Timely Tracking of a Wiener Process With Single Bit Quantization

TL;DR

This paper introduces a novel single bit quantization strategy for tracking a Wiener process with an energy-efficient sensor, incorporating an additional symbol for non-transmission, and proposes three methods balancing accuracy and computational complexity.

Contribution

It presents a new quantization scheme with three decision regions and develops three methods, including an optimal, a low-complexity, and a Gaussian approximation approach.

Findings

All three methods achieve similar mean-squared error performance.

The methods effectively handle random delays in transmission.

The proposed strategies improve energy efficiency in process tracking.

Abstract

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.