On Joint Compression and Information Embedding When Watermarks and Covertexts Are Correlated

A joint compression and public digital watermarking system with correlated watermark source and covertext source (M, S) is investigated in this paper. More specifically, for a given distortion level D between S and a watermarked signal X and a given compression rate R_c for X, the watermark source M can be fully recovered with high probability at the end of a public watermark decoder after the watermarked signal is disturbed by a fixed memoryless attack channel p(yx) if and only if H(M) les _maxp(x,um,s) min{R_c - I(M, S; U, X) + I(M; U, Y), I(U; Y) - I(U; M, S) + I(M; U, Y)}, where the maximization is taken over all auxiliary random variables U (with finite alphabet U) and X jointly distributed with (M, S, X, Y) according to p(m, s, u, x, y) = p(m, s)p(u, xm, s)p(yx) such that Ed(S, X) les D