Relationship between quantization and distribution rates of digitally watermarked data

We consider a watermarking system where 2^nRw distinct Gaussian watermarks are embedded in respective copies of an n-dimensional i.i.d. Gaussian image. Copies are distributed to customers in digital form, using R_Q bits per image dimension. We establish the rate region for the pair (R_Q, R_W) such that (i) the average quadratic distortion between the original image and each distributed copy is no more than a specified level; and (ii) the error probability in decoding the embedded watermark in the distributed copy approaches zero asymptotically in n