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Quadratic permutation polynomial interleavers over integer rings haverecently received attention in practical turbo coding systems from deep spaceapplications to mobile communications. In this correspondence, a necessary andsufficient condition that determines the least degree inverse of a quadraticpermutation polynomial is proven. Moreover, an algorithm is provided toexplicitly compute the inverse polynomials.

On Inverses for Quadratic Permutation Polynomials over Integer Rings