The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Interleavers for turbo codes using permutation polynomials over integer rings
IEEE Transactions on Information Theory
On maximum contention-free interleavers and permutation polynomials over integer rings
IEEE Transactions on Information Theory
Permutation Polynomial Interleavers: An Algebraic-Geometric Perspective
IEEE Transactions on Information Theory
Analysis of Cubic Permutation Polynomials for Turbo Codes
Wireless Personal Communications: An International Journal
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It is known that the equivalence of interleavers for turbo codes using quadratic permutation polynomials (QPPs) over integer rings can be exactly determined by the so-called quadratic null polynomials (QNPs) over integer rings. For generating QNPs or higher order null polynomials (NPs), some theoretical results have been obtained in previous literature. In this letter, it is proved that the coefficients of previously obtained QNPs are not only sufficient but also necessary for generating any QNPs. Based on the necessary and sufficient conditions for generating QNPs and QPPs, the enumeration of QPPs excluding their equivalence is presented. The obtained results are helpful to investigate the algebraic structure of QPP interleavers as well as to avoid the equivalence in the design of QPP interleavers.