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In a real-time transmission scenario, messages are transmitted through achannel that is subject to packet loss. The destination must recover themessages within the required deadline. In this paper, we consider a setup wheretwo different types of messages with distinct decoding deadlines aretransmitted through a channel that can introduce burst erasures of a length atmost $B$, 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 decodingdeadline $T_v$ ($T_v > T_u$) is referred to as a less urgent message.  We propose a merging method to encode two message streams of differenturgency 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 aclosed-form upper limit on its achievable sum rate. Moreover, we presentexplicit constructions within a finite field that scales quadratically with theimposed delay, ensuring adherence to the upper bound. In a given parameterconfiguration, we rigorously demonstrate that the sum rate of our proposedstreaming codes consistently surpasses that of separate encoding, which servesas a baseline for comparison.

Multiplexed Streaming Codes for Messages With Different Decoding Delays in Channel with Burst and Random Erasures