  The sum-capacity is studied for a K-user degraded Gaussian multiaccess relay
channel (MARC) where the multiaccess signal received at the destination from
the K sources and relay is a degraded version of the signal received at the
relay from all sources, given the transmit signal at the relay. An outer bound
on the capacity region is developed using cutset bounds. An achievable rate
region is obtained for the decode-and-forward (DF) strategy. It is shown that
for every choice of input distribution, the rate regions for the inner (DF) and
outer bounds are given by the intersection of two K-dimensional polymatroids,
one resulting from the multiaccess link at the relay and the other from that at
the destination. Although the inner and outer bound rate regions are not
identical in general, for both cases, a classical result on the intersection of
two polymatroids is used to show that the intersection belongs to either the
set of active cases or inactive cases, where the two bounds on the K-user
sum-rate are active or inactive, respectively. It is shown that DF achieves the
capacity region for a class of degraded Gaussian MARCs in which the relay has a
high SNR link to the destination relative to the multiaccess link from the
sources to the relay. Otherwise, DF is shown to achieve the sum-capacity for an
active class of degraded Gaussian MARCs for which the DF sum-rate is maximized
by a polymatroid intersection belonging to the set of active cases. This class
is shown to include the class of symmetric Gaussian MARCs where all users
transmit at the same power.
