# Joint Extremum Compression and Detection of a Time-Delayed Signal for Distributed Sensing

arXiv: https://arxiv.org/abs/2607.10874 · HTML: https://mlsanity.com/paper/2607.10874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 54 references that are in the map.
- First posted on arXiv 12 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms](https://mlsanity.com/paper/2001.08877/) (2020)
- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [One-Bit MUSIC](https://mlsanity.com/paper/1901.05109/) (2019)
- [Distributed Estimation of Gaussian Correlations](https://mlsanity.com/paper/1805.12472/) (2018)
- [A Fundamental Limit of Distributed Hypothesis Testing Under Memoryless Quantization](https://mlsanity.com/paper/2206.12232/) (2022)
- [One-Bit Direct Position Determination of Narrowband Gaussian Signals](https://mlsanity.com/paper/2010.15640/) (2020)
- [A Joint Data Compression and Time-Delay Estimation Method For Distributed Systems via Extremum Encoding](https://mlsanity.com/paper/2404.09244/) (2024)
- [Distributed Blind Source Separation based on FastICA](https://mlsanity.com/paper/2410.19112/) (2024)
- [Multi-bit Distributed Detection of Sparse Stochastic Signals over Error-Prone Reporting Channels](https://mlsanity.com/paper/2411.03612/) (2024)
- [Extremum Encoding for Joint Baseband Signal Compression and Time-Delay Estimation for Distributed Systems](https://mlsanity.com/paper/2412.18334/) (2024)
- [Extremum-Based Joint Compression and Detection for Distributed Sensing](https://mlsanity.com/paper/2603.27733/) (2026)

## Abstract (arXiv)

We study the problem of joint compression and detection in distributed sensing systems, motivated by applications such as device-to-device connectivity in IoT networks and distributed radar. In such systems, spatially separated sensors must collaboratively decide whether their observations stem from a common underlying signal, while communicating over highly bandwidth-limited links. We consider a fundamental, insightful model in which one sensor (the encoder) observes a continuous-time realization of a stationary bandlimited Gaussian process, while the other sensor (the decoder) observes a delayed and noisy version of that signal, with an unknown delay. The encoder is allowed to transmit only a k-bit message to the decoder to assist in making a binary decision: either the observations are statistically independent, or they are time-shifted noisy versions of the same signal. We propose a low-complexity extremum-based scheme that exploits the structure of the signal to enable reliable decision-making under tight communication constraints. We derive nonasymptotic upper bounds on the false alarm and mis-detection probabilities of our method, as well as a simplified asymptotic bound for the latter. Representative simulations demonstrate that the proposed scheme outperforms the prevalent 1-bit-per-sample quantization baseline and a Fisher-information-based compression benchmark, while closely approaching an information-theoretic (nonrealizable) rate-distortion benchmark.