Permutation Polynomial Interleavers: An Algebraic-Geometric Perspective
  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 permutation polynomials over integer rings that generate   maximum-spread interleavers is presented. New properties of   permutation polynomial interleavers are investigated from an   algebraic-geometric perspective resulting in a new non-linearity metric   for interleavers. A new interleaver metric that is a function of both   the non-linearity metric and the spread factor is proposed.   It is numerically demonstrated that the spread factor has a   diminishing importance with the block length. A table of good   interleavers for a variety of interleaver lengths according to the   new metric is listed. Extensive computer simulation results with impressive   frame error rates confirm the efficacy of the new metric. Further,   when tail-biting constituent codes are used, the resulting turbo   codes are quasi-cyclic. 
Oscar Y. Takeshita