Capacity Results for Erasure Broadcast Channels with Intermittent Feedback

Abstract

Recently, we showed that, rather surprisingly, the capacity region of the two-user erasure broadcast channel with global delayed channel state information (CSI) can be achieved with single-user delayed CSI only. More precisely, we assumed one receiver does not provide its channel state to the other two nodes (the other receiver and the transmitter), while the other receiver reveals its state globally with unit delay. In this work, we consider a more general setting in which feedback links are intermittent. To be precise, at any time instant, each receiver broadcasts its CSI, and this information either becomes available to the other two nodes or gets erased. For this setting, we develop a new set of outer bounds to capture the intermittent nature of the feedback links. These outer bounds depend on the probability that both feedback links are erased rather than the individual erasure probability of each feedback link. This result matches our earlier findings for the single-user delayed CSI scenario. We also provide a capacity-achieving recursive communication protocol for the scenario in which feedback links are fully correlated.