On multiterminal source coding with list decoding constraints

We consider the Heegard-Berger source coding problem with multiple decoders, and list decoding constraints for some of the decoders. The decoders with list decoding constraint output a list of likely source sequences and we desire the true source sequence to be in the list with high probability. When list decoding constraints are imposed on all decoders, we characterize the rate-list size region for arbitrary distributed source and side informations. For the two decoders setting with list decoding constraint on one decoder and per-symbol distortion constraint on the other, we characterize the rate-distortion-list size region when the side information of the decoder with per-symbol distortion constraint is less noisy than the side information of the list decoding decoder. We then extend this result to a three decoders setting. For the case where the side information of the list decoding decoder is less noisy than the side information of the decoder with per-symbol distortion constraint, we characterize the rate-distortion-list size region under an additional common reconstruction constraint at the encoder.