On the capacity of state-dependent Gaussian cognitive interference channel

A Gaussian cognitive interference channel with state (G-CICS) is studied. In this paper, we focus on the two-sender, two-receiver case and consider the communication situation in which two senders transmit a common message to two receivers. Transmitter 1 knows only messageW1, and transmitter 2, referred to as the cognitive user, knows both messagesW1 andW2 and also the channel’s states sequence non-causally. Receiver 1 needs to decode onlyW1 while receiver 2 needs to decode both messages. In this paper, we investigate the weak and moderate interference case where we assume that the channel gain a satisfies |a| ≤ 1. In addition, inner and outer bounds on the capacity region are derived in the regime of high state power, i.e., the channel state sequence has unbounded variance. First, we show that the achievable rate by Gelfand-Pinsker coding vanishes in the high state power regime under a condition over the channel gain. In contrast, we propose a transmission scheme (based on lattice codes) that can achieve positive rates, independent of the interference. Our transmission scheme can achieve the capacity region in a high signal-to-noise ratio (SNR) regime. Also, regardless of all channel parameters, the gap between the achievable rate region and the outer bound is at most 0.5 bits.