Streaming Erasure Codes over the Multiple Access Relay Channel

Applications where multiple users communicate with a common server and desire low latency are common and increasing. This paper studies a network with two source nodes, one relay node and a destination node, where each source nodes wishes to transmit a sequence of messages, through the relay, to the destination, who is required to decode the messages with a strict delay constraint $T$. The network with a single source node has been studied in \cite{Silas2019}. We start by introducing two important tools: the delay spectrum, which generalizes delay-constrained point-to-point transmission, and concatenation, which, similar to time sharing, allows combinations of different codes in order to achieve a desired regime of operation. Using these tools, we are able to generalize the two schemes previously presented in \cite{Silas2019}, and propose a novel scheme which allows us to achieve optimal rates under a set of well-defined conditions. Such novel scheme is further optimized in order to improve the achievable rates in the scenarios where the conditions for optimality are not met.