The limitation of permutation polynomial interleavers for turbo codes and a scheme for dithering permutation polynomials

In this letter, partial upper bounds on minimum distance for turbo codes with permutation polynomial (PP) based interleavers over integer rings are derived using the fact that PPs are equivalent to a family of linear permutation polynomials (LPPs). It is shown that upper bounds on minimum distance of turbo codes using higher order PP based interleavers are bounded by a function of the number of equivalent LPPs for PPs. Besides, it is shown that when the constant terms of LPPs are dithered, the resulting dithered LPP interleavers perform better than the quadratic permutation polynomial (QPP) based interleavers used in long term evolution (LTE) standard or than other good QPP or cubic permutation polynomial (CPP) based interleavers given in the literature.