Optimal Coding Strategies for Bidirectional Broadcast Channels Under Channel Uncertainty

Bidirectional relaying is a promising approach to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. Bidirectional relaying applies to three-node networks, where a relay establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. First, the two nodes transmit their messages to the relay which decodes them. Then, the relay broadcasts a reencoded message in such a way that both nodes can decode their intended message using their own message as side information. We consider uncertainty in the channel state information (CSI) and assume that all nodes only know that the channel over which the transmission takes place is from a pre-specified set of channels. In this work, we concentrate on the second phase, which is called the compound bidirectional broadcast channel. We present a robust coding strategy which enables reliable communication under channel uncertainty and show that this strategy actually achieves the compound capacity. Further, we analyze scenarios where either the receivers or the transmitter have perfect CSI. We show that CSI at the receivers does not affect the maximal achievable rates, while CSI at the transmitter improves the capacity region. A numerical example and a game-theoretic interpretation complete this work.