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In this paper, we study some fundamental performance limits of blind data hiding against desynchronization attacks. These attacks are modeled in addition to independent Gaussian noise to the marked signal, followed by linear, time-invariant filtering. We study a joint estimator-decoder which estimates the desynchronization attack parameters and uses these estimates in the decoding step. We propose a coding scheme based on distortion-compensated quantization index modulation and derive the estimation accuracy of the attack parameters via Fisher information and a Cramer-Rao type bound. For illustration purposes, we report estimation and decoding results on several attacks, including classical ones (scaling and fractional shifts) and some new ones. The results are in close agreement with our bounds and tightly quantify the performance loss due to desynchronization and the influence of code block length. Thus our results demonstrate the high performance of a joint estimation-decoding approach.