  In this fourth part of our multi-part papers, classes of interference
networks with a sequence of less-noisy receivers are identified for which a
successive decoding scheme achieve the sum-rate capacity. First, the
two-receiver networks are analyzed: it is demonstrated that the unified outer
bounds derived in Part III of our multi-part papers are sum-rate optimal for
network scenarios which satisfy certain less-noisy conditions. Then, the
multi-receiver networks are considered. These networks are far less understood.
One of the main difficulties in the analysis of such scenarios is how to
establish useful capacity outer bounds. In this paper, a novel technique
requiring a sequential application of the Csiszar-Korner identity is developed
to establish powerful single-letter outer bounds on the sum-rate capacity of
multi-receiver interference networks which satisfy certain less-noisy
conditions. By using these outer bounds, a full characterization of the
sum-rate capacity is derived for general interference networks of arbitrary
large sizes with a sequence of less-noisy receivers. Some generalizations of
these outer bounds are also presented each of which is efficient to obtain the
exact sum-rate capacity for various scenarios.
