Bidirectional Broadcast Channel With Random States Noncausally Known at the Encoder

In this work, coding for a discrete memoryless broadcast channel with random states and two receivers is studied. Each receiver knows one of the two information messages at the sender and wants to know the other one. Assuming the channel state sequence is noncausally known at the sender, an achievable rate region based on the Gel'fand–Pinsker coding strategy is derived and an outer bound to the capacity region is presented. Further, the capacity region for the special case where in addition one receiver knows the channel state is established. An equivalent characterization of an achievable rate region characterizing convex set is derived using Shannon's concept of transmit strategies. This characterization is used to derive an Arimoto–Blahut-like algorithm including a stopping criterion to compute the weighted rate-sum maxima, which can be used to characterize the whole achievable rate region. The tradeoff between the input distribution and the impact of the channel state, the necessity of the time-sharing operation, and the additive Gaussian channel case assuming Costa's choice of auxiliary random variables are discussed by examples.