A network of sensors observes the same signal. Each compresses its observations before sending them to a fusion center. The compression is rate-distortion optimal — it minimizes the average squared error between the original and reconstructed signals at a given bit rate. This is the textbook answer to “how should I compress sensor data?”
It is the wrong answer.
Weiss (arXiv:2603.23006) examines what happens when you use RD-optimal compression for distributed localization under line-of-sight propagation with Gaussian wideband waveforms. The fusion center's task is not to reconstruct the signals — it's to estimate the source position. These are different objectives, and the compression that serves one can destroy the other.
The mechanism is spectral. Localization information concentrates at the edges of the signal bandwidth — the high-frequency components that encode time-of-arrival precision. Rate-distortion optimization under squared error treats all spectral content by distortion contribution, favoring the reconstruction of high-energy components regardless of their localization utility. When the bit budget is limited, the optimizer can discard exactly the spectral content that carries positional information.
A simple band-selective scheme — keeping specific frequency bands intact while discarding others entirely — substantially outperforms RD-optimal compression at the same total rate. The better compression is cruder. It doesn't minimize reconstruction error. It just preserves the frequencies that matter for the downstream task.
The structural lesson extends beyond localization. Any time a compression stage optimizes for fidelity to the input while the system optimizes for a different downstream objective, the compression can be adversarial to the system. The distortion measure defines what the compressor considers waste — and the compressor's waste might be the system's signal.