Channel Resolvability with a FullDuplex DecodeandForward Relay We study the minimum randomness required at a source node to approximately produce a chosen i.i.d. distribution at a destination, while a relay assists in the process. In the classical relay problem, the relay does not have any message of its own to transmit, and only retransmits a function of its observation. In the resolvability problem the variable of interest is the randomness rate, therefore we assume the relay does not have access to any randomness outside what it observes at its input, i.e., the relay output is a deterministic function of its input. A blockMarkov scheme is used in which the relay decodes the source message to assist with the approximation of the i.i.d. output. In addition, the relay extracts randomness from its noisy channel observation in each block and uses it in the next block to improve the resolvability rate. The careful handling of this randomness recycling, in order to avoid the introduction of unwanted dependencies, is a key part of the contribution of this paper.

Capacity Results for Erasure Broadcast Channels with Intermittent Feedback Recently, we showed that, rather surprisingly, the capacity region of the twouser erasure broadcast channel with global delayed channel state information (CSI) can be achieved with singleuser 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 singleuser delayed CSI scenario. We also provide a capacityachieving recursive communication protocol for the scenario in which feedback links are fully correlated.