Arimoto-Blahut algorithm for the bidirectional broadcast channel with side information

The bidirectional broadcast channel with random states known at the encoder denotes a broadcast channel with two receivers where each receiver knows the message intended for the other and the transmitter knows the channel state. For such a channel we derive an Arimoto-Blahut-like algorithm to compute the weighted-rate sum maxima. To this end we provide an equivalent characterization of the achievable rate region using Shannon´s method of transmit strategies, which we use to show that the optimal coding does not gain from time-sharing. Finally, the trade-off of the input distribution and the impact of the random state is discussed in two examples.