Streaming Codes for Multicast Over Burst Erasure Channels

We study low-delay erasure correction codes in a real-time streaming setup. The encoder observes a stream of source packets and outputs the channel packets in a causal fashion, which are broadcast to two receivers over burst-erasure channels. Each receiver must decode the source packets sequentially with a deadline of T_i, while its channel can introduce an erasure burst of maximum length B_i, where i ∈ {1,2} and w.l.o.g. B₂ > B1. We study the associated capacity as a function of the burst lengths and decoding deadlines. We observe that the operation of the system can be divided into two main regimes. The so-called large-delay regime corresponds to the case when either T₁ ≥ B₂ or T₂ ≥ B₁ + B₂. We show that for these parameters, the optimal code is obtained through simple modifications of previously proposed single-user codes by Martinian et al. and the diversity embedded streaming codes proposed by Badr et al. When both T₁ <; B₂ and T₂ <; B₁ + B₂, the system is said to be in the low-delay regime. We propose a new code construction and establish its optimality when T₂ ≥ T₁ + B₁. In the case when T₂ <; T₁ + B₁, we establish upper and lower bounds on the capacity and characterize the exact capacity when either T₁ = B₁ or T₂ = B₂. Our upper bounds in the low-delay regime are based on novel information theoretic arguments that capture the tension between the decoding constraints at the two receivers.