Self-Inverse Interleavers for Turbo Codes

In this work we introduce and study a set of new interleavers based on permutation polynomials and functions with known inverses over a finite field Fq for using in turbo code structures. We use Monomial, Dickson, Möbius and Rédei functions in order to get new interleavers. In addition we employ Skolem sequences in order to find new interleavers with known cycle structure. As a byproduct we give an exact formula for the inverse of every Rédei function. The cycle structure of Rédei functions are also investigated. Finally, self-inverse versions of permutation functions are used to construct interleavers. These interleavers are their own de-interleavers and are useful for turbo coding and turbo decoding. Experiments carried out for selfinverse interleavers constructed using these kind of permutation polynomials and functions show excellent agreement with our theoretical results.