Practical Capacity of Digital Watermark as Constrained by Reliability

This paper presents a theoretic analysis of watermark capacity. First, a simplified watermark scheme is postulated. In the scheme, detection yields a multidimensional vector, in which each dimension is assumed to be i.i.d. (independent and identically distributed) and follow the Gaussian distribution. The major constraint on the capacity is detection reliability, which is one of the most important measures of the utility of watermarks. The problem is to figure out the maximum amount of information payload with the reliability requirement still satisfied. The reliability is represented by three kinds of error rates: the false positive error rate, the false negative error rate, and the bit error rate. These error rates are formulated under certain assumptions, and the theoretical capacity can be determined by setting the bounds on all of the error rates. Further, experiments were performed to verify the theoretic analysis, and it was shown that this approach yields a good estimate of the capacity of a watermark.