标题： 及时跟踪具有单比特量化的一维维纳过程 显示英文标题

标题： Timely Tracking of a Wiener Process With Single Bit Quantization

摘要： 我们考虑通过利用单比特量化策略在周期采样的情况下，使用节能传感器及时跟踪维纳过程的问题。与传统的单比特量化器不同，传统的单比特量化器仅利用传输的比特来传递信息，在我们的码本中，我们使用一个额外的“$\emptyset$”符号来编码“\emph{不传输}”事件。因此，我们的量化函数由三个决策区域组成，而不是传统的两个区域。 首先，我们提出了一种最优量化方法，其中最优量化函数是通过对量化误差分布进行跟踪得到的。然而，这种方法需要高计算成本，并且可能不适用于节能传感器。因此，我们提出了两种附加的低复杂度方法。 在最后一位感知方法中，三种预定义的量化函数对双方设备都可用，并且它们根据最后传输的比特切换量化函数。在高斯近似方法中，我们假设量化误差可以近似为高斯分布，从而计算出单一的量化函数。虽然以前的方法需要恒定延迟假设，但这种方法也可以处理随机延迟。 我们观察到，这三种方法在均方误差和传输成本方面表现相似。 显示英文摘要

摘要： We consider the problem of timely tracking of a Wiener process via an energy-conserving sensor by utilizing a single bit quantization strategy under periodic sampling. Contrary to conventional single bit quantizers which only utilize the transmitted bit to convey information, in our codebook, we use an additional `$\emptyset$' symbol to encode the event of \emph{not transmitting}. Thus, our quantization functions are composed of three decision regions as opposed to the conventional two regions. First, we propose an optimum quantization method in which the optimum quantization functions are obtained by tracking the distributions of the quantization error. However, this method requires a high computational cost and might not be applicable for energy-conserving sensors. Thus, we propose two additional low complexity methods. In the last-bit aware method, three predefined quantization functions are available to both devices, and they switch the quantization function based on the last transmitted bit. With the Gaussian approximation method, we calculate a single quantization function by assuming that the quantization error can be approximated as Gaussian. While previous methods require a constant delay assumption, this method also works for random delay. We observe that all three methods perform similarly in terms of mean-squared error and transmission cost.