Performance analysis and error exponents of asymmetric watermarking systems

Digital watermarking is an important technique to protect intellectual property right and to transmit useful secondary data. This paper investigates the performance analysis and error exponents of asymmetric watermarking systems. Asymmetric watermarking provides potentially better levels of security. Its detection is much different from commonly used watermarking detectors, particularly when both gain factors and exact values of the watermark are not known to the detector. Optimum detectors are constructed in this paper. To handle unwieldy computations of large matrices, we develop equivalent yet more practical detectors in the frequency domain using asymptotic analysis techniques. Due to the nonlinearity nature of these detectors, their performance analysis is challenging, especially when the size of the watermark becomes large. Gaussian approximations using the central limit theorem is limited in modeling the performance. To obtain fundamental performance limits, we go a step further to make use of asymptotic statistical analysis techniques to derive the exact error exponents. The analytical method gives insights into the performance of asymmetric watermarking, and paves the way toward seeking efficient watermarks for more general asymmetric watermarking systems.