On the Achievable Rate Sum for Symmetric Gaussian Interference Channels

We compute the exact rate sum of a symmetric Gaussian interference channel for the HanKobayashi region with Gaussian signaling for a subset of parameters in the weak interference regime. In this subset we identify three regimes of operation: an initial set where treating interference as noise is optimal, an intermediate regime where one employs a time-sharing strategy (with power control) between treating interference as noise and time-division multiplexing (TDM), and finally a regime where TDM is optimal. Beyond this regime our techniques do not yield the exact sum-rate, however we do observe that one can achieve rates above those prescribed by TDM, even for values of a that are close to 1.