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 model that introduces either one burst erasure of length at most $B$, or $N$ random erasures in any fixed-sized sliding window. The message with a short decoding deadline $T_{\mathrm{u}}$ is referred to as an urgent message, while the other one with a decoding deadline $T_{\mathrm{v}}$ ($T_{\mathrm{v}} > T_{\mathrm{u}}$) is referred to as a less urgent message. We consider the scenario where $T_{\mathrm{v}} > T_{\mathrm{u}} + B$ and propose a non-trivial achievable region $\mathcal{R}$ for the aforementioned channel model. We propose a novel merging approach to encode two message streams of different urgency levels into a single flow and present explicit constructions for encoding, contributing to the establishment of the achievability of region $\mathcal{R}$. Our comprehensive analysis demonstrates that this region encompasses the rate pairs of existing encoding schemes and coincides with the capacity region in burst channel scenarios. Lastly, we investigate the property of the achievable region $\mathcal{R}$, proving that it is the largest one obtained from all the rate pairs under the merging method.

翻译：在实时传输场景中，消息通过易受数据包丢失影响的信道进行传输。接收端必须在规定时限内恢复消息。本文研究一种传输设置：两种具有不同解码时限的消息通过信道模型传输，该信道会在任意固定大小的滑动窗口内引入一个长度至多为 $B$ 的突发擦除，或 $N$ 个随机擦除。解码时限较短 $T_{\mathrm{u}}$ 的消息称为紧急消息，而解码时限 $T_{\mathrm{v}}$（$T_{\mathrm{v}} > T_{\mathrm{u}}$）较长的消息称为非紧急消息。我们考虑 $T_{\mathrm{v}} > T_{\mathrm{u}} + B$ 的场景，并为上述信道模型提出了一个非平凡的、可达的区域 $\mathcal{R}$。我们提出了一种新颖的合并方法，将两个不同紧急程度的消息流编码为单一数据流，并给出了显式的编码构造，从而为区域 $\mathcal{R}$ 的可达性提供了支撑。全面的分析表明，该区域包含了现有编码方案的速率对，并且在突发信道场景中与容量区域重合。最后，我们研究了可达区域 $\mathcal{R}$ 的性质，证明其是通过合并方法获得的所有速率对中最大的区域。