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

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 polynomials (QPPs) and cubic permutation polynomials (CPPs). Based on the necessary and sufficient conditions for the coefficients of the second and third degree polynomials to be QPP and CPP, respectively and on the Chinese remainder theorem, in this paper we determine the number of true different QPPs that cannot be reduced to linear permutation polynomials (LPPs), and the number of true different CPPs that cannot be reduced to QPPs or LPPs. This is of particular interest when we need to find QPP or CPP based interleavers for turbo codes.