Binomial training algorithm for neuromorphic photonics applied to channel equalization

In this work, we propose, for the first time, to the best of our knowledge, a photonic time-delayed neural network with a binomial training algorithm for channel equalization. The developed optical neural network structure, composed of temporal delay lines with phase and amplitude modulators, is numerically implemented, with the training and subsequent evaluation performed using experimentally acquired data from a real optical transmission system, enabling improvements in the bit error rate (BER) and the eye diagram of on-off keying (OOK) input signals at 10 Gb/s in the case of 100 km single-mode fiber transmission. The photonic time-delayed neural network with eight delay lines proposed proved to be efficient even in worst-case scenarios, restoring a highly degraded signal with a fully closed-eye diagram, making it open. This paper also evaluated the generalization capacity of the photonic neural network developed with 30 distinct experimental datasets. After equalization, 93.3% of the transmitted bit sequences stand below the forward error correction (FEC) limit, demonstrating a satisfactory generalization capability. Thus, the contribution of our work lies in the combined integration of a delay-line-based photonic neural structure with a binomial combinatorial training method. This algorithm enables discrete, hardware-friendly optimization over amplitude and phase modulators, making it well-suited for photonic integrated circuits.