Multiplexed Coding for Multiple Streams With Different Decoding Delays

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.