Asynchronous Stochastic Decoder for Spread Spectrum Digital Watermarking

We propose decoding algorithms that introduce asynchronous dynamics and a stochastic algorithm for spread spectrum digital watermarking. A synchronous deterministic decoder was used for existing decoding algorithms based on Bayes' estimation. Adopting asynchronous dynamics makes it possible to suppress the occurrences of oscillatory solutions and introducing a stochastic algorithm makes it possible to obtain either an optimal or a sub optimal solution against local minima. We used computer simulation to compare four different types of algorithms, i.e., a synchronous deterministic one, an asynchronous deterministic one, a synchronous stochastic one, and an asynchronous stochastic one. The results showed that asynchronous dynamics have a lower bit error rate than synchronous dynamics, especially in the case when the loading rate is large. We also found that stochastic algorithms provide lower bit error rates than deterministic ones for both synchronous and asynchronous dynamics. The asynchronous stochastic decoder shows the best performance in using these algorithms.