Digital watermarking systems are required to embed as much information as possible in a digital media without the perceptual distortion as well as to extract it correctly with high probabilities, even though the media is subjected to many kinds of operations. To this end, guided scrambling (GS) techniques, usually used for a recording channel, are applied to digital watermarking systems. A simple GS scheme can make the power of a watermark signal larger against the power of media noise under the condition of preserving the perceptual fidelity, resulting in smaller error probabilities of the retrieved watermark bits. In addition, watermarking systems based on the GS can have more robustness to some specified operations if the prior information on the operations is given to the embedder. JPEG compression is a good example of such an operation when still images are transmitted over the Internet. In order for watermark signals to be more tolerable to the known JPEG attack, the GS-based watermark embedder is informed of advance knowledge of the JPEG compression. Further, a configuration of the GS concatenated with turbo coding is introduced to lower the bit error rate more.

Guided Scrambling (GS) is used for control of the runlength within code blocks, such as d or k, as well as for DC component suppression. A code designed by the GS technique, called a weakly constrained code, does not strictly guarantee the imposed k-constraint, but rather generates code blocks that violate the prescribed constraint with very low probability. In this case, the code rate and efficiency become very high, compared with typical RLL codes using a small constrained length. In this paper, weakly constrained codes based on the convolutional GS and GF-addition GS generate the weakly k-constraint sequences. The probability that a code block violates the k-constraint is measured. To show the superior performance of the GS, the occurrence probability of each runlength is also investigated and compared with the 24/25(0, 8) block code which has a high code rate and adheres to channel constraints. We also compare it with the runlength distribution of a maxentropic RLL sequence and show that the statistical property of the GS-encoded sequences is similar to that of the maxentropic RLL sequence on runlength distribution.

The DC component suppressing method, called Guided Scrambling (GS), has been proposed, where a source bit stream within a data block is subjected to several kinds of scrambling and a RLL (Run Length Limited) coding to make the selection set of channel bit streams, then the one having the least DC component is selected. Typically, this technique uses a convolutional operation or GF (Galois field) conversion. A review of their respective symbol error properties has revealed important findings. In the former case, the RS (Reed-Solomon) decoding capability is reduced because error propagation occurs in descrambling. In the latter case, error propagation of a data block length occurs when erroneous conversion data occurs after RS decoding. This paper introduces expressions for determining the decoded symbol error probabilities of the two schemes based on these properties. The paper also discusses the difference in code rates between the two schemes on the basis of the result of calculation using such expressions.