Universal Decoding of Watermarks Under Geometric Attacks

Designing watermarking codes that can with stand 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_thetas, thetas isin thetas_n, representing the geometric attack. The decoder does not known the value of thetas. We show that under regularity conditions, there exists a universal decoder for this problem, and we explicitly identify it