A1 Refereed original research article in a scientific journal
On the Degree of the Inverse of Quadratic Permutation Polynomial Interleavers
Authors: Lahtonen J, Ryu J, Suvitie E
Editors: Frank R Kschischang
Publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication year: 2012
Journal: IEEE Transactions on Information Theory
Journal name in source: IEEE TRANSACTIONS ON INFORMATION THEORY
Journal acronym: IEEE T INFORM THEORY
Number in series: 6
Volume: 58
Issue: 6
First page : 3925
Last page: 3932
Number of pages: 8
ISSN: 0018-9448
DOI: https://doi.org/10.1109/TIT.2012.2190492(external)
Abstract
An integral component of a turbo code is a carefully designed interleaver. Interleavers based on quadratic permutation polynomials (modulo N) were introduced by Sun and Takeshita. They have several good properties and have been selected to be used in a cellular phone system. Ryu and Takeshita later initiated the study of the related deinterleavers. Here we extend this latter work and introduce a very efficient method for computing the (degree of the) lowest degree polynomial giving the deinterleaver. Our approach is based on combining two techniques. The Chinese remainder theorem allows us to study one prime power factor of N at a time. Our other technique is to first present the inverse function as a power series with integer coefficients. Modulo N that series is actually a polynomial. The polynomials yielding the same function form a coset of the ideal of identically vanishing polynomials. With the aid of a known Grobner basis of that ideal we then finally identify a minimal degree polynomial within the given coset.
An integral component of a turbo code is a carefully designed interleaver. Interleavers based on quadratic permutation polynomials (modulo N) were introduced by Sun and Takeshita. They have several good properties and have been selected to be used in a cellular phone system. Ryu and Takeshita later initiated the study of the related deinterleavers. Here we extend this latter work and introduce a very efficient method for computing the (degree of the) lowest degree polynomial giving the deinterleaver. Our approach is based on combining two techniques. The Chinese remainder theorem allows us to study one prime power factor of N at a time. Our other technique is to first present the inverse function as a power series with integer coefficients. Modulo N that series is actually a polynomial. The polynomials yielding the same function form a coset of the ideal of identically vanishing polynomials. With the aid of a known Grobner basis of that ideal we then finally identify a minimal degree polynomial within the given coset.
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