Source coding with common reconstruction and action-dependent side information

We determine the rate region of a source coding problem with common reconstruction and action-dependent side information where an action sequence is taken by an encoder over a rate-limited link. We show that the rate region depends only on the sum-rate and the sum-rate distortion and cost function is characterized. The result serves as a fundamental limit in transmission scenarios where the encoder wants to control and monitor the quality of the decoder´s reconstruction via the respective uses of action sequences and a common reconstruction constraint.