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A simple method to determine the number of true different quadratic and cubic permutation polynomial based interleavers for turbo codes

Author

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  • Lucian Trifina

    (“Gheorghe Asachi” Technical University of Iasi)

  • Daniela Tarniceriu

    (“Gheorghe Asachi” Technical University of Iasi)

Abstract

Interleavers are important blocks of the turbo codes, their types and dimensions having a significant influence on the performances of the mentioned codes. If appropriately chosen, the permutation polynomial (PP) based interleavers lead to remarkable performances of these codes. The most used interleavers from this category are quadratic permutation polynomial (QPP) and cubic permutation polynomial (CPP) based ones. In this paper, we determine the number of different QPPs and CPPs that cannot be reduced to linear permutation polynomials (LPPs) or to QPPs or LPPs, respectively. They are named true QPPs and true CPPs, respectively. Our analysis is based on the necessary and sufficient conditions for the coefficients of second and third degree polynomials to be QPPs and CPPs, respectively, and on the Chinese remainder theorem. This is of particular interest when we need to find QPP or CPP based interleavers for turbo codes.

Suggested Citation

  • Lucian Trifina & Daniela Tarniceriu, 2017. "A simple method to determine the number of true different quadratic and cubic permutation polynomial based interleavers for turbo codes," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(1), pages 147-171, January.
    • Handle: RePEc:spr:telsys:v:64:y:2017:i:1:d:10.1007_s11235-016-0166-2
    DOI: 10.1007/s11235-016-0166-2
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    Cited by:

    1. Lucian Trifina & Daniela Tarniceriu, 2018. "Determining the number of true different permutation polynomials of degrees up to five by Weng and Dong algorithm," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 67(2), pages 211-215, February.
    2. Lucian Trifina & Daniela Tarniceriu, 2019. "When Is the Number of True Different Permutation Polynomials Equal to 0?," Mathematics, MDPI, vol. 7(11), pages 1-14, October.

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