Asymptotically optimum embedding strategy for one-bit watermarking under Gaussian attacks

The problem of asymptotically optimum watermark detection and embedding has been addressed in a recent paper by Merhav and Sabbag where the optimality criterion corresponds to the maximization of the false negative error exponent for a fixed false positive error exponent. In particular Merhav and Sabbag derive the optimum detection rule under the assumption that the detector relies on the second order statistics of the received signal (universal detection under limited resources), however the optimum embedding strategy in the presence of attacks and a closed formula for the negative error exponents are not available. In this paper we extend the analysis by Merhav and Sabbag, by deriving the optimum embedding strategy under Gaussian attacks and the corresponding false negative error exponent. The improvement with respect to previously proposed embedders are shown by means of plots.