Streaming Codes for Multicast Over Burst Erasure Channels
Ahmed Badr, Devin Lui, Ashish J. Khisti · IEEE Transactions on Information Theory · 2015
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 Ti, while its channel can introduce an erasure burst of maximum length Bi, 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≥ B2or 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 T12and T21+ 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 T21+ B1, we establish upper and lower bounds on the capacity and characterize the exact capacity when either T1= B1or 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.