著作名稱：  Advanced crosstalk reduction in an N × N twostage AWGbased switch with odd N 
年度：  2021 
類別： 
期刊論文
Optik

摘要：  When multiple signals of the same wavelength cross an arrayed waveguide grating (AWG) at the same time, crosstalk of the same wavelength can severely degrade the quality of the signals. An N × N twostage AWGbased switch architecture was proposed in an earlier study to tackle the crosstalk problem, where each scheduling decision is represented by a permutation, and a permutation is called klegal if signals with the same wavelength appear at most k times. The study showed that each permutation can be decomposed into two 4legal permutations. In addition, for an N × N switch with 4 ≤ N ≤ 12, it showed that each permutation can be decomposed into two 2legal permutations, π1 and π2, where π1 is chosen from a small set Π1. But no specific method was proposed to show how to generate Π1. In this paper, we further reduce the crosstalk of the 2stage AWGbased switch for every odd N by lowering the number of signals using the same wavelength in each decomposed permutation. We derive various sufficient conditions for permutations to be decomposed into two permutations, τ1 and τ2, where τ1 is 1legal and τ2 is 2legal. In addition, to decompose each permutation into permutations τ1 and τ2, with the proviso that τ1 and τ2 exist, we propose an algorithm to generate a more compact set than Π1, even less than half, to choose τ1. 
關鍵字：  
著作名稱：  Reducing conversion range in wavelength exchange networks 
年度：  2021 
類別： 
期刊論文
IET COMMUNICATIONS

摘要：  Alloptical crossconnects need to perform switching not only in the space domain, but also in the wavelength domain. Switching in the wavelength domain requires wavelength converters (WCs), and WCs capable of simultaneously performing multiple wavelength conversions have been invented. We can use multiple stages of such WCs to form a wavelength exchange network to allow an even larger number of simultaneous wavelength conversions. However, WCs with a full conversion range are often difficult to implement. In the paper, we develop new techniques and theories that can reduce the conversion range requirement and still maintain the full connectivity of alloptical space/wavelength switches. 
關鍵字：  optical networks 
著作名稱：  Power Minimization in MicroringBased Benes Networks 
年度：  2018 
類別： 
期刊論文
IEEE Trans. Commun.

摘要：  An NoC (network on chip) constructed with silicon photonic microrings can be implemented with CMOS technology
and integrated with processor cores on the same die. Each microring in the NoC has two switching states, one consuming significantly less power than the other. Different routing schemes can lead to different numbers of microrings in the highpower consumption state, and result in different power consumptions for the NoC. In an earlier work, a loopingbased routing algorithm was proposed which exploits the different power consumption characteristics of the two switching states of a microring so as to minimize the power consumption of a Benestype NoC; but this algorithm cannot provide an optical solution. In this paper, we will show the necessary and sufficient conditions for finding the optimal solution for a Benestype NoC. We also present a new routing algorithm. Compared with the algorithm of the previous work, the new algorithm can reduce the number of microrings in the highpowerconsumption state by as many as (n−2) ·2n−2 in a 2n×2n Benestype NoC for certain interconnection patterns. 
關鍵字：  Photonic microring, power minimization, Benes network. 
著作名稱：  Nonblocking Multirate 2Stage Networks 
年度：  2018 
類別： 
期刊論文
IEEE Commun. Lett.

摘要：  A 2stage network is the most compact multistage interconnection network (MIN) for interconnecting small switches to form a large one. For larger networks, the switches in each stage can be replaced with 2stage networks to reduce crosspoint cost. The 2stage network preserves only conditional nonblockingness, while a multirate 2stage network
preserves nonblockingness. Multirate MINs have been exploited in many prior works, but multirate 2stage networks have not previously been studied. In this letter, we prove the necessary and sufficient conditions for strictly nonblocking, rearrangeable nonblocking, and repackable nonblocking multirate 2stage networks. The results can be directly applied to the architecture design of elastic optical networks which allocate a flexible use of the spectrum to each connection, as each space switch is replaced with a bandwidthvariable wavebandconverting switch, which has fullrange conversion capability. 
關鍵字：  Multirate networks, 2stage networks, strictly nonblocking (SNB), rearrangeable nonblocking (RNB), repackable nonblocking (RPNB), elastic optical networks. 
著作名稱：  Construction of Nonblocking Wavelength/Space Switches with AWGs and WSSes 
年度：  2017 
類別： 
期刊論文
Applied Sciences

