On the Optimal Delay Growth Rate of Multi-Hop Line Networks: Asymptotically Delay-Optimal Designs and the Corresponding Error Exponents
On the Optimal Delay Growth Rate of Multi-Hop Line Networks: Asymptotically Delay-Optimal Designs and the Corresponding Error Exponents
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DOI：
10.1109/tit.2023.3283802
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发表时间：
2023-10
影响因子：
2.5
通讯作者：
Dennis Ogbe;Chih-Chun Wang;D. Love
中科院分区：
文献类型：
--
作者：
Dennis Ogbe;Chih-Chun Wang;D. Love
多跳线路网络已成为现代和日益密集的通信网络的重要抽象模型。此外，实时和关键任务服务的增长创造了对低延迟通信的高需求并增加了对低延迟通信的研究兴趣。这些事实的结合激发了从延迟与吞吐量的角度对 $L$ 跳线路网络的数据传输方案进行新的研究。为此，这项工作定义了一个称为目标吞吐量 $R$ 的延迟放大因子的指标，用 ${\mathsf {DAF}}(R)$ 表示，它表征了（渐近）延迟相对于跳数的增长率。我们表明，所有现有的中继方案，例如解码转发（DF），都有 $\lim _{R\nearrow C} {\mathsf {DAF}}(R)=\Omega (L)$ ，这与几十年来延迟相对于 $L$ 线性增长的看法是一致的。然后，我们设计一个满足 $\lim _{R\nearrow C} {\mathsf {DAF}}(R)=1$ 的方案，如果瓶颈跳是最后一跳，即其渐近延迟相对于 $L$ 不增长。结果表明，这种线性增长的延迟是现有 DF 设计的产物，并且可以通过新的以延迟为中心的解决方案来超越它并达到真正的基本极限。在这项工作的后半部分，我们进一步证明，如果允许变长编码和一位停止反馈，我们可以放宽最后一跳的条件瓶颈，并且对于任意线路网络达到 $\lim _{R\nearrow C} {\mathsf {DAF}}(R)= 1$。
Multi-hop line networks have emerged as an important abstract model for modern and increasingly dense communication networks. In addition, the growth of real-time and mission-critical services has created high demand for and increased research interest in low-latency communications. The combination of these facts motivates a new investigation of data transmission schemes for $L$ -hop line networks from a delay-vs-throughput perspective. To this end, this work defines a metric called the delay amplification factor for a target throughput $R$ , denoted by ${\mathsf {DAF}}(R)$ , which characterizes the growth rate of the (asymptotic) delay with respect to the number of hops. We show that all existing relay schemes, e.g., Decode-&-Forward (DF), have $\lim _{R\nearrow C} {\mathsf {DAF}}(R)=\Omega (L)$ , which is consistent with the decades-old perception that delay grows linearly with respect to $L$ . We then design a scheme satisfying $\lim _{R\nearrow C} {\mathsf {DAF}}(R)=1$ , if the bottleneck hop is the last hop, i.e., its asymptotic delay does not grow with respect to $L$ . The results imply that this linearly growing delay is an artifact of the existing DF designs, and it is possible to surpass it and attain the true fundamental limit with a new delay-centric solution. In the second half of this work, we further show that if variable-length coding and one-bit stop-feedback are allowed, we can relax the condition bottleneck being the last hop and attain $\lim _{R\nearrow C} {\mathsf {DAF}}(R)= 1$ for any arbitrary line networks.