State-Dependent Broadcast Channels with Reversible Input Constraints

joint message communication and input reconstruction problem over a two-user state-dependent degraded discrete-memoryless broadcast channel is considered. The state process is assumed to be independent and identically distributed (i.i.d.), and known non-causally at the transmitter as well as the non-degraded receiver. The two receivers have to decode the messages from the transmitter, while the degraded receiver also needs to estimate the channel input codeword to meet a prescribed distortion limit. A complete characterization of the optimal rates versus distortion performance is provided. The tight characterization is also illustrated by means of an example of an additive binary broadcast channel with a Hamming distortion constraint for the input reconstruction at the degraded receiver.