On joint information embedding and lossy compression in the presence of a stationary memoryless attack channel

We consider the problem of optimum joint information embedding and lossy compression with respect to a fidelity criterion. The decompressed composite sequence (stegotext) is distorted by a stationary memoryless attack, resulting in a forgery which in turn is fed into the decoder, whose task is to retrieve the embedded information. The paper characterizes the maximum achievable embedding rate, R_e, (the embedding capacity, C_e) as a function of the compression (composite) rate R_c and the allowed average distortion level, Δ, such that the average probability of error in decoding the embedded message can be made arbitrarily small for sufficiently large block length. We characterize the embedding capacity and demonstrate how it can be approached in principle. We also provide a single-letter expression of the minimum achievable composite rate as a function of R_e and Δ, below which there exists no reliable embedding scheme.