is the design of communication strategies that strike the right balance between control signaling and source compression across the two hops.

Related Work
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As mentioned, the original paper [@Permuter] considered a point-to-point system with a single encoder and a single decoder. Various works have extended the results in [@Permuter] to multi-terminal models. Specifically, [@Weissman_multi; @Ahmadi_ISIT'11] considered a set-up analogous to the Heegard-Berger problem [@HB; @Kaspi], in which the side information may or may not be available at the decoder. The more general case in which both decoders have access to the same vending machine, and either the side information produced by the vending machine at the two decoders satisfy a degradedness condition, or lossless source reconstructions are required at the decoders is solved in [@Weissman_multi]. In [@Ahmadi_DSC], a distributed source coding setting that extends [@Berger-Yeung] to the case of a decoder with a side information VM is investigated, along with a cascade source coding model to be discussed below. Finally, in [@Compression; @with; @actions], a related problem is considered in which the sequence to be compressed is dependent on the actions taken by a separate encoder.

The problem of characterizing the rate-distortion region for cascade source coding models, even 