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In this work, coding for channel with partial state information at the decoder is studied. Specifically, the model under consideration assumes that the encoder is provided with full channel state information (CSI) in a noncausal manner, and the decoder is provided with partial state knowledge, quantified by a rate limit. Coding of side information intended for the channel decoder is a Wyner-Ziv like problem, since the channel output depends statistically on the state, thus serving as side information in retrieving the encoded state. Therefore, coding for such a channel involves the simultaneous solution of a Wyner-Ziv problem and a related Gel'fand-Pinsker problem. A single-letter characterization of the capacity of this channel is developed, that involves two rate constraints, in the form of Wyner-Ziv and Gel'fand-Pinsker formulas. Applications are suggested to watermarking problems, where a compressed version of the host signal is present at the decoder. Two main models are examined: the standard watermarking problem, where the decoder is interested only in the embedded information, and the reversible information embedding problem, where the decoder is interested also in exact reproduction of the host. For both problems, single-letter characterizations of the region of all achievable rate-distortion triples (R, Rd, D) are given, where R is the embedding rate, Rd is the rate limit of the compressed host at the decoder, and D is the average distortion between the host and the composite data set (stegotext). For reversible information embedding, two stages of attack are considered, modeled by a degraded broadcast channel, where the weaker (degraded) channel represents the second attack, and both decoders are required to fully reproduce the host.