  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.
