Error Correction in Polynomial Remainder Codes With Non-Pairwise Coprime Moduli and Robust Chinese Remainder Theorem for Polynomials


This paper investigates polynomial remainder codes with non-pairwise coprime moduli. We first take into account a strong reconstruction downside for polynomials from erroneous residues when the degrees of all residue errors are assumed small, namely, the strong Chinese Remainder Theorem (CRT) for polynomials. It primarily 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 range of errors with small degrees in the residues. We finally get a stronger residue error correction capability in the way that apart from the number of errors that can be corrected within the previous existing result, some errors with tiny degrees will be also corrected within the residues. With this newly obtained result, improvements in uncorrected error chance and burst error correction capability in information transmission are illustrated.

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