  An encoder wishes to minimize the bit rate necessary to guarantee that a
decoder is able to calculate a symbolwise function of a sequence available only
at the encoder and a sequence that can be measured only at the decoder. This
classical problem, first studied by Yamamoto, is addressed here by including
two new aspects: (i) The decoder obtains noisy measurements of its sequence,
where the quality of such measurements can be controlled via a cost-constrained
"action" sequence; (ii) Measurement at the decoder may fail in a way that is
unpredictable to the encoder, thus requiring robust encoding. The considered
scenario generalizes known settings such as the Heegard-Berger-Kaspi and the
"source coding with a vending machine" problems. The rate-distortion-cost
function is derived and numerical examples are also worked out to obtain
further insight into the optimal system design.
