We consider a communication setup where two source streams with different decoding deadlines, must be simultaneously transmitted over a single channel subjected to burst erasures. The encoder multiplexes the two source streams into a single stream of channel-packets. The decoder must recover the two source streams sequentially by their corresponding deadlines. One of the streams, the urgent stream, has a smaller delay than the other stream. We study the capacity region for such a setting for a certain range of system parameters. We divide the system into three different cases based on the relative values of the delays. For each case we provide achievability and converse bounds, which match under certain conditions. Our proposed coding scheme involves a careful construction of the parity check packets by jointly coding across the two streams despite different deadlines. Interestingly it is possible to transmit the urgent stream at a certain positive rate even when the sum rate equals the capacity associated with the less urgent stream. A separation based approach where we apply separate single-stream codes to each stream is suboptimal. Although our capacity results assume a simplistic channel model with a single erasure burst, we further demonstrate that our proposed code constructions also provide significant performance gains in simulations over statistical channel models with random bursts.

We study a setting where two source streams with different decoding deadlines must be transmitted over a burst erasure channel. The source streams are multiplexed into a single stream of channel-packets at the encoder and transmitted over a packet erasure channel. The decoder must recover the source-packets within each stream sequentially, by their corresponding deadlines. We consider the burst-erasure channel model and characterize the capacity region for a certain range of system parameters. We show that the operation of the system can be divided into three different regimes based on the relative values of decoding deadlines. On the achievability side, we show that jointly coding across the two streams, despite their different deadlines, is necessary to achieve capacity. On the converse side we develop information theoretic outer bounds on the capacity region. We find that the capacity region exhibits a “corner point” where we can transmit the urgent stream at a positive rate, yet attain a sum-rate equal to the capacity of the non-urgent stream.

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.