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This paper investigates polynomial remainder codes with non-pairwise coprimemoduli. We first consider a robust reconstruction problem for polynomials fromerroneous residues when the degrees of all residue errors are assumed small,namely robust Chinese Remainder Theorem (CRT) for polynomials. It basicallysays that a polynomial can be reconstructed from erroneous residues such thatthe degree of the reconstruction error is upper bounded by $\tau$ whenever thedegrees of all residue errors are upper bounded by $\tau$, where a sufficientcondition for $\tau$ and a reconstruction algorithm are obtained. By releasingthe constraint that all residue errors have small degrees, another robustreconstruction is then presented when there are multiple unrestricted errorsand an arbitrary number of errors with small degrees in the residues. By makingfull use of redundancy in moduli, we obtain a stronger residue error correctioncapability in the sense that apart from the number of errors that can becorrected in the previous existing result, some errors with small degrees canbe also corrected in the residues. With this newly obtained result,improvements in uncorrected error probability and burst error correctioncapability in a data transmission are illustrated.

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