Optimal Multiplexed Erasure Codes for Streaming Messages with Different Decoding Delays

Abstract

This paper considers multiplexing two sequences of messages with two different decoding delays over a packet erasure channel. In each time slot, the source constructs a packet based on the current and previous messages and transmits the packet, which may be erased when the packet travels from the source to the destination. The destination must perfectly recover every source message in the first sequence subject to a decoding delay T v and every source message in the second sequence subject to a shorter decoding delay T u ≤ T v . We assume that the channel loss model introduces a burst erasure of a fixed length B on the discrete timeline. Under this channel loss assumption, the capacity region for the case where T v ≤ T u + B was previously solved. In this paper, we fully characterize the capacity region for the remaining case T v > T u + B.