This paper investigates streaming codes for three-node relay networks under burst packet erasures with a delay constraint $T$. In any sliding window of $T+1$ consecutive packets, the source-to-relay and relay-to-destination channels may introduce burst erasures of lengths at most $b_1$ and $b_2$, respectively. Let $u = \max\{b_1, b_2\}$ and $v = \min\{b_1, b_2\}$. Singhvi et al. proposed a construction achieving the optimal rate when $u\mid (T-u-v)$. In this paper, we present an extended delay profile method that attains the optimal rate under a relaxed constraint $\frac{T - u - v}{2u - v} \leq \left\lfloor \frac{T - u - v}{u} \right\rfloor$ and it strictly cover restriction $u\mid (T-u-v)$. %Furthermore, we demonstrate that the optimal rate for streaming codes is not achievable when $0< T-u-v<v$ under the convolutional code framework.

翻译：本文研究在三节点中继网络中，针对突发数据包擦除且具有延迟约束$T$的流码设计。在任意长度为$T+1$个连续数据包的滑动窗口内，源节点到中继节点以及中继节点到目的节点的信道可能分别引入最大长度为$b_1$和$b_2$的突发擦除。令$u = \max\{b_1, b_2\}$，$v = \min\{b_1, b_2\}$。Singhvi等人提出了一种在$u\mid (T-u-v)$条件下达到最优速率的构造方法。本文提出一种扩展延迟剖面方法，在放宽的约束条件$\frac{T - u - v}{2u - v} \leq \left\lfloor \frac{T - u - v}{u} \right\rfloor$下实现最优速率，该条件严格覆盖了原限制$u\mid (T-u-v)$。%此外，我们证明在卷积码框架下，当$0< T-u-v<v$时无法实现流码的最优速率。