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

Abstract

Based on unique decoding of the polynomial residue code with non-pairwise coprime moduli, a polynomial with degree less than that of the least common multiple (lcm) of all the moduli can be accurately reconstructed when the number 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 distance of the code, the unique decoding may fail and lead to a large reconstruction error. In this paper, assuming that all the residues are allowed to have errors with small degrees, we consider how to reconstruct the polynomial as accurately as possible in the sense that a reconstructed polynomial is obtained with only the last τ number of coefficients being possibly erroneous, when the residues are affected by errors with degrees upper bounded by τ . In this regard, we first propose a multilevel robust Chinese remainder theorem (CRT) for polynomials, namely, a trade-off between the dynamic range of the degree of the polynomial to be reconstructed and the residue error bound τ is formulated. Furthermore, a simple closed-form reconstruction algorithm is also proposed.

Novel DOAs estimation method based on Doppler aided Chinese remainder theorem with all phase DFT for multiple targets in sparse array

“…This paper proposes a novel scheme to achieve DOAs estimation for multiple signal sources by solving ambiguity. Inspired by [24–28], this paper adopts robust and closed Chinese remainder theorem (RCCRT), which is a popular and common method for solving ambiguity, as effective tool to address phase ambiguity problem. In summary, our main contributions of this paper are listed as follows.…”