This work studies linear interference networks, both wired and wireless, with no channel state information at the transmitters (CSIT) except a coarse knowledge of the end-to-end one-hop topology of the network that only allows a distinction between weak (zero) and significant (non-zero) channels and no further knowledge of the channel coefficients' realizations. The network capacity (wired) and DoF (wireless) are found to be bounded above by the capacity of an index coding problem for which the antidote graph is the complement of the given interference graph. The problems are shown to be equivalent under linear solutions. An interference alignment perspective is then used to translate the existing index coding solutions into the wired network capacity and wireless network DoF solutions, as well as to find new and unified solutions to different classes of all three problems.

Revised for the IEEE Transactions on Information Theory