With the development of cloud computing, Internet of Things (IoT), virtual reality/augmented reality (VR/AR), ultra-high definition television (UHDTV) and artificial intelligence (AI) technology, global data center traffic is experiencing another wave of explosive growth, motivating the pressing requirements of high-bandwidth and low-power short-reach optical interconnects to provide the ubiquitous connectivity for massive processing units from advanced chips to large-scale data centers. In essence, communication technology is to transmit energy from one entity to another, where information is parsed with best probability at the receiver. Optics participate in the communication between two electrical entities will introduce extra electro-optical (EO) and optical-electro (OE) conversions, and how to build a concise and effective optical interconnects with minimized hardware and algorithm complexity will become a long-term research and development challenge.

Recently, a product of bandwidth density and energy efficiency is used as a figure-of-metric to evaluate the performance of the I/O technologies. It has been found that large penalties will occur when communications is leaving the chip, package and board [1]. Therefore, this minimalist optical interconnects design will present more significance for signaling length required for off-board and rack-scale communication as (1) this solution will directly compete with electrical counterparts in terms of energy, bandwidth density and cost, and (2) the shorter the communication distance, the much more connections required in the applications. Specifically, for the 100 Gbps optical I/O solution, intensity modulation and direct detection (IM-DD) scheme based on vertical cavity surface emitting laser (VCSEL) is still the most simplest solution benefiting from low power consumption and manufacturing cost, having been widely used with sustainable commercial success [2], [3], [4].

However, with the continuous improvement of single-channel bandwidth, this solution will suffer complex nonlinear distortion problem including relative intensity noise (RIN) of the laser, mode partition noise (MPN), mode dispersion in multimode fiber, nonlinear effects caused by bandwidth limitations of optoelectronic devices, and nonlinear interference caused by high-order modulation formats such as 4-level pulse amplitude modulation (PAM-4) [5], [6], [7], [8]. With limited solutions from hardware innovations, researchers have proposed many advanced digital signal processing (DSP) techniques for pre-processing or equalizing signals at the transmitter or receiver, including Feed Forward Equalizer (FFE) and Decision Feedback Equalizer (DFE) [9], Maximum Likelihood Sequence Estimation Equalizer (MLSE) [10], Volterra Equalizer (VE) [11], Neural Network Based Equalizer (NNE) [12], [13]. However, these advanced linear and nonlinear equalization algorithms, especially for VE and NNE, while having strong nonlinear compensation performance, also come with extremely high computational complexity and training costs, which limits the hardware deployment of these algorithms. To address this issue, numerous optimization schemes based on the original equalization algorithms have been proposed to reduce the computational complexity during the algorithm training and prediction processes. Examples of such optimization schemes include the lookup-table (LUT)-MLSE algorithm [14], the neural network equalizer based on pruning algorithms [12], [15] and hardware deployment of pruned neural network based nonlinear equalizer [16], etc. Most recently, a nonlinear equalization algorithm based on Reservoir Computing (RC), a neural network model with a simple network structure and neat training method, is widely discussed by researchers [17], [18]. Unlike NNE, which requires dozens of iterations of training on the dataset, RC-based equalizer has a strong ability to process time-domain signals in an adaptive manner by using single iteration of linear regression on the dataset, which shows better chance of practical implementation with similar training way as widely-used adaptive equalization. However, RC-based solution will also require large computing capability to construct nonlinear model by building random connected reservoir architecture.

In this paper, we propose a distributed reservoir computing (D-RC) based nonlinear equalizer, which optimizes the multiplication and addition operations during algorithm training and prediction by reusing the input data injection into the reservoir. While maintaining the performance of nonlinear compensation, the amount of computing resources including multiplication and addition units is largely reduced. The 106 Gbps PAM4 IM-DD signal data is demonstrated using a co-packaged optical transmitter module to verify and test the performance of the proposed nonlinear equalizer. Key parameters affecting the nonlinear compensation performance of this proposed algorithm are discussed to achieve better nonlinear compensation performance. Experimental results show that compared to neural network and Volterra series based equalizers, both RC and D-RC exhibit concise and low-complexity training processes while achieving similar levels of nonlinear compensation performance. Furthermore, D-RC significantly reduces the computational complexity in the inference phase compared to RC. We believe that incorporating simplified nonlinear equalization into VCSEL based co-packaged optical interconnects can preserve their inherent advantages of low cost, low power consumption. This minimalist optical interconnects approach will become a promising paradigm to overcome the penalty of the product of bandwidth density and energy efficiency that induced when communication leaving packages.