Erasure coding for real-time streaming

We consider a real-time streaming system where messages are created sequentially at the source, and are encoded for transmission over a packet erasure channel. Each message must subsequently be decoded at the receiver within a given delay from its creation time. We consider code design and maximum message rates when all messages must be decodable by their respective deadlines under a specified set of erasure patterns (erasure model). Specifically, we provide a code construction that achieves the optimal rate for an asymptotic number of messages, under erasure models containing a limited number of erasures per coding window, per sliding window, and containing erasure bursts of a limited length.