On Cascade Source Coding with A Side Information "Vending Machine"
  The model of a side information "vending machine" accounts for scenarios in which acquiring side information is costly and thus should be done efficiently. In this paper, the three-node cascade source coding problem is studied under the assumption that a side information vending machine is available either at the intermediate or at the end node. In both cases, a single-letter characterization of the available trade-offs among the rate, the distortions in the reconstructions at the intermediate and at the end node, and the cost in acquiring the side information are derived under given conditions. 
Behzad Ahmadi, Osvaldo Simeone, Chiranjib Choudhuri, and Urbashi Mitra
cs.IT math.IT