On the Sum Capacity of the Gaussian X Channel in the Mixed Interference Regime

In this paper, we analyze the Gaussian X channel in the mixed interference regime. In this regime, multiple access transmission to one of the receivers is shown to be close to optimal in terms of sum rate. Three upper bounds are derived for the sum capacity in the mixed interference regime, and the subregions where each of these bounds dominate the others are identified. The genie-aided sum capacity upper bounds derived also show that the gap between sum capacity and the sum rate of the multiple access transmission scheme is small for a significant part of the mixed interference region. For any \delta > 0, the region where multiple access transmission to one of the receivers is within \delta from sum capacity is determined.Comment: To be presented at ISIT 2015, Hong Kong, Chin

On the Sum Rate of a 2 x 2 Interference Network

In an M x N interference network, there are M transmitters and N receivers with each transmitter having independent messages for each of the 2^N -1 possible non-empty subsets of the receivers. We consider the 2 x 2 interference network with 6 possible messages, of which the 2 x 2 interference channel and X channel are special cases obtained by using only 2 and 4 messages respectively. Starting from an achievable rate region similar to the Han-Kobayashi region, we obtain an achievable sum rate. For the Gaussian interference network, we determine which of the 6 messages are sufficient for maximizing the sum rate within this rate region for the low, mixed, and strong interference conditions. It is observed that 2 messages are sufficient in several cases.Comment: Theorem 4 in previous version removed. See https://arxiv.org/abs/1505.06317 for updated result