Source coding with composite side information at the decoder

We consider a source-coding scenario in which composite side information is available at the decoder, viz. part of it is known non-causally, whereas the other part is available only causally - by this combining the treatment of Wyner and Ziv with that of Weissman and El Gamal. We then consider the joint source-channel coding problem of transmitting a source with composite side information at the decoder over a channel with composite side information at the encoder. We show that the separation principle between source coding with composite side information and its dual channel problem holds, thus extending the result of Merhav and Shamai to the case of composite side informations. These results provide a unified framework for treating the causal side information case, the non-causal stateinformation case, as well as a mixture of the two.