Successive Omniscience

Because the exchange of information among all the users in a large network can take a long time, a successive omniscience protocol is proposed. Namely, subgroups of users first recover the information of other users in the same subgroup at an earlier stage called local omniscience. Then, the users recover the information of all other users at a later stage called global omniscience. To facilitate the information exchange, a distributed storage system is used, so that users can conveniently upload and download messages through some reliable central servers. The minimum upload bandwidth is characterized and a bandwidth-storage trade-off is discovered. The results reveal the new connections to the problem of secret key agreement and, consequently, provide meaningful interpretations of a recently proposed multivariate mutual information measure that was inspired by the secret key agreement problem.