  The source-coding problem with side information at the decoder is studied
subject to a constraint that the encoder---to whom the side information is
unavailable---be able to compute the decoder's reconstruction sequence to
within some distortion. For discrete memoryless sources and finite
single-letter distortion measures, an expression is given for the minimal
description rate as a function of the joint law of the source and side
information and of the allowed distortions at the encoder and at the decoder.
The minimal description rate is also computed for a memoryless Gaussian source
with squared-error distortion measures. A solution is also provided to a more
general problem where there are more than two distortion constraints and each
distortion function may be a function of three arguments: the source symbol,
the encoder's reconstruction symbol, and the decoder's reconstruction symbol.
