Interactive Decoding of a Broadcast Message

We develop communication strategies for the rate-constrained interactive decoding of a message broadcast to a group of interested users. This situation differs from the relay channel in that all users are interested in the transmitted message, and from the broadcast channel because no user can decode on its own. We focus on two-user scenarios, and describe a baseline strategy that uses ideas of coding with decoder side information. One user acts initially as a relay for the other. That other user then decodes the message and sends back random parity bits, enabling the first user to decode. We show how to improve on this scheme’s performance through a conversation consisting of multiple rounds of discussion. While there are now more messages, each message is shorter, lowering the overall rate of the conversation. Such multi-round conversations can be more efficient because earlier messages serve as side information known at both encoder and decoder. We illustrate these ideas for binary erasure channels. We show that multi-round conversations can decode using less overall rate than is possible with the single-round scheme.