Message and Causal Asymmetric State Transmission over the State-Dependent Degraded Broadcast Channel

We study data transmission and asymmetric state communication over a state-dependent two-user discrete memoryless degraded broadcast channel. In our model the encoder, to whom the state information is available either strictly-causally or causally, in addition to transmitting data reliably to each of the users must also provide the 'higher quality' user with a description of the memoryless state sequence with some defined fidelity. The capacity region - i.e. the set of attainable rate-pairs given a maximal-allowed distortion when the state reconstruction fidelity is measured using a single-letter distortion function - is computed in the absence as well as in the presence of feedback from the 'higher quality' output to the encoder. In the no-feedback cases we also study the constrained source-coding problem wherein the encoder is required to form a reconstruction that should predict the decoder's reconstruction within a given distortion, and establish the respective capacity regions. Finally, in the strictly-causal setting without feedback and when the encoder is required to form a reconstruction that should coincide with the decoder's reconstruction with probability close to one we characterize the Common-Reconstruction capacity region.