Symmetric two-user Gaussian interference channel with common message with very low interference

We consider symmetric two-user Gaussian interference channel with common messages. We derive an upper bound on the sum capacity, and show that the upper bound is tight in the very low interference regime, where the optimal transmission scheme is to send no common messages and each receiver treats interference as noise. Our result shows that although the availability of common messages provides a cooperation opportunity for transmitters, in the low interference regime the presence of common messages does not help increase the sum capacity.