Determining the number of different cubic permutation polynomial based interleavers for lengths in the LTE standard

Abstract

Interleavers are important blocks from turbo codes structure, their type and dimensions having a significant influence on the performances of the mentioned codes. The permutation polynomial (PP) based interleavers lead to remarkable performances of these codes, if they are appropriately chosen. 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 third degree polynomial to be CPP, in this paper we determine the number of true different CPPs that cannot be reduced to QPPs or linear permutation polynomials (LPPs), for the lengths from the LTE standard (multiple of 8). This is of particular interest when we need to find CPP interleavers for turbo codes.