论文标题
跟踪每单位沟通有限的自动回归过程
Tracking an Auto-Regressive Process with Limited Communication per Unit Time
论文作者
论文摘要
发件人观察到来自高维AR [1]过程的样品，该样本只能传达每单位时间的有限多数位与接收器。接收者试图每次实时立即对过程值进行估计。我们考虑了一个慢采样制度中的时间间隙通信模型，在两个采样瞬间之间发生多个通信插槽。我们提出了一个连续的更新方案，该方案使用采样瞬间之间的通信来完善对最新样本的估计并研究以下问题：收集多个插槽的交流以发送更好的精制估计，使接收者更加详细地等待每次改进，或者要快速但放松并在每个沟通机会中发送新信息？我们表明，具有理想球形代码的快速但松散的连续更新方案对于大尺寸而言是普遍渐近的最佳选择。但是，固定尺寸的大多数实用量化代码不符合此最优性所需的理想性能，并且它们通常会以固定添加误差的形式具有偏见。有趣的是，我们的分析表明，在存在此类错误的情况下，快速但松动的方案不是一个最佳选择，并且明智选择的更新频率优于它。
Samples from a high-dimensional AR[1] process are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.
