Gaussian-based optical networks-on-chip: Performance analysis and optimization

https://doi.org/10.1016/j.nancom.2020.100286Get rights and content

Highlights

  • With the topology advantage of Gaussian network, Gaussian-based ONoCs is established.

  • A formal analysis model for the Gaussian-based ONoCs is proposed and evaluated.

  • The analysis model is suitable for using arbitrary 5-ports all-pass optical routers.

  • An optimization method is also explored to make Gaussian-based ONoCs more available.

Abstract

Compared with optical networks-on-chip (ONoCs) based on traditional topology such as mesh, torus, and fat-tree, Gaussian-based ONoCs have significant topological advantages in the network diameter and average jump distance. However, the intrinsic loss and crosstalk noise, which are inevitably inherent elements in basic optical devices, can lead to severe degradation of network performance and even restrict the normal communication of ONoCs. Therefore, in this paper, a numerical analysis model for analyzing the worst-case crosstalk noise and optical signal-to-noise ratio (OSNR) in Gaussian-based ONoCs is proposed. According to the all-pass characteristic of Gaussian-based ONoCs, the 5-ports all-pass optical routers are selected, which make the proposed model suitable for Gaussian-based ONoCs using arbitrary 5-ports all-pass optical routers. In addition, a numerical simulation is presented, which uses the Cygnus and optimized crossbar optical routers to verify the feasibility of the proposed analytical model. The simulation results show that the OSNR of Gaussian-based ONoCs decreases sharply with the network scale enlargement, the insertion loss and crosstalk noise tremendously limits the network scale. Furthermore, in order to make the Gaussian-based ONoCs more available, an optimization method is also proposed for improving network performance. The optimization method choose the best optical link between two arbitrary communication points, which can effectively avoid the worst case and greatly improve the performance of Gaussian-based ONoCs.

Introduction

A family of two-dimensional toroidal networks was proposed and classified as Gaussian networks, which has obvious topological advantages over traditional mesh and torus networks in network diameter and average hop distance. More specifically, Gaussian networks have smaller network diameter and shorter average hop distance for the same node degree and network size, thus they are considered as a promising topology candidate when designing multiprocessor systems [1], [2]. At present, there are some researches that focus on the architecture based on Gaussian networks. For instance, Gaussian integers were proposed to define a broad family of toroidal networks [1]. Different architectural issues of the Dense Gaussian Networks were analyzed and their topological advantages were also transformed into real network advantages [3]. The bufferless routing in the Gaussian macrochip was another content that researchers were interested in, and a bufferless routing algorithm adapted to the Gaussian macrochip was designed [4]. Moreover, an all-to-all broadcast algorithm was proposed to achieve the minimum total delay for all-to-all broadcasting by ensuring a balanced traffic load in all dimensions in Gaussian networks [5]. And the reconfigurable Gaussian networks with their properties were proposed and studied, as well as the reconfigurable rules used to design Gaussian networks on-chips automatically [6].

Most of the above researches are based on electrical interconnected on-chip Gaussian networks. Compared with the traditional electrical networks-on-chip (ENoCs), ONoCs have advantages of higher bandwidth, lower latency and lower power consumption [7], [8], [9], [10], which are more suitable for the developments of integrating more processor cores on a single chip [11], [12], [13], [14]. As a result, ONoCs are crucial for the development of the future multi-core systems on-chip [15], [16], [17], [18]. However, due to the presence of large number of waveguide crossings and microring resonators in the ONoCs architecture, the inherent properties of their own physical materials lead to the inevitable encounter loss and crosstalk noise when the optical signals pass through these devices. Although the magnitude of the devices level is infinitesimal, as the network size increases, crosstalk noise in the optical signal accumulates, resulting in severe degradation of network performance, which restricts the scale expansion of the network [19], [20].

