# Source Coding for a Wiener Process

arXiv: https://arxiv.org/abs/2504.01929 · HTML: https://mlsanity.com/paper/2504.01929/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 4 of 4)

- [Age of Information: An Introduction and Survey](https://mlsanity.com/paper/2007.08564/) (2020)
- [Selective Encoding Policies for Maximizing Information Freshness](https://mlsanity.com/paper/2004.06091/) (2020)
- [Timely Multi-Process Estimation Over Erasure Channels With and Without Feedback: Signal-Independent Policies](https://mlsanity.com/paper/2303.13485/) (2023)
- [The Role of Early Sampling in Age of Information Minimization in the Presence of ACK Delays](https://mlsanity.com/paper/2308.07905/) (2023)

## Built on by (most cited first, 1 of 1)

- [Timely Tracking of a Wiener Process With Single Bit Quantization](https://mlsanity.com/paper/2505.01419/) (2025)

## Abstract (arXiv)

We develop a novel source coding strategy for sampling and monitoring of a Wiener process. For the encoding process, we employ a four level ``quantization'' scheme, which employs monotone function thresholds as opposed to fixed constant thresholds. Leveraging the hitting times of the Wiener process with these thresholds, we devise a sampling and encoding strategy which does not incur any quantization errors. We give analytical expressions for the mean squared error (MSE) and find the optimal source code lengths to minimize the MSE under this monotone function threshold scheme, subject to a sampling rate constraint.