In this paper, we obtain new sum capacity results for the Gaussian many-to-one and one-to-many interference channels. 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. First, by careful Fourier-Motzkin elimination, we obtain the HK achievable rate region for the K-user Gaussian many-to-one and one-to-many channels in simplified form, i.e., only in terms of the K rates $R_1$, $R_2$,..., $R_K$. We also obtain the achievable sum rate using Fourier-Motzkin elimination. Then, to obtain sum capacity results, we derive genie-aided upper bounds that match the achievable sum rate of simple HK schemes under certain channel conditions.
['Abhiram Gnanasambandam', 'Ragini Chaluvadi', 'Srikrishna Bhashyam']
On the Sum Capacity of Many-to-one and One-to-many Gaussian Interference Channels