Nowadays, various studies on the impact of crosstalk noise on network communication are concentrated on several common communication architectures, such as mesh, torus, fat-tree and so on. Formal methods were proposed respectively to analyze the worst-case signal power, crosstalk noise power, and optical signal-to-noise ratio (OSNR) in arbitrary mesh-based, folded-torus-based and fat-tree-based ONoCs [20], [21], [22]. The power loss and crosstalk noise generated by the waveguide crossing perform an essential role in the degradation of the network performance [23], [24], [25]. Moreover, some research efforts have attempted to reduce power loss and crosstalk noise. For example, a multimode interference (MMI)-based wire waveguide crossing instead of the conventional plain waveguide crossing was proposed to reduce the loss and crosstalk [26]. A metal-free integrated elliptical reflector for waveguide turnings and crossings was presented to achieve crosstalk noise less than 30 dB [27]. A waveguide crossing mechanism based on impedance matched metamaterials with large absolute values of negative refractive indexes was proposed, and its crosstalk noise and insertion loss are negligible [28]. However, there is almost no crosstalk noise analysis on the Gaussian-based ONoCs. Therefore, applying the topology advantages of Gaussian network to the structural design of ONoCs, it is very important to analyze the impact of power loss and crosstalk noise on network performance.

In addition, the lower limit of network performance in a specific ONoCs architecture depends on the worst-case link performance. Consequently, in order to guarantee the reliability of optical communication on-chip, we propose a numerical analysis model to analyze the worst-case OSNR of Gaussian-based ONoCs and provide an optimization method to further improve network performance. We employ the Cygnus and optimized crossbar optical routers in the numerical simulation to demonstrate the feasibility of the proposed model in this paper. Simulation results show that as the network scale increases, the accumulation of crosstalk noise and power loss increase, which will cause that the OSNR drops sharply. To solve these problems, we further present an optimization method for Gaussian-based ONoCs, which can select the best optical path according to the distribution of the positions of the two communication processor cores. We evaluate the performance of Gaussian-based ONoCs with optimization method. The proposed path optimization method can effectively avoid the worst-case OSNR link, and significantly improve the OSNR performance of the communication link.

Section snippets

Theoretical analysis for Gaussian-based ONoCs

Gaussian network can be described by a Gaussian graph [29], that is, each node and the connection of its network corresponds to a vertex and an undirected edge in a Gaussian graph. Gaussian graph are generally represented by Gaussian integers. The Gaussian integer set is a subset of a complex set, consisting of a complex number in which both the imaginary part and the real part are integers [30], denoted as: Z[i]={x+yi|x,yZ}

Given a nonzero Gaussian integer Z[i]=M+Ni, we can derive a network

Numerical simulation and evaluation

In order to verify the feasibility of the proposed analytical model, we present a numerical simulation example based on MATLAB and Optisystem. The all-pass Cygnus and optimized crossbar optical routers are used, the structure is shown in Fig. 5. The waveguide size is 400×200nm, the diameter of micro-resonator is around 10μm, and the other special parameters involved are listed in Table 1.

Simulation results are shown in Figs. 6 to 8. It can be obtained that the longest link in the third

Performance optimization

From the numerical simulation results, we can observe that as the size of the network increases, OSNR drastically decreases and even below zero, which means that the noise power at the destination node is greater than the signal power, and in this case, the communication quality will be severely damaged. In order to make the Gaussian on-chip networks more available, we propose an optimization method to improve the OSNR of the communication link, that is the choice of the best path between two

Conclusion

The accumulation of crosstalk noise will seriously degenerate the network performance, reduce the OSNR and limit the network scalability. In this paper, we propose an analysis model from three aspects of basic devices, optical routers and networks to analyze the crosstalk noise and OSNR of the worst case in Gaussian-based ONoCs. This numerical analysis model is suitable for Gaussian-based ONoCs using arbitrary 5-ports all-pass optical routers. At the same time, we also use Cygnus and optimized

