Calculation of watermarking capacities of private Laplacian watermarking systems with the magnitude-error distortion measure under fixed attacks is addressed. First, in the case of an additive Laplacian attack, a nice closed-form formula for the watermarking capacities is derived, which involves only the distortion level and the parameter of the Laplacian attack. Second, in the case of an arbitrary additive attack, a general, but slightly more complicated formula for the watermarking capacities is given. Finally, calculation of the joint compression and private watermarking rate region of Laplacian watermarking systems with an additive Laplacian attack is considered.
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