Rate-Distortion with a Limited-Rate Helper to the Encoder and Decoder

Consider the rate-distortion problem, in which a helper sends a common limited-rate message both to the encoder and decoder based on side information at its disposal. We characterize the region of achievable rates and distortions for this problem. We derive these regions explicitly for binary doubly symmetric sources with Hamming distortion, and for Gaussian sources with square error distortion. We also consider the more general problem where additional side information is available at the decoder and provide a single letter characterization of the region of achievable rates and distortions for the case in which the helper’s information and the additional decoder side information are independent given the source. Finally, we examine the case where the helper has the freedom to send different messages, at different rates, to the encoder and the decoder. We show that “more help” to the encoder than to the decoder does not yield any performance gain and that in such cases the freedom to send different messages to the encoder and the decoder yields no gain over the case of a common message. Further, in this setting of different messages, the rate to the encoder can be strictly less than that to the decoder with no performance loss. Index Terms Rate-distortion, side information, entropy-power inequality, Mrs. Gerber’s Lemma.