CRediT authorship contribution statement

Tingting Song: Conceptualization, Methodology, Software, Validation, Formal analysis, Data curation, Writing - original draft, Writing - review & editing, Visualization. Yiyuan Xie: Resources, Supervision, Writing - review & editing, Funding acquisition. Yichen Ye: Visualization, Writing - review & editing. Yingxue Du: Software. Bocheng Liu: Data curation. Yong Liu: Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Tingting Song was born in Shaanxi, China, in 1992. She received the B.Sc. degree from Northwest University, Shaanxi, China, in 2014. She received the M.Sc. degree from Southwest University, Chongqing, China, in 2017. And she is currently working toward the Ph.D. degree at the School of Electronic and Information Engineering, Southwest University, Chongqing, China. Her current research interests include optical networks-on-chip, ultrahigh optical communications, optical devices and optical

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  • Tingting Song was born in Shaanxi, China, in 1992. She received the B.Sc. degree from Northwest University, Shaanxi, China, in 2014. She received the M.Sc. degree from Southwest University, Chongqing, China, in 2017. And she is currently working toward the Ph.D. degree at the School of Electronic and Information Engineering, Southwest University, Chongqing, China. Her current research interests include optical networks-on-chip, ultrahigh optical communications, optical devices and optical computing.

    Yiyuan Xie was born in Shaanxi, China, in 1980. He received the Ph.D. degree in optical engineering from the Chinese Academy of Science, Beijing, China, in 2009. He was a Visiting Scholar with the Hong Kong University of Science and Technology, Hong Kong. He is currently a professor at the School of Electronic and Information Engineering, Southwest University, Chongqing, China. His current research interests include optical networks on-chip, ultrahigh optical communications, optical chaotic secure communication, and optical data centers. He has authored or coauthored more than 60 papers in peer-reviewed journals and international conferences.

    Yichen Ye was born in Zhejiang, China, in 1992. He received the B.Eng. degree from Northwest University, Shannxi, China, in 2015. He is currently working toward the Ph.D. degree at the School of Electronic and Information Engineering, Southwest University, Chongqing, China. His current research interests include surface plasmon polaritons, optical devices, and optical computing.

    Yingxue Du was born in Henan, China, in 1993. She received B.Sc. Degree in Electronic and Information Engineering from Xinyang Normal University, Xinyang, China, in 2014. She received the M.Sc. degree from Southwest University, Chongqing, China, in 2018. Her research interests include optical networks-on-chip, ultrahigh optical communications, and optical channel coding.

    Bocheng Liu was born in Gansu, China, in 1993. He received B.Sc. degree in Electronic and Information Engineering from Northwest Normal University, Lanzhou, China, in 2016. He received M.Sc. degree at the School of Electronic and Information Engineering, Southwest University, Chongqing, China. He is currently pursuing the Ph.D. degree at the School of Electronic and Information Engineering, Southwest University, Chongqing, China. His research interests include secure communication, bifurcation and chaos, nonlinear dynamical systems, and information safety.

    Yong Liu was born in Sichuan, China, in 1970. He received the M.S. degree from the University of Electronic Science and Technology of China, Chengdu, China, in 1994, and the Ph.D. degree from Eindhoven University of Technology, Eindhoven, Netherlands, in 2004. In 2000, he joined the COBRA Research Institute, Eindhoven University of Technology. Since 2007, he has been a Professor at the University of Electronic Science and Technology of China. He is the author or coauthor of more than 200 journal and conference papers. He received Chinese National Science Fund for Distinguished Young Scholars in 2009 and Chinese Chang Jiang Scholar in 2013. His research interests include optical nonlinearities and applications, optical signal processing, and optical fiber technologies. Prof. Liu was the recipient of an IEEE Lasers and Electro-Optics Society Graduate Student Fellowship in 2003.

    This work was supported by the Natural Science Foundation of Chongqing, China City under Grant Nos. cstc2016jcyjA0581, by the Postdoctoral Science Foundation of China under Grant Nos. 2016M590875, by the Fundamental Research Funds for the Central Universities, China under Grant XDJK2018B012.

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