  The recently proposed set-up of source coding with a side information
"vending machine" allows the decoder to select actions in order to control the
quality of the side information. The actions can depend on the message received
from the encoder and on the previously measured samples of the side
information, and are cost constrained. Moreover, the final estimate of the
source by the decoder is a function of the encoder's message and depends
causally on the side information sequence. Previous work by Permuter and
Weissman has characterized the rate-distortion-cost function in the special
case in which the source and the "vending machine" are memoryless. In this
work, motivated by the related channel coding model introduced by Kramer, the
rate-distortion-cost function characterization is extended to a model with
in-block memory. Various special cases are studied including block-feedforward
and side information repeat request models.
