On Joint Information Embedding and Lossy Compression in the Presence of a Stationary Memoryless Attack Channel

We consider the problem of optimum joint public 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 goal of this paper is to characterize the maximum achievable embedding rate (the embedding capacity ) as a function of the compression (composite) rate and the allowed average distortion level , such that the average probability of error in decoding of 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 and , below which there exists no reliable embedding scheme.