Optimal sparse-QIM codes for zero-rate blind watermarking

The problem of blind watermarking of an arbitrary host signal in ℝ 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.