(2002) Dirty-paper trellis codes for watermarking. In: 2002 INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOL II, PROCEEDINGS. (pp. 129 - 132). IEEE
This tutorial paper reviews the theory and design of codes for hiding or embedding information in signals such as images, video, audio, graphics, and text.
Our study for the Gaussian source model extends the dirty paper coding result by Costa to the case of a weighted power constraint with the weights only known to the transmitter.
Informed coding is the practice of representing watermark messages with patterns that are dependent on the cover Works. This requires the use of a dirty-paper code, in which each message is represented by a large number of alternative vectors. Most previous dirty-paper codes are based on lattice codes, in which each code vector, or pattern, is a point in a regular lattice. While such codes are very efficient to implement, they suffer from inherent weakness against valumetric scaling, such as changes in audio volume or image brightness. In the present paper, we present an alternative to lattice codes that is inherently robust to valumetric scaling. This code is based on a trellis that has been modified so that each bit value may be coded by traversing several alternative arcs. A Viterbi decoder is used in the detector to identify the path with the highest correlation to the input Work. Since relative correlation values are unaffected by valumetric scaling, the same message will be detected no matter how the input has been scaled.
Dirty paper trellis codes are a form of watermarking with side information. These codes have the advantage of being invariant to valumetric scaling of the coverWork. However, the original proposal requires a computational expensive second stage, informed embedding, to embed the chosen code into the coverWork. In this paper, we present a computational efficient algorithm for informed embedding. This is accomplished by recognizing that all possible code words are uniformly distributed on the surface of a high n-dimensional sphere. Each codeword is then contained within an (n - 1)-dimensional region which defines an n-dimensional cone with the centre of the sphere. This approximates the detection region. This is equivalent to the detection region for normalized correlation detection, for which there are known analytic methods to embed a watermark in a cover Work. We use a previously described technique for embedding with a constant robustness. However, rather than moving the cover Work to the closest Euclidean point on the defined surface, we find the point on the surface which has the smallest perceptual distortion. Experimental results on 2000 images demonstrate a 600-fold computational improvement together with an improved quality of embedding.