  We obtain new sum capacity results for the Gaussian many-to-one and
one-to-many interference channels in channel parameter regimes where the sum
capacity was known only up to a constant gap. Simple Han-Kobayashi (HK)
schemes, i.e., HK schemes with Gaussian signaling, no time-sharing, and no
common-private power splitting, achieve sum capacity under the channel
conditions for which the new results are obtained. To obtain sum capacity
results, we show that genie-aided upper bounds match the achievable sum rate of
simple HK schemes under certain channel conditions.
