Matched and Euclidean-Mismatched Decoding on Fourier-Curve Constellations with Tangent Noise

2026-04-16

AI Summary

This study investigates the performance gap and error behavior between matched decoding and Euclidean mismatched decoding in finite Fourier curve constellations under tangent-space artificial noise. By modeling the noise as a rank-one covariance Gaussian perturbation, the authors derive exact pairwise error probabilities under Euclidean metrics for arbitrary symbol pairs and establish a Gaussian expectation expression for matched decoding over bi-tangent orthogonal symbol pairs. For the first time, they analytically reveal how noise scaling and constellation density jointly affect mismatched decoding performance. In the case of uniform even-sized constellations, explicit distance spectra and symbol error upper bounds are provided for all offset classes. Full-codebook Monte Carlo simulations validate the theoretical results, confirming the exactness of matched decoding for antipodal symbol pairs and establishing a new analytical benchmark for evaluating mismatched decoding performance.

Technology Category

• Machine Learning: Evaluation and Analysis
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

We study matched and Euclidean-mismatched decoding on finite Fourier-curve constellations with tangent-space artificial noise. Each hypothesis induces a Gaussian law with symbol-dependent rank-one covariance. We derive exact Euclidean pairwise errors for arbitrary pairs and an exact Gaussian-expectation representation for matched decoding on bilaterally tangent-orthogonal pairs. For uniform even constellations, the Euclidean side yields explicit distance spectra and symbol-error bounds across all offset classes; the matched side is exact on antipodal pairs and benchmarked numerically at the full-codebook level via Monte Carlo. By isolating the detection-theoretic consequence of tangent-space artificial noise, these results clarify analytically how noise fraction and constellation density enter the mismatch behavior; secrecy-rate implications require additional channel and adversary modeling.

Problem

• matched decoding
• Euclidean-mismatched decoding
• Fourier-curve constellations
• tangent noise
• pairwise error

Innovation

• Fourier-curve constellations
• tangent-space noise
• matched decoding
• Euclidean-mismatched decoding
• pairwise error probability