摘要：  In this paper, we how to use two technologies, AWG (arrayedwaveguide grating) and WSS (wavelength selective switches), to design nonblocking wavelength/space optical cross connects. An AWG is a passive device and can route multiple wavelengths simultaneously. However, to apply AWGs, there are several issues to consider, including the wavelength conversion range, crosstalk, and switch size constraint. We show a decomposition technique for designing
an AWGbased nonblocking wavelength/space switch. The decomposition is carried out in a transformed space network. The new technique is simpler in concept and more flexible in setting switch sizes. We also study another class of wavelength/space switches that are based on WSSes and compare the two approaches in terms of the scalability, switch size constraint, and number of WCs (wavelength converters) required. 
關鍵字：  arrayedwaveguide grating (AWG); wavelength selective switch (WSS); nonblocking networks; Clos networks 
著作名稱：  Repackable multiLog_2 N networks 
年度：  2016 
類別： 
期刊論文
Theoretical Computer Science

摘要：  MultiLog_2 N networks have a wide range of applications in telecommunications. In this paper, we present a new type of nonblocking multiLog_2 N networks, called repackable nonblocking, wherein rearrangement activities are required only during the departures, but not upon arrivals. Furthermore, the frequency of rearrangement activities is so low that under many circumstances, they perform like strictly nonblocking networks but with a much lower hardware complexity. 
關鍵字：  MultiLog_2 N networks; Photonic switching; Repackable networks 
著作名稱：  Exploiting TwoWavelength Switching Capability of Silicon Photonic Microrings 
年度：  2013 
類別： 
期刊論文
Journal of Lightwave Technology

摘要：  Silicon photonic microrings have the capability of
handling two wavelengths simultaneously and this capability does
not exist in other types of photonic switching technologies, such
as directional couplers or MEMS. Exploiting this twowavelength switching capability has not been done before. In this paper, we use this capability to construct a new type of microringbased nonblocking optical interconnects. For a 4 4 network, the new architecture only needs four rings. In contrast, the conventional crossbarbased architecture requires 16 rings. For medium size switches, such as 8 ports or 16 ports, the new architecture also requires significantly fewer rings than conventional crossbar
switches of the same sizes. 
關鍵字：  Nonblocking networks, silicon photon rings. 
著作名稱：  Crosstalk Analysis for Microring Based Optical Interconnection Networks 
年度：  2012 
類別： 
期刊論文
Journal of Lightwave Technology

摘要：  Recently a new approach was proposed to tackle the wavelength nonuniformity problem of the silicon photonic ring technology. By lowering the Q value of the ring, the likelihood of finding a common operating wavelength can be significantly increased. But lowering Q will increase the crosstalk level in such a network. This crosstalk problem can be tackled with a generalized space dilation technique.
Since crosstalk is a central issue of this approach, computing the crosstalk level accurately is critical for a microringbased photonic interconnect. Prior work on crosstalk analysis for interconnects based on directional couplers assumed that the extinction ratios are the same for the two switching states. But this is usually not the case for silicon photonic microrings. In this paper, we develop an analytical model for analyzing the crosstalk level in a microringbased optical interconnection network. The analytical approach presented in the paper can be used for studying the crosstalk problem in optical networks based on other optical switching technologies.

關鍵字：  crosstalk, silicon photonic microrings. 
著作名稱：  A New Approach to the Wavelength NonUniformity Problem of Silicon Photonic Microrings 
年度：  2011 
類別： 
期刊論文
Journal of Lightwave Technology

摘要：  Light modulators and switches based on silicon photonic microrings can be fabricated with the conventional CMOS technology. For the first time, an optical interconnect integrated on a VLSI electronic die can be realistically envisioned. In spite of this exciting development, there is still one fundamental problem that must be overcome: wavelength nonuniformity, which is a result of miniaturization of the ring and the precision limit of the current fabricating process. Existing electronic or thermooptical tuning methods are simply not scalable.
An approach that combines techniques from both the device and architecture points of view is presented in this paper. It intends to show how the devicelevel wavelength nonuniformity problem can be tackled at the architecture level. An analytical model is also developed for evaluating the probability of finding a common wavelength among multiple microring resonators. The model can provide useful insights into the design of any microringbased interconnection network. 
關鍵字：  silicon photonic microrings, networks on chip, crosstalk, switching networks. 
著作名稱：  FaultTolerant General Beneš Networks 
年度：  2023 
類別： 
期刊論文
IEEE Transactions on Communications

摘要：  Beneš networks are wellknown rearrangeable nonblocking (RNB) multistage networks. The socalled conventional Beneš networks are based on 2x2 switches. In this paper, Beneš network is a general term used to refer to an NxN nnary Beneš network. Such networks, denoted by B(n, t), where N n^t and t > 2, are based on regular nxn switches, and are RNB as well. A Beneš network is constructed recursively from a 3stage Clos network. For an NxN RNB Clos network C(n, m, r), where N n^r and m > n, the maximum allowable number of noncontact faults in each single shell for realizing any permutation has been investigated in an earlier study, where shell k in a network consists of both the kth and the kthtolast node stages. That study showed that, for a given integer N, an RNB C(n, n, r) network with larger nn switches leads to tolerance of more noncontact faults in shell 1. In this paper, for an NxN B(n, t) network, we study the maximum allowable number, say f_k, of noncontact faults for any permutation not only in each single shell k, but also in all shells simultaneously under the fault condition that at most f_k noncontact faults are arbitrarily located in the switches in each shell k. We call the former the fault tolerance capability in a single shell, and the latter the fault tolerance capability of the network. We show that a larger switch size, i.e., nxn, in an NxN B(n, t) network leads to a higher fault tolerance capability of the network and a higher fault tolerance capability in each nonmiddle shell. An NxN Beneš network B(n, t) considers only the value of N which is a power of n. To consider a flexible N with N n^sxq, where s > 2, 1 q n and qn, which means that n is divisible by q, we propose in this paper an NxN RNB Beneštype network using regular nxn switches, which is called an extended Beneš and denoted by B(n, s, q). Both Beneš and extended Beneš networks are based on regular switches, and they have better scalabilities than a Clos network. We define a network’s fault tolerance rate as the ratio of the fault tolerance capability to the total crosspoints in the network. For given integers N and n, we derive that the fault tolerance capability and fault tolerance rate of an NxN Beneš (or extended Beneš) network are higher than or equal to those of an NxN RNB C(n, n, r) network, and the former outperforms the latter in most cases. 
關鍵字：  Fault tolerance, switching networks, Beneš networks, Clos networks, noncontact fault, rearrangeable. 
著作名稱：  Rearrangeability and repackability of a multicast wavelengthspacewavelength elastic optical network 
年度：  2023 
類別： 
期刊論文
Optical Switching and Networking

摘要：  Elastic optical networks (EONs) have been introduced to meet the demands of the rapidly growing Internet. These networks can efficiently keep up with the emerging bandwidthhungry and highly dynamic services, and can support multicast services using techniques like the path, tree or subtree methods. A multicast wavelengthspacewavelength (MWSW) network is a switching node architecture for EONs, which adopts the subtree method to support multicast connections. An MWSW network consists of three node stages in which wavelength, space and wavelength switches are used, respectively. A nonblocking MWSW network guarantees that any connection between a free input and a free output can always be realized, and studying the nonblockingness of a network has attracted much attention from researchers. Sufficient conditions, in terms of the number of middle space switches, for an MWSW network to be strictsense nonblocking (SNB) or widesense nonblocking (WSNB) were examined in an earlier study. It is known that SNB networks usually incur a higher hardware cost, for instance, the number of middle space switches, compared to WSNB, rearrangeably nonblocking (RNB), or repackably nonblocking (RPNB) networks. This paper studies the rearrangeability and repackability of MWSW networks, and derives the sufficient and necessary conditions for an MWSW network to be RNB (or RPNB). The results show that the derived sufficient conditions for being RNB (or RPNB) require significantly fewer middle switches for SNB and WSNB networks, and the RPNB results require fewer middle switches than those for RNB in most cases. 
關鍵字：  Elastic optical networks (EONs), Optical switching fabrics, Multicast Subtree scheme, Rearrangeable nonblocking (RNB), Repackable nonblocking (RPNB) 
著作名稱：  Nonblocking conditions for a multicast WSW