  We study the Han-Kobayashi (HK) achievable sum rate for the two-user
symmetric Gaussian interference channel. We find the optimal power split ratio
between the common and private messages (assuming no time-sharing), and derive
a closed form expression for the corresponding sum rate. This provides a finer
understanding of the achievable HK sum rate, and allows for precise comparisons
between this sum rate and that of orthogonal signaling. One surprising finding
is that despite the fact that the channel is symmetric, allowing for asymmetric
power split ratio at both users (i.e., asymmetric rates) can improve the sum
rate significantly. Considering the high SNR regime, we specify the
interference channel value above which the sum rate achieved using asymmetric
power splitting outperforms the symmetric case.
