Nested lattice codes for the state-dependent Gaussian interference channel with a common message

In this paper, we consider the generalized point-to-point Additive White Gaussian Noise (AWGN) channel with state: The State-Dependent Gaussian Interference Channel (SD-GIC) with a common message in which two senders transmit a common message to two receivers. Transmitter 1 knows only message W₁ while transmitter 2 in addition W₁ also knows the channel state sequence non-causally. In this paper, we consider the strong interference case where the channel state has unbounded variance. First, we show that a scheme based on Gelfand-Pinsker coding cannot achieve the capacity within a constant gap for channel gains smaller than unity. In contrast, we propose a lattice-based transmission scheme that can achieve the capacity region in the high SNR regime. Our proposed scheme can achieve the capacity region to within 0.5 bit for all values of channel parameters.