  We consider lossy source coding when side information affecting the
distortion measure may be available at the encoder, decoder, both, or neither.
For example, such distortion side information can model reliabilities for noisy
measurements, sensor calibration information, or perceptual effects like
masking and sensitivity to context. When the distortion side information is
statistically independent of the source, we show that in many cases (e.g, for
additive or multiplicative distortion side information) there is no penalty for
knowing the side information only at the encoder, and there is no advantage to
knowing it at the decoder. Furthermore, for quadratic distortion measures
scaled by the distortion side information, we evaluate the penalty for lack of
encoder knowledge and show that it can be arbitrarily large. In this scenario,
we also sketch transform based quantizers constructions which efficiently
exploit encoder side information in the high-resolution limit.
