Capacity of compound state-dependent channels with states known at the transmitter

Abstract

The problem of sending information over compound state-dependent channels with non-causal state information available at only the transmitter is investigated. We prove a coding theorem and its strong converse establishing the capacity of this scenario for the case of discrete memoryless channels. Specific results are derived for additive white Gaussian noise channels corrupted by an additive Gaussian interference which is available at the transmitter only. We focus on the case where such interference may be absent on the channel, but the transmitter is unaware of this. Applications of the compound channels with non-causal state information arise in the context of multicast and cognitive radio channels, broadcast channels with imperfect channel knowledge and robust dirty-paper coding.