Quantization index modulation: a class of provably good methods for digital watermarking and information embedding

We consider the problem of embedding one signal (e.g., a digital watermark), within another "host" signal to form a third, "composite" signal. The embedding is designed to achieve efficient tradeoffs among the three conflicting goals of maximizing the information-embedding rate, minimizing the distortion between the host signal and composite signal, and maximizing the robustness of the embedding. We introduce new classes of embedding methods, termed quantization index modulation (QIM) and distortion-compensated QIM (DC-QIM), and develop convenient realizations in the form of what we refer to as dither modulation. Using deterministic models to evaluate digital watermarking methods, we show that QIM is "provably good" against arbitrary bounded and fully informed attacks, which arise in several copyright applications, and in particular it achieves provably better rate distortion-robustness tradeoffs than currently popular spread-spectrum and low-bit(s) modulation methods. Furthermore, we show that for some important classes of probabilistic models, DC-QIM is optimal (capacity-achieving) and regular QIM is near-optimal. These include both additive white Gaussian noise (AWGN) channels, which may be good models for hybrid transmission applications such as digital audio broadcasting, and mean-square-error-constrained attack channels that model private-key watermarking applications.