Layered lattice coding for the symmetric Gaussian X channel

We develop achievable sum rate expressions for the Gaussian X channel at finite SNR using layered lattice coding with interference alignment. For different regimes of channel parameter h, we consider different decoding strategies including successive decoding and compute-and-forward decoding. For some regimes of h, we characterize the sum-rate capacity to within constant bits by using successive decoding. For a set of h that satisfy certain feasibility conditions, we show that compute-and-forward decoding outperforms a timesharing MAC-based lower bound. However, we find that the direct application of compute-and-forward results in high sensitivity of computation rates to the variation of h. Therefore, we introduce a channel steering method to significantly reduce the fluctuation in achievable sum-rate and consistently achieve high rates. We subsequently compare the achievable sum-rate with a new upper bound to demonstrate the value of channel steering.