A relationship between quantization and watermarking rates in the presence of additive Gaussian attacks

A system which embeds watermarks in n-dimensional Gaussian data and distributes them in compressed form is studied. The watermarked/compressed data have to satisfy a distortion constraint, and the watermark has to be recoverable in a private scenario (in which the original data are available at the watermark detector). The performance of the system in the presence of additive Gaussian attacks is considered, and the region of achievable quantization and watermarking rate pairs (R_Q,R_W) is established. Moreover, two surprising facts are demonstrated: (1) at low R_Q, the maximum achievable R_W is the same as when there are no attacks; and (2) at high (but finite) R_Q, the maximum achievable R_W is the same as when there is no compression (R_Q=∞). Finally, the performance of related schemes is also discussed.