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The recently proposed set-up of source coding with a side information"vending machine" allows the decoder to select actions in order to control thequality of the side information. The actions can depend on the message receivedfrom the encoder and on the previously measured samples of the sideinformation, and are cost constrained. Moreover, the final estimate of thesource by the decoder is a function of the encoder's message and dependscausally on the side information sequence. Previous work by Permuter andWeissman has characterized the rate-distortion-cost function in the specialcase in which the source and the "vending machine" are memoryless. In thiswork, motivated by the related channel coding model introduced by Kramer, therate-distortion-cost function characterization is extended to a model within-block memory. Various special cases are studied including block-feedforwardand side information repeat request models.

Source Coding with in-Block Memory and Causally Controllable Side Information