Source Coding with a Causal Helper

A multi-terminal network, in which an encoder is assisted by a side-information-aided helper, describes a memoryless identically distributed source to a receiver, is considered. The encoder provides a non-causal one-shot description of the source to both the helper and the receiver. The helper, which has access to causal side-information, describes the source to the receiver sequentially by sending a sequence of causal descriptions depending on the message conveyed by the encoder and the side-information subsequence it has observed so far. The receiver reconstructs the source causally by producing on each time unit an estimate of the current source symbol based on what it has received so far. Given a reconstruction fidelity measure and a maximal allowed distortion, we derive the rates-distortion region for this setting and express it in terms of an auxiliary random variable. When the source and side-information are drawn from an independent identically distributed Gaussian law and the fidelity measure is the squared-error distortion we show that for the evaluation of the rates-distortion region it suffices to choose the auxiliary random variable to be jointly Gaussian with the source and side-information pair.