  This third part of the paper is related to the study of information flow in
networks with strong interference. First, the two-receiver networks are
considered. A unified outer bound for the capacity region of these networks is
established. It is shown that this outer bound can be systematically translated
into simple capacity outer bounds for special cases such as the two-user
Classical Interference Channel (CIC) and the Broadcast Channel with Cognitive
Relays (BCCR) with common information. For these channels, special cases are
presented where our outer bounds are tight, which yield the exact capacity.
More importantly, by using the derived outer bounds, a strong interference
regime is identified for the general two-receiver interference networks with
any arbitrary topology. This strong interference regime, which is represented
by only two conditions, includes all previously known results for simple
topologies such as the two-user CIC, the cognitive radio channel, and many
others. Then, networks with arbitrary number of receivers are considered.
Finding non-trivial strong interference regime for such networks, specifically
for the CICs with more than two users, has been one of the open problems in
network information theory. In this paper, we will give a solution to this
problem. Specifically, a new approach is developed based on which one can
obtain strong interference regimes not only for the multi-user CICs but also
for any interference network of arbitrary large sizes. For this development,
some new technical lemmas are proved which have a central role in the
derivations. As a result, this paper establishes the first non-trivial capacity
result for the multi-user classical interference channel. A general formula is
also presented to derive strong interference conditions for any given network
topology.
