On Information Embedding When Watermarks and Covertexts Are Correlated

A new digital watermarking scenario is studied, where a watermark M correlated with a covertext S is to be transmitted by embedding M into S. The configuration of this scenario is different from that treated in existing digital watermarking works, where watermarks are assumed independent of covertexts. Assume that the pair (M, S) is drawn from an independently and identically distributed sequence. A necessary and sufficient condition is derived under which the watermark M can be recovered with high probability at the end of a watermark decoder after the watermarked signal is disturbed by a fixed memoryless attack channel p_Y|X(y|x). Specifically, it is shown that in the case of public watermarking where the covertext S is not accessible to the watermark decoder, M can be recovered with high probability if and only if H(M) les max_{p(x,u|m,s):Ed(S,X)lesD}[I(U);M,S) - I(U; M, S) + I(M;U,Y)], where the maximum is taken over all auxiliary random variables U and X jointly distributed with M and S and satisfying Ed(S, X) les D. In particular, the result implies that the Shannon separation theorem can not be extended to this scenario, 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 for combined source coding and Gel´fand Pinsker channel coding