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In this letter, optimal additive noise is characterized for parameter estimation based on quantized observations. First, optimal probability distribution of noise that should be added to observations is formulated in terms of a Cramer-Rao lower bound (CRLB) minimization problem. Then, it is proven that optimal additive ??noise?? can be represented by a constant signal level, which means that randomization of additive signal levels is not needed for CRLB minimization. In addition, the results are extended to the cases in which there exists prior information about the unknown parameter and the aim is to minimize the Bayesian CRLB (BCRLB). Finally, a numerical example is presented to explain the theoretical results.