Cascade source coding with a side information vending machine

The model of a side information vending machine (VM) accounts for scenarios in which the measurement of side information sequences can be controlled via the selection of cost-constrained actions. In this paper, the three-node cascade source coding problem is studied under the assumption that a side information VM is available at the intermediate and/or end node of the cascade. A single-letter characterization of the achievable tradeoff among the transmission rates, distortions in the reconstructions at the intermediate and end node, and cost for acquiring the side information is derived for a number of relevant special cases. It is shown that a joint design of the description, source, and control signals used to guide the selection of the actions at downstream nodes is generally necessary for an efficient use of the available communication links. In particular, for all the considered models, layered coding strategies prove to be optimal, whereby the base layer fulfills two network objectives: 1) determining the actions of downstream nodes and 2) simultaneously providing a coarse description of the source. Design of the optimal coding strategy is shown via examples to depend on both the network topology and action costs. Examples also illustrate the involved performance tradeoffs across the network.