Capacity of Erasure Broadcast Channels with Single-User Delayed CSI and Common Messages

摘要

SG downlink communications are expected to suffer more from the intermittent link connectivity, and studying the erasure broadcast channel (BC) provides the fundamental understanding of their performance. Recently, the capacity region of two-user erasure BC with single-user delayed channel state information (CSI) was characterized, where one receiver does not provide its channel state to the transmitter and the other receiver, while the other receiver feeds back its state globally with unit delay. Surprisingly, the capacity region with single-user delayed CSI matches that of the erasure BC with global delayed CSI of both users. When two links have same erasure probabilities, this result is valid even when a common message intended for both users is required besides two private messages. The capacity in this case is easily achieved by adding a phase multicasting the common message after the transmission of private messages. However, when erasure probabilities are unequal, this scheme is clearly not capacity-achieving since the rate of the last phase will be limited by the weaker user having larger erasure probability. We propose a scheme which transmits the common message with rate higher than the link capacity of the weaker user in the last phase but still can ensure the decodability. The key is to simultaneously create equations of the common message at the weaker receiver and re-transmit private bits before the last phase. The proposed scheme achieves the converse under unequal link erasure probabilities, and the capacity with common and private messages is fully characterized under single-user delayed CSI.