Broadcast Channels and Input-Cost Side Information

We consider two problems: the first one is input constrained channels where the cost function depends on a state, and the state is known only to the encoder. We show that this model is similar both in theoretical aspects and in practical coding aspects to the problem of source coding with distortion side information. We explore the capacity loss due to not knowing the cost state at the decoder and show that it is small under various assumptions. This model plays an important role in the second problem we consider, which is broadcast channel. We explore the gap between the best known single letter achievable region and the true capacity region, using tools developed for the first problem.