A Relationship between Quantization and Distribution Rates of Digitally Fingerprinted Data

Abstract

This paper considers a fingerprinting system where$2^{n R_W}$ distinct Gaussian fingerprints are embedded inrespective 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.By means of a coding theorem, a rate regionfor the pair $(R_Q, R_W)$ is established such that (i) theaverage quadratic distortion between the original imageand each distributed copy does not exceed a specified level;and (ii) the error probability in decoding the embedded fingerprintin the distributed copy approaches zero asymptotically in $n$.