On the equivalence of interleavers for turbo codes using quadratic permutation polynomials over integer rings
On the equivalence of interleavers for turbo codes using quadratic permutation polynomials over integer rings
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整数环上二次置换多项式的Turbo码交织器的等价性
DOI：
10.1109/lcomm.2010.03.091695
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
V. Tarokh
中科院分区：
文献类型：
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作者：
H. Zhao;P. Fan;V. Tarokh
整数环上的二次置换多项式（quadratic permutation polynomials，QPP）Turbo码的伪码等价性可以由整数环上的二次零多项式（quadratic null polynomials，QNP）精确地确定。对于产生QNP或高阶零多项式，已有文献给出了一些理论结果。在这封信中，它证明了先前获得的QNP的系数不仅是足够的，而且是必要的，以产生任何QNP。基于生成QNP和QPP的充分必要条件，给出了排除其等价性的QPP的枚举。所得结果有助于研究QPP双稳态振荡器的代数结构，避免QPP双稳态振荡器设计中的等价问题。
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.