Optimal Streaming Erasure Codes over the Three-Node Relay Network

This paper investigates low-latency streaming codes for a three-node relay network. The source transmits a sequence of messages (streaming messages) to the destination through the relay between them, where the first-hop channel from the source to the relay and the second-hop channel from the relay to the destination are subject to packet erasures. Every source message must be recovered perfectly at the destination subject to a maximum decoding delay of T time slots, meaning that a message generated at a time slot must be recovered within the subsequent T time slots. In any sliding window of T + 1 time slots, we assume no more than N-1 and N-2 erasures are introduced by the first-hop channel and second-hop channel respectively. Under this channel loss assumption, we fully characterize the maximum achievable rate in terms of T, N-1 and N-2.