The propagation dynamics of 7-core multi-core fibers (MCFs) with identical and three-types of cores are analytically derived based on the coupled-mode theory. The mode coupling dynamics can be aperiodic with transmission distance for MCF with identical cores. For MCFs with heterogeneous cores, it is found that even though signals from different core groups will not couple with each other, the coupling within their own group is significantly affected by the presence of other core groups. Joint signal processing techniques to mitigate mode coupling induced-cross-talks such as least mean square (LMS) algorithm and maximum likelihood (ML) detection are investigated and corresponding transmission performance are determined for coherent as well as intensity modulated formats. It is shown that aperiodic mode coupling in intensity modulated systems induces cross-talks that are difficult to eliminate through signal processing. The analytical insights may help in optimizing MCF designs and corresponding signal processing techniques for future high capacity MCF transmission systems.