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Permutation polynomial based interleavers for turbo codes over integer rings: theory and applications

Ryu, Jong Hoon

Abstract Details

2007, Doctor of Philosophy, Ohio State University, Electrical Engineering.
Turbo codes are a class of high performance error correcting codes (ECC) and an interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions of interleavers are of particular interest because they admit analytical designs and simple, practical hardware implementation. Sun and Takeshita have shown that the class of quadratic permutation polynomials over integer rings provides excellent performance for turbo codes. Recently, quadratic permutation polynomial (QPP) based interleavers have been proposed into 3rd Generation Partnership Project Long Term Evolution (3GPP LTE) draft for their excellent error performance, simple implementation and algebraic properties which admit parallel processing and regularity. In some applications, such as deep space communications, a simple implementation of deinterleaver is also of importance. In this dissertation, a necessary and sufficient condition is proven for the existence of a quadratic inverse polynomial (deinterleaver) for a quadratic permutation polynomial over an integer ring. Further, a simple construction is given for the quadratic inverse. We also consider the inverses of QPPs which do not admit quadratic inverses. It is shown that most 3GPP LTE interleavers admit quadratic inverses. However, it is shown that even when the 3GPP LTE interleavers do not admit quadratic inverses, the degrees of the inverse polynomials are less than or equal to 4, which allows a simple implementation of the deinterleavers. An explanation is argued for the observation. The minimum distance and its multiplicity (or the first a few terms of the weight distribution) of error correcting codes are used to estimate the error performance at high signal-to-noise ratio (SNR). We consider efficient algorithms that find an upper bound (UB) on the minimum distance of turbo codes designed with QPP interleavers. Permutation polynomials have been extensively studied, but simple coefficient tests for permutation polynomials over integer rings are only known for limited cases. A simple necessary and sufficient coefficient test is proven for cubic permutation polynomials over integer rings. A possible application is in the design of interleavers for turbo codes.
Hesham El Gamal (Advisor)

Recommended Citations

Citations

  • Ryu, J. H. (2007). Permutation polynomial based interleavers for turbo codes over integer rings: theory and applications [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1181139404

    APA Style (7th edition)

  • Ryu, Jong Hoon. Permutation polynomial based interleavers for turbo codes over integer rings: theory and applications. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1181139404.

    MLA Style (8th edition)

  • Ryu, Jong Hoon. "Permutation polynomial based interleavers for turbo codes over integer rings: theory and applications." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1181139404

    Chicago Manual of Style (17th edition)