Indirect rate distortion problems

The output of a source, the first of the two arguments of a distortion function, is seen by an encoder through a noisy channel. A decoder sees the encoder\´s signal through the usual communication channel. The second argument of the distortion function is obtained from the decoder\´s output via another noisy channel. The Dobrushin-Tsybakov reduction of this problem to a direct one is shown to follow at once from a "disconnection principle" for conditional expectations. The same principle applies to more general situations such as i) dependence between the noise variables acting in the input and output channels and ii) side information available only at the decoder.