On the Capacity Region of Gaussian Broadcast Channels under Two-Sided Noisy Feedback

The capacity region of several multiuser models in information theory can be enlarged by utilizing feedback of the received symbols. This is in contradiction to the discrete memoryless case, where feedback is known not to change the capacity. In this paper, we consider two broadcast models with noisy feedback from both the receivers. The models are derived from a standard memoryless scalar GBC, where two intermediate passive nodes are assumed to be observing the transmissions via separate noisy links corrupted by independent AWGN. In our first model, the scalar output from each intermediate node is passed through two additional independent AWGN links, called feedback and forward links. The output of the feedback link is observed by the transmitter as feedback, whereas only the forward link is observed by the corresponding decoder. We derive conditions that are both necessary and sufficient for feedback to enlarge the capacity region. In the second model, the two outputs of a standard GBC are observed by the respective decoders, but the transmitter observes the sum of the symbols at the receivers using causal feedback. We show that such a feedback has no effect on the capacity region.