Nonlinearity Degree for CPP, 4-PP, and 5-PP Interleavers for Turbo Codes

Permutation polynomial (PP) interleavers for turbo codes can be efficiently designed if properly simple metrics are used. One of these metrics is the nonlinearity degree. For quadratic PP interleavers the nonlinearity degree can be computed with a simple formula depending on the interleaver length and on the coefficient of the second degree term. In this paper we propose three algorithms to efficiently compute the nonlinearity degree of the PP interleavers of degrees 3, 4, and 5. Lower bounds on the nonlinearity degree of the PP interleavers of the three degrees are achieved. The nonlinearity degree computing times with the proposed algorithms are much smaller compared to those using the direct method. The proposed algorithms are usefull in founding good higher degree PP interleavers.