Cramer-Rao Bound on Watermark Desynchronization Parameter Estimation Accuracy

摘要

Various decoding algorithms have been proposed in the literature to combat desynchronization attacks on quantization index modulation (QIM) blind watermarking schemes. Nevertheless, these results have been fairly poor so far. The need to investigate fundamental limitations on the decoder's performance under a desynchronization attack is thus clear. In this paper, we look at the class of estimator-decoders which estimate the desynchronization attack parameter(s) for using in the decoding step. We model the desynchronization attack as an arbitrary (but invertible) linear time-invariant (LTI) system. We then come up with an encoding-decoding scheme for these attacks on cubic QIM watermarking schemes, and derive Cramer-Rao bounds on the estimation error for the desynchronization parameter at the decoder. As an example, we consider the case of a cyclic shift attack and present some numerical findings.