Comparison of Photonic Reservoir Computing Systems for Fiber Transmission Equalization

Abstract

In recent years, various methods, architectures, and implementations have been proposed to realize hardware-based reservoir computing (RC) for a range of classification and prediction tasks. Here we compare two photonic platforms that owe their computational nonlinearity to an optically injected semiconductor laser and to the optical transmission function of a Mach-Zehnder modulator, respectively. We numerically compare these platforms in a delay-based reservoir computing framework, in particular exploring their ability to perform equalization tasks on nonlinearly distorted signals at the output of a fiber-optic transmission line. Although the non-linear processing provided by the two systems is different, both produce a substantial reduction of the bit-error-rate (BER) for such signals of up to several orders of magnitude. We show that the obtained equalization performance depends significantly on the operating conditions of the physical systems, the size of the reservoir and the output layer training method.

Limitations of the Recall Capabilities in Delay-Based Reservoir Computing Systems

“…The laser in our case is governed by a Hopf normal form. The output dimension of the system is in this example 4 capabilities from time series predictions [27,28] over an equalization task on nonlinearly distorted signals [29] up to fast word recognition [30]. More general analysis showed the general and task-independent computational capabilities of semiconductor lasers [31].…”

Emulating complex networks with a single delay differential equation

“…where a = W x −1 for > 1 and a 1 = g(W in u), (45) up to exponentially small terms. The reason for this limit behavior lies in the nature of the local couplings.…”

“…Machine Learning is another rapidly developing application area of delay systems [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. It is shown recently that DDEs can successfully realize a reservoir computing setup, theoretically [41][42][43][44]46,[48][49][50], and implemented in optoelectronic hardware [30,32,39].…”

Comprehensive Performance Analysis of a VCSEL-Based Photonic Reservoir Computer

“…Called a Time Delay Reservoir (TDR), this concept has been highly useful to develop photonic ANNs based on different devices [8]- [10]. Amongst these, Semiconductor Lasers (SLs) have shown to be excellent candidates for photonic TDRs due to their GHz speed and highly complex dynamics, demonstrating successful ultrafast operation across multiple processing tasks [5], [11]. Vertical Cavity Surface Emitting Lasers (VCSELs) are particularly attractive for photonic RC systems due to their technological maturity, reduced cost, low energy operation, ease of integration in 2D/3D architectures, unique polarization properties, and for their extraordinary potential bandwidth that could rise the processing rate to THz [12], [13].…”