S. Lin, “The Least Stringent Sufficient Condition on the Optimality of a Suboptimally Decoded Codeword Using the Most Reliable Basis,” Proc. of ISIT, pp. 430, Ulm, Germany, June 1997.

    Google Scholar 

  11. D. Chase, “A New Class for Decoding Block Codes with Channel Measurement Information,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 170–182, Jan. 1972.

    Article  MathSciNet  Google Scholar 

  12. T. Kaneko, T. Nishijima and S. Hirasawa, “An Improvement of Soft-Decision Maximum-Likelihood Decoding Algorithm Using Hard-Decision Bounded-Distance Decoding,” IEEE Trans. Inform. Theory, vol. 43, pp. 1314–1319, July 1997.

    Article  MATH  MathSciNet  Google Scholar 

  13. T. Koumoto, T. Kasami and S. Lin, “A Sufficient Condition for Ruling Out Some Useless Test Error Patterns in Iterative Decoding Algorithms,” IEICE Trans. on Fundamentals, vol. E81-A, No. 2, pp. 321–326, Feb. 1998.

    Google Scholar 

  14. T. Kasami, Y. Tang, T. Koumoto and T. Fujiwara, “Sufficient Conditions for Ruling-Out Useless Iterative Steps in a Class of Iterative Decoding Algorithms,” to appear in IEICE Trans. Fundamentals, vol. E82-A, Oct. 1999.

    Google Scholar 

  15. T. Koumoto and T. Kasami, “An Iterative Decoding Algorithm Based on Information of Decoding Failure,” Proc. of the 20th SITA, pp. 325–328, Matsuyama, Japan, Dec. 1997.

    Google Scholar 

  16. G. D. Forney, Jr., “Generalized Minimum Distance Decoding,” IEEE Trans. Inform. Theory, vol. IT-2, pp. 125–181, Apr. 1966.

    Article  MathSciNet  Google Scholar 

  17. T. Koumoto and T. Kasami, “Analysis and Improvement on GMD-like Decoding Algorithms,” Proc. of ISITA, pp. 419–422, Mexico City, Mexico, Oct. 1998.

    Google Scholar 

  18. N. Tendolkar and C. P. Hartmann, “Generalization of Chase Algorithms for Soft Decision Decoding of Binary Linear Codes,” IEEE Trans. Inform. Theory, vol. IT-30, pp. 714–721, Sept. 1984.

    Article  MathSciNet  Google Scholar 

  19. Y. H. Han, C. R. P. Hartman, and C. C. Chen, “Efficient Priority-First Search Maximum-Likelihood Soft-Decision Decoding of Linear Block Codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 1514–1523, Sept. 1993.

    Article  MATH  MathSciNet  Google Scholar 

  20. T. Kasami and T. Koumoto, “Computational Complexity for Computing Sufficient Conditions on the Optimality of a Decoded Codeword,” Technical Report of NAIST, Japan, NAIST-IS-TR98008, July 1998.

    Google Scholar 

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Kasami, T. (1999). On Integer Programming Problems Related to Soft-Decision Iterative Decoding Algorithms. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_5

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  • DOI: https://doi.org/10.1007/3-540-46796-3_5

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