with conventional side information sequences (i.e., without VMs as in Fig. \[fig:intro\]) at Node 2 and Node 3, is generally open. We refer to [@Ravi] and references therein for a review of the state of the art on the cascade problem and to [@Vasudevan] for the cascade-broadcast problem.

In this work, we focus on the cascade source coding problem with side information VMs. The basic cascade source coding model consists of three nodes arranged so that Node 1 communicates with Node 2 and Node 2 to Node 3 over finite-rate links, as illustrated for a computer network scenario in Fig. \[fig:fig1\] and schematically in Fig. \[fig:intro\]-(a). Both Node 2 and Node 3 wish to reconstruct a, generally lossy, version of source $X$ and have access to different side information sequences. An extension of the cascade model is the cascade-broadcast model of Fig. \[fig:intro\]-(b), in which an additional broadcast link of rate $R_{b}$ exists that is received by both Node 2 and Node 3.

![($a$) Cascade source coding problem and ($b$) cascade-broadcast source coding problem.[]{data-label="fig:intro"}](intro)

Two specific instances of the models in Fig. \[fig:intro\] for which a characterization of the rate-distortion performance has been found are the settings considered in [@Chia] 