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首页> 外文期刊>Communications, IEEE Transactions on >Error Correction in Polynomial Remainder Codes With Non-Pairwise Coprime Moduli and Robust Chinese Remainder Theorem for Polynomials
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Error Correction in Polynomial Remainder Codes With Non-Pairwise Coprime Moduli and Robust Chinese Remainder Theorem for Polynomials

机译：非对偶余数模和多项式的稳健中国剩余定理的多项式余数代码中的纠错

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摘要

This paper investigates polynomial remainder codes with non-pairwise coprime moduli. We first consider a robust reconstruction problem for polynomials from erroneous residues when the degrees of all residue errors are assumed small, namely, the robust Chinese Remainder Theorem (CRT) for polynomials. It basically says that a polynomial can be reconstructed from its erroneous residues such that the degree of the reconstruction error is upper bounded by whenever the degrees of all residue errors are upper bounded by , where a sufficient condition for and a reconstruction algorithm are obtained. By relaxing the constraint that all residue errors have small degrees, another robust reconstruction is then presented when there are multiple unrestricted errors and an arbitrary number of errors with small degrees in the residues. We finally obtain a stronger residue error correction capability in the sense that apart from the number of errors that can be corrected in the previous existing result, some errors with small degrees can be also corrected in the residues. With this newly obtained result, improvements in uncorrected error probability and burst error correction capability in data transmission are illustrated.
机译：本文研究了具有非成对余数模数的多项式余数代码。当所有残差的误差都被假定为较小时，我们首先考虑从错误残差得到的多项式的鲁棒重构问题，即多项式的鲁棒中国剩余定理（CRT）。基本上说，可以从错误的残差中重构多项式，使得只要所有残差错误的度都以上限为上限，则重构误差的度为上限，从而获得了充足的条件和重构算法。通过放宽所有残差均具有小度的约束，当残差中存在多个无限制的误差以及任意数量的小度误差时，可以提出另一种鲁棒的重构方法。从某种意义上说，我们最终将获得更强大的残差纠错能力，除了可以在以前的现有结果中纠正的错误数量之外，还可以在残差中纠正一些小程度的错误。利用该新获得的结果，示出了数据传输中未校正错误概率和突发错误校正能力的改进。

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