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首页> 外文期刊>IEEE Transactions on Information Theory >On quadratic inverses for quadratic permutation polynomials over integer rings
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On quadratic inverses for quadratic permutation polynomials over integer rings

机译：关于整数环上的二次置换多项式的二次逆

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摘要

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Sun and Takeshita have recently shown that the class of quadratic permutation polynomials over integer rings provides excellent performance for turbo codes. In this correspondence, a necessary and sufficient condition is proven for the existence of a quadratic inverse polynomial for a quadratic permutation polynomial over an integer ring. Further, a simple construction is given for the quadratic inverse. All but one of the quadratic interleavers proposed earlier by Sun and Takeshita are found to admit a quadratic inverse, although none were explicitly designed to do so. An explanation is argued for the observation that restriction to a quadratic inverse polynomial does not narrow the pool of good quadratic interleavers for turbo codes.
机译：交织器是用于turbo码的信道编码性能的关键组件。代数构造特别令人感兴趣，因为它们接受分析设计和简单实用的硬件实现。 Sun和Takeshita最近表明，整数环上的二次置换多项式的类别为Turbo码提供了出色的性能。在这种对应关系中，证明了对于整数环上的二次置换多项式的二次逆多项式的存在的必要和充分条件。此外，给出了二次逆的简单构造。发现Sun和Takeshita早先提出的二次交织器中的所有一个都可以接受二次逆，尽管没有明确设计这样做。有人为这种观察提出了一种解释，即对二次逆多项式的限制不会使turbo码的良好二次交织池变窄。

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