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A Robust Generalized Chinese Remainder Theorem for Two Integers

机译:两个整数的鲁棒广义汉语剩余定理

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A generalized Chinese remainder theorem (CRT) for multiple integers from residue sets has been studied recently, where the correspondence between the remainders and the integers in each residue set modulo several moduli is not known. A robust CRT has also been proposed lately to robustly reconstruct a single integer from its erroneous remainders. In this paper, we consider the reconstruction problem of two integers from their residue sets, where the remainders not only are out of order but also may have errors. We prove that two integers can be robustly reconstructed if their remainder errors are less than M/8 , where M is the greatest common divisor of all the moduli. We also propose an efficient reconstruction algorithm. Finally, we present some simulations to verify the efficiency of the proposed algorithm. This paper is motivated from and has applications in the determination of multiple frequencies from multiple undersampled waveforms.
机译:最近已经研究了残差集中多个整数的广义中文余量定理(CRT),其中余数与每个残差集中的整数模之间的对应关系未知。最近还提出了一种健壮的CRT,以从其错误的余数中稳健地重建单个整数。在本文中,我们考虑了两个整数从其残差集开始的重构问题,其中余数不仅乱序,而且可能存在误差。我们证明,如果两个整数的余数误差小于M / 8,则可以稳健地重建两个整数,其中M是所有模数的最大公约数。我们还提出了一种有效的重建算法。最后,我们提出了一些仿真来验证所提出算法的效率。本文的灵感来自于并应用于从多个欠采样波形中确定多个频率。

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