Multiplexed Streaming Codes for Messages With Different Decoding Delays in Channel with Burst and Random Erasures
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In a real-time transmission scenario, messages are transmitted through a channel that is subject to packet loss. The destination must recover the messages within the required deadline. In this paper, we consider a setup where two different types of messages with distinct decoding deadlines are transmitted through a channel that can introduce burst erasures of a length at most B, or N random erasures. The message with a short decoding deadline T_u is referred to as an urgent message, while the other one with a decoding deadline T_v (T_v > T_u) is referred to as a less urgent message. We propose a merging method to encode two message streams of different urgency levels into a single flow. We consider the scenario where T_v > T_u + B. We establish that any coding strategy based on this merging approach has a closed-form upper limit on its achievable sum rate. Moreover, we present explicit constructions within a finite field that scales quadratically with the imposed delay, ensuring adherence to the upper bound. In a given parameter configuration, we rigorously demonstrate that the sum rate of our proposed streaming codes consistently surpasses that of separate encoding, which serves as a baseline for comparison.
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