We analyze the impact of side information about the distortion measure in problems of quantization. We show that such "distortion side information" is not only useful at the encoder, but that under certain conditions, knowing it only at the encoder is as good as knowing it at both encoder and decoder, and knowing it at only the decoder is useless. Thus, distortion side information is a natural complement to side information about the source signal, as studied by Wyner and Ziv, which if available only at the decoder is often as good as knowing it at both encoder and decoder. Furthermore, when both types of side information are present, we characterize the penalty for deviating from the often sufficient configuration of encoder-only distortion side information and decoder-only signal side information.
Emin Martinian, Gregory W. Wornell, Ram Zamir