Study on Interleaver Design for Turbo Codes Using Permutation Polynomials Over Integer Rings

Some properties of permutation polynomials over integer rings, mainly the 3ⁿ case, are studied and some conclusions are drawn. A decision theorem for 3ⁿ case and a proof of the MCF property for size pⁿ permutation polynomial-based interleaver are presented. A design criterion for interleavers based on third degree permutation polynomial is proposed to select the coefficients of the polynomials. Simulation results show that these interleavers can achieve near performance of S-random interleavers, and for short frame size, they outperform S-random interleavers.