Quadratic permutation polynomials (QPPs) have been widely studied and used asinterleavers in turbo codes. However, less attention has been given to cubicpermutation polynomials (CPPs). This paper proves a theorem which statessufficient and necessary conditions for a cubic permutation polynomial to be anull permutation polynomial. The result is used to reduce the search complexityof CPP interleavers for short lengths (multiples of 8, between 40 and 352), byimproving the distance spectrum over the set of polynomials with the largestspreading factor. The comparison with QPP interleavers is made in terms ofsearch complexity and upper bounds of the bit error rate (BER) and frame errorrate (FER) for AWGN and for independent fading Rayleigh channels. Cubicpermutation polynomials leading to better performance than quadraticpermutation polynomials are found for some lengths.
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