In this paper, channel coding strategies for the problem of communication over a two-user Z-interference channel (ZIC) in the presence of non-causal side information (NSI) at transmitters are presented. First, an achievable rate region for the general discrete memoryless ZIC-NSI is derived using rate splitting technique, superposition coding, Gel’fand–Pinsker-type binning scheme and joint typicality decoding. Next, the capacity region of a special case of the orthogonal ZIC-NSI is characterized. Then, the Gaussian version of the channel called the Gaussian Doubly Dirty ZIC (GDD-ZIC) is defined and a general outer bound to the capacity region of the GDD-ZIC is presented. After that, an inner bound for the sum-capacity of the channel using Costa's dirty paper coding is derived and thereby it is shown that Costa's strategy cannot achieve any positive rates over the GDD-ZIC for the case of strong state-interference. Finally, lattice-based achievable rates for the GDD-ZIC are obtained. These lattice-based rates are independent of the state-interference powers and thus, lattice-strategies are able to achieve positive rates for the case of strong state-interference. Moreover, it is shown that lattice-strategies are optimal for a class of the GDD-ZIC.

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