Up to five degree permutation polynomial interleavers for short length LTE turbo codes with optimum minimum distance

The permutation polynomial (PP) interleavers are ones of the most attractive and popular deterministic interleavers for turbo codes. Quadratic permutation polynomial (QPP) interleavers have been extensively studied since 2005. QPPs of short lengths with optimum minimum distances were given in 2006 by Rosnes and Takeshita. In this paper, we give PPs of degree 3, 4 and 5 with optimum minimum distances and lowest corresponding codeword multiplicities for turbo codes with recursive convolutional component codes from LTE standard and dual trellis termination. Then, we compare these PP interleavers in terms of truncated upper bounds (TUB) of frame error rate (FER) at high SNR for AWGN channel. We have obtained many PPs of degree 3, 4 or 5 with the smallest TUB(FER). A tradeoff between the error rate performance and implementation complexity is highlighted by means of the minimum number of LPPs from the Parallel Linear PP (PLPP) representation of PPs, so that the coefficients of linear terms of the component LPPs of PLPP are equal to one another.