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Based on unique decoding of the polynomial residue code with non-pairwisecoprime moduli, a polynomial with degree less than that of the least commonmultiple (lcm) of all the moduli can be accurately reconstructed when thenumber of residue errors is less than half the minimum distance of the code.However, once the number of residue errors is beyond half the minimum distanceof the code, the unique decoding may fail and lead to a large reconstructionerror. In this paper, assuming that all the residues are allowed to have errorswith small degrees, we consider how to reconstruct the polynomial as accuratelyas possible in the sense that a reconstructed polynomial is obtained with onlythe last $\tau$ number of coefficients being possibly erroneous, when theresidues are affected by errors with degrees upper bounded by $\tau$. In thisregard, we first propose a multi-level robust Chinese remainder theorem (CRT)for polynomials, namely, a trade-off between the dynamic range of the degree ofthe polynomial to be reconstructed and the residue error bound $\tau$ isformulated. Furthermore, a simple closed-form reconstruction algorithm is alsoproposed.

Robust Polynomial Reconstruction via Chinese Remainder Theorem in the Presence of Small Degree Residue Errors