Iterative estimation of amplitude scaling on distortion-compensated dither modulation

The vulnerability of quantization-based data hiding schemes to amplitude scaling requires the formulation of countermeasures to this relatively simple attack. Parameter estimation is one possible approach, where the applied scaling is estimated from the received signal at the decoder. This estimate can be used to correct the mismatch with respect to the quantization step assumed by the decoder prior to decoding. In this work we first review previous approaches utilizing parameter estimation as a means of combating the scaling attack on DC-DM. We then present a method for joint iterative decoding and maximum likelihood estimation of the scaling factor for this quantization-based method. The estimation method exploits the reliabilities provided by the nearoptimal iterative decoding process in order to successively refine the estimate. The complexity of this problem is tackled using the expectation maximization algorithm. By performing estimation in cooperation with the decoding process, reliable estimation is possible at very low watermark-to-noise power ratios by using sufficiently low rate codes.