A1 Refereed original research article in a scientific journal

On the Degree of the Inverse of Quadratic Permutation Polynomial Interleavers




AuthorsLahtonen J, Ryu J, Suvitie E

EditorsFrank R Kschischang

PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

Publication year2012

JournalIEEE Transactions on Information Theory

Journal name in sourceIEEE TRANSACTIONS ON INFORMATION THEORY

Journal acronymIEEE T INFORM THEORY

Number in series6

Volume58

Issue6

First page 3925

Last page3932

Number of pages8

ISSN0018-9448

DOIhttps://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.



Last updated on 2024-26-11 at 15:32