Permutation Polynomial Interleavers: An Algebraic-Geometric Perspective

@article{Takeshita2007PermutationPI,
  title={Permutation Polynomial Interleavers: An Algebraic-Geometric Perspective},
  author={Oscar Y. Takeshita},
  journal={IEEE Transactions on Information Theory},
  year={2007},
  volume={53},
  pages={2116-2132}
}
  • O. Takeshita
  • Published 12 January 2006
  • Computer Science
  • IEEE Transactions on Information Theory
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are important because they admit analytical designs and simple, practical hardware implementation. The spread factor of an interleaver is a common measure for turbo coding applications. Maximum-spread interleavers are interleavers whose spread factors achieve the upper bound. An infinite sequence of quadratic PPs over integer rings that generate maximum-spread interleavers is… 
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    2006 IEEE International Symposium on Information Theory
  • 2006
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A new interleaver metric that is a function of both the non-linearity metric and the spread factor is proposed and, when tail-biting constituent codes are used, the resulting turbo codes are quasi-cyclic.
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TLDR
The conditions for a QPP interleaving to be equivalent to an ARP interleaver are extended for cubic permutation polynomial (CPP) interleavers and it is shown that the CPPInterleavers are always equivalent to a ARPinterleavers with disorder degree greater than one and smaller than the interlever length.
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A class of deterministic interleavers for turbo codes (TCs) based on permutation polynomials over /spl Zopf//sub N/ is introduced, which can be algebraically designed to fit a given component code.
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    IEEE Transactions on Information Theory
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TLDR
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A general case is found that outperforms the random interleavers for every size of the finite field tested and raises the question of which are the parameters needed to determine how good an interleaver is.
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TLDR
A new interleaver design for turbo codes with short block length based on the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder corresponding to its parity bits is described.
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