A generalization of the problem of dirty paper coding is considered in which (possibly different) noisy versions of the state information, assumed to be i.i.d. Gaussian random variables, are available at the encoder and at the decoder. This paper derives the maximum achievable rate formula for this general problem. This general setup encompasses the cases where the state information is perfectly known either at the encoder or decoder or at both. Moreover, it generalizes the analysis to cases where the state information is known only partially. In addition, this paper shows that in realistic situations where the AWGN noise power is not known at the encoder, partial information at the decoder can increase the maximum achievable rate with respect to Costa's coding setup. Our setup is relevant for practical applications such as watermarking under desynchronization attacks.