Passive Phase-Aware Hadamard Decoding: Analytical and Machine-Learning Approaches
Hadamard-coded optical receivers typically rely on stable interference conditions, which can motivate active optical phase control. We investigate a fixed, intensity-only decoder that embeds four populated modes in an eight-mode interferometer and provides six complementary trigonometric observables through simultaneous power measurements. An analytic transition decoder uses the resulting sign-change patterns without continuous optical phase stabilization. The receiver's intensity-to-observable map is inverted exactly, and an identifiability analysis characterizes exceptional phase configurations and conditional noise sensitivity. An ideal, equal-photon-budget comparison with conventional four-port Hadamard decoding illustrates the potential value of the additional outputs without implying an unconditional advantage. Measurements on programmable photonic processors give 96.19% accuracy for the analytical decoding experiment; a complementary machine-learning analysis reports 98.31% on a held-out experimental trace. These results demonstrate an intensity-only, phase-aware approach to differential Hadamard decoding under the tested conditions, while larger codebooks and hardware-level energy benefits remain topics for future investigation.