# Determining the Number of Permutation Polynomial-Based Interleavers in Terms of Their Length

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## Abstract

In this chapter we give and prove formulas for determining the number of true different PP interleavers of a certain degree according to their length. To determine when two PPs with different coefficients lead to the same permutation, the equivalence conditions between PPs are required and they are presented in Sect. 4.2. The method used to determine the number of true different PPs is based on the Chinese Remainder Theorem and it is presented in Sect. 4.3. Formulas for determining the number of all true different QPPs and CPPs are obtained in Sects. 4.4 and 4.5, respectively. Formulas for determining the number of true different CPPs, 4-PPs and 5-PPs, under Zhao and Fan sufficient conditions (Zhao and Fan 2007), are obtained in Sects. 4.6.1–4.6.3, respectively. In Sect. 4.7, the algorithm from Weng and Dong (2008) is used to obtain the number of all true different PPs of degrees up to five. Determining the lengths of PP-based interleavers for which the number of all true different PPs of degree up to five is equal to 0 are obtained in Sect. 4.8. Finally, determining the lengths of PP-based interleavers for which the number of true different PPs of any degree under Zhao and Fan sufficient conditions is equal to 0 are obtained in Sect. 4.9.

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