Broadcasting with feedback

The availability of noiseless feedback in an additive white Gaussian noise channel can considerably improve the rate of decay of error-probability with blocklength [1]. A doubly exponential error decay can be attained even in the presence of an additive interference term non-causally known at the transmitter alone [2]. Adapting this result, we show that the capacity region of a Gaussian broadcast channel (GBC) can be enlarged even when the feedback is available from only one of the receivers. We also demonstrate an explicit capacity achieving transmission strategy for the physically degraded GBC with feedback, with the decay of error doubly exponential in the number of transmissions specific to a given message.