On State-Dependent Streaming Erasure Codes over the Three-Node Relay Network

This paper investigates low-latency adaptive streaming codes for a three-node relay network. A source node transmits a sequence of source packets (messages) to the destination through a relay node. We focus on a particular case where the link connecting the source and relay nodes is almost reliable, but the link connecting the relay to the destination is not. The relay node can observe the erasure pattern that has occurred in the transmission between the source node and itself and adapt its relaying strategy based on that observation. Every source packet must be perfectly recovered by the destination with a strict delay T, as long as the number of erasures in the relay-to-destination link lies below some design parameter. We then characterize capacity as a function of such design parameter. The achievability scheme employs two different relaying strategies, based on whether an erasure has or has not occurred in the link from source to relay. The converse is proven by analyzing a periodic erasure pattern and lower bounding the minimum redundancy across channel packets. We show that the achievable rate can be improved compared to non-adaptive schemes previously proposed, indicating that exploiting the knowledge of the erasure pattern by the relay node is essential in achieving capacity.