This paper shows a link between the dispersion and the nonlinearity degree of QPP (quadratic permutation polynomial) interleavers. An upper bound for the dispersion of QPP interleavers is derived. This upper bound is computed very simple, only depending on the coefficient of x2 of the polynomial and of the length of interleaver. The comparison with the real dispersion of QPP interleavers given by Takeshita in  leads to insignificant difference. Searching of QPP interleavers based on a metric including upper bound of dispersion and D parameter is equivalent with that based on metric.
Trifina, Lucian; Tarniceriu, Daniela; and Munteanu, Valeriu
"On Dispersion and Nonlinearity Degree of QPP Interleavers,"
Applied Mathematics & Information Sciences: Vol. 06:
3, Article 1.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol06/iss3/1