Universal Decoding of Watermarks Under Geometric Attacks

by Pierre Moulin

Designing watermarking codes that can withstand geometric and other
desynchronization attacks is a notoriously difficult problem. 
One may ask whether these difficulties are due to limitations of current 
codes, or rather to fundamental limitations on achievable performance.
We model the attack channel as the cascade of a memoryless channel
and a smooth, invertible mapping $T_{\theta}, \theta \in \Theta_n$,
representing the geometric attack. 
The decoder does not known the value of $\theta$.
We show that under regularity conditions, there exists a universal decoder
for this problem, and we explicitly identify it.