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In this paper, we consider the searching for good turbo code interleavers. Especially, we focus on the permutation polynomial interleavers. Three key properties (i.e. spread factor, dispersion, and edge effects) of turbo code interleavers are investigated, and two new metrics alpha and beta are proposed for turbo code interleavers. Good permutation polynomial interleavers for turbo codes of various lengths are found by these metrics. Computer simulations show that interleavers with small α or β will lead to the poor performance of turbo codes. Furthermore, turbo codes with good permutation polynomial interleavers found by these metrics always outperform the well-known s- random interleavers. Moreover, turbo codes with good cubic permutation polynomial interleavers found by these metrics are superior to the quadratic permutation polynomial interleavers adopted as turbo code interleavers in the 3rd generation partnership project long term evolution and its advance.