While binning is a fundamental approach to blind data embedding and watermarking, an attacker may devise various strategies to reduce the effectiveness of practical binning schemes. The problem analyzed in this paper is design of worst-case noise distributions against L-dimensional lattice quantization index modulation (QIM) watermarking codes. The cost functions considered are 1) probability of error of the maximum-likelihood decoder, and 2) the more tractable Bhattacharyya upper bound on error probability, which is tight at low embedding rates. Both problems are addressed under the following constraints on the attacker's strategy: the noise is independent of the marked signal, blockwise memoryless with block length L, and may not exceed a specified quadratic-distortion level. The embedder's quadratic distortion is limited as well. Three strategies are considered for the embedder: optimization of the lattice inflation parameter (also known as Costa parameter), dithering, and randomized lattice rotation. Critical in this analysis are the symmetry properties of QIM nested lattices and convexity properties of probability of error and related functionals of the noise distribution. We derive the minmax optimal embedding and attack strategies and obtain explicit solutions as well as numerical solutions for the worst-case noise. The role of the attacker's memory is investigated; in particular, we demonstrate the remarkable effectiveness of impulsive-noise attacks as L increases. The formulation proposed in this paper is also used to evaluate the capacity of lattice QIM under worst-noise conditions.

This paper examines the role of attacker's memory in quantization index modulation (QIM) watermarking systems. First we derive the attacker's noise distribution that maximizes probability of error of the detector. Next, we derive QIM code parameters that are minmax optimal. The minmax optimal embedding strategy involves randomized lattice rotations, and the corresponding worst noise distributions are isotropic.

Perceptual watermarking methods are designed to be transparent and robust to attacks. A perceptual model based on just noticeable difference levels introduces amplitude constraints on the watermark and the noise generated by an attacker. Two problems are considered: (1) detection performance for embedding a single bit in n data; (2) Shannon capacity. In both cases, the original host data are known to the receiver. Both problems are formulated as games involving a suitable cost function (Bhattacharyya distance and mutual information, respectively). The watermarker and the attacker design probability distributions in order to maximize and minimize, respectively, the cost function. The optimal distributions are quite different from the uniform distributions that have been previously used in the watermarking literature.

The problem of blind watermarking of an arbitrary host signal in /spl Ropf//sup n/ under squared-error distortion constraints and Gaussian attacks is considered in this paper. While distortion-compensated lattice quantization index modulation (QIM), using nearly spherical Voronoi cells, is known to be asymptotically capacity-achieving in this setup, our results suggest that such schemes are suboptimal in terms of error probability when the number of possible messages is subexponential in n. Our conjecture is substantiated by examples involving low-dimensional lattices and is related to the simplex conjecture in coding theory.

Quantization Index Modulation (QIM) methods are widely used for blind data embedding and watermarking. Given a QIM watermarking code, we ask what is the attacker's noise distribution that maximizes probability of error of the detector. For memoryless attacks, the problem is reduced to a convex programming problem. Next, we derive QIM code parameters that are minmax optimal.