Multi-terminal source coding with action dependent side information

We consider multi-terminal source coding with a single encoder and multiple decoders where either the encoder or the decoders can take actions which affect the quality or availability of the side information present at the decoders, subjected to an additional cost constraint on the actions taken. For the scenario where a joint action is taken at the decoders, we characterize the rate-cost trade-off region for lossless source coding, and give an achievability scheme for lossy source coding for two decoders which is optimum for several special cases. For the case where the encoder takes actions, we characterize the rate-cost trade-off for a class of lossless source coding scenarios with multiple decoders.