Broadcast channel with degraded source random variables and receiver side information

The problem of sending a pair of correlated sources through a broadcast channel with correlated side information at the receivers is studied from a joint source-channel coding perspective. Sufficient and necessary conditions are provided for reliable transmission. The two conditions are identical except for the left-hand side of one of three inequalities. For two special cases the problem is solved completely: when one side information is a function of the sources, and when a certain Markov property is satisfied on the sources and side information.