  In this second part of our multi-part papers, the information flow in
degraded interference networks is studied. A full characterization of the
sum-rate capacity for the degraded networks with any possible configuration is
established. It is shown that a successive decoding scheme is sum-rate optimal
for these networks. Also, it is proved that the transmission of only a certain
subset of messages is sufficient to achieve the sum-rate capacity in such
networks. Algorithms are presented to determine this subset of messages
explicitly. According to these algorithms, the optimal strategy to achieve the
sum-rate capacity in degraded networks is that the transmitters try to send
information for the stronger receivers and, if possible, avoid sending the
messages with respect to the weaker receivers. The algorithms are easily
understood using our graphical illustrations for the achievability schemes
based on directed graphs. The sum-rate expression for the degraded networks is
then used to derive a unified outer bound on the sum-rate capacity of arbitrary
non-degraded networks. Several variations of the degraded networks are
identified for which the derived outer bound is sum-rate optimal. Specifically,
noisy interference regimes are derived for certain classes of
multi-user/multi-message interference networks. Also, for the first time,
network scenarios are identified where the incorporation of both successive
decoding and treating interference as noise achieves their sum-rate capacity.
Finally, by taking insight from our results for degraded networks, we establish
a unified outer bound on the entire capacity region of the general interference
networks. These outer bounds for a broad range of network scenarios are tighter
than the existing cut-set bound.
