E-capacity analysis of data-hiding channels with geometrical attacks

In a data hiding communications scenario, geometrical attacks lead to a loss of reliable communications due to synchronization problems when the applied attack is unknown. In our previous work, information-theoretic analysis of this problem was performed for theoretic setups, i.e., when the length of communicated data sequences asymptotically approaches infinity. Assuming that the applied geometrical attack belongs to a set of finite cardinality, it is demonstrated that it does not asymptotically affect the achievable rate in comparison to the scenario without any attack. The main goal of this paper is to investigate the upper and lower bounds on the rate reliability function that can be achieved in the data hiding channel with some geometrical state. In particular, we investigate the random coding and sphere packing bounds in channels with random parameter for the case when the interference (channel state) is not taken into account at the encoder. Furthermore, only those geometrical transformations that preserve the input dimensionality and input type class are considered. For this case we are showing that similar conclusion obtained in the asymptotic case is valid, meaning that within the class of considered geometrical attacks the rate reliability function is bounded in the same way as in the case with no geometrical distortions