In digital media transfer, geometrical transformations desynchronize the communications between the encoder and the decoder. Therefore, an attempt to decode the message based on the direct output of the channel with random geometrical state fails. The main goal of this paper is to analyze the conditions of reliable communications based on structured codebooks in channels with geometrical transformations. Structured codebooks include codewords that have some features or statistics designed for synchronization purposes. In the design of capacity approaching data-hiding codes, host interference problem should be resolved. The solution to this problem is to perform the message coding based on random binning dependent on host-state. On the other hand, to achieve robustness to geometrical transformations, the codewords should have host independent statistics and encoding should be performed using random coding. To satisfy these conflicting requirements we propose Multiple Access Channel (MAC) framework where the message is split between two encoders designed based on the random binning and random coding principles. The message encoded according to random coding additionally serves for synchronization purposes. Sequentially, all existing methods that are proposed for reliable communications in channels with geometrical transformations are analyzed within the proposed MAC set-up. Depending on the particular codebook design, we classify these methods into two main groups: template-based codebooks and redundant codebooks. Finally, we perform the analysis of security leaks of each codebook structure in terms of complexity of the worst case attack.