Successive omniscience

The problem of successive omniscience is formulated for the study of a recently proposed multivariate mutual information measure. In this problem, a set of users want to achieve omniscience, i.e., recover the private sources of each other by exchanging messages. However, the omniscience is achieved in a successive manner such that local subgroups of users can first achieve local omniscience, i.e., recover the private sources of other users in the same subgroups. Global omniscience among all users is achieved by an additional exchange of messages. This formulation can be motivated by a distributed storage system that enables file sharing among groups of users. It is shown that the multivariate mutual information can be used to characterize the minimum storage required as well as the conditions under which local omniscience can be achieved for free without increasing the total communication rate required for global omniscience. Our results provide new interpretations of the multivariate mutual information.