Combined Source Coding and Watermarking

A new problem termed as combined source coding and watermarking is investigated, where an independently and identically distributed (iid) source M correlated with an iid host signal S is to be transmitted by embedding M into S. A necessary and sufficient condition is derived under which the source M can be recovered with high probability from a watermarked signal disturbed by a fixed memoryless attack channel p(y|x). Specifically, it is shown that M can be recovered with high probability if and only if H(M) is less than or equal to max{I(U;Y) - I(U;M,S) + I(M;U,Y) : U,X}, where the maximization is taken over all auxiliary random variables U and X such that the distortion between S and X is less than or equal to a prescribed distortion level D. In particular, the result implies that the Shannon separation theorem can not be extended to this case, that is, it is still possible to transmit M reliably even when H(M) is strictly greater than the watermarking capacity. A similar result is also established in the case of combined source coding and Gelfand-Pinsker channel coding