In a world of extreme noise, the 'distance' between signals doesn't matter anymore—only the angle you look at them from.
April 14, 2026
Original Paper
From Distance to Angle: One-Shot Detection Under Additive White Cauchy Noise
arXiv · 2604.08949
The Takeaway
Standard communication theory says we recover info by measuring the distance between signals, but this fails in heavy 'Cauchy' noise environments. This research proves that in chaotic interference, we must switch to purely geometric, angle-based detection to get data through.
From the abstract
We study one-shot detection under additive white Cauchy noise (AWCN) using finite constellations, with emphasis on the geometric mechanisms governing symbol-level reliability. Under isotropic Cauchy noise, the maximum-likelihood rule induces the same Euclidean Voronoi decision regions as in the Gaussian case, so the distinction lies not in the decision geometry itself but in how probability mass is distributed over these fixed regions. In the small-noise regime, we derive a reciprocal distance-s