In this paper, we characterize capacity region of the Gaussian doubly dirty two-way channel (TWC) with partial side information at users, where there are two additive interference signals that, although similar to the channel noise sequences, corrupt the transmitted signals but are non-causally and partially known to the users. First, by employing adaptation (considering the previously received signals in encoding process), we derive an adaptive outer bound on the capacity region of the channel. Then, we utilize lattice strategies and obtain a non-adaptive inner bound that coincides with the adaptive outer bound and hence gives the capacity region. This also shows that for the doubly dirty TWC with partial side information, adaptation is useless and cannot increase the capacity region. Finally, we prove that Costa’s dirty paper coding is optimal like lattice strategies and therefore, the Gaussian doubly dirty TWC is an instance of multi-user channels in which lattice strategy and Costa’s strategy have the same performance from the capacity region perspective. It is worth noting that our results subsume the previous related works as special cases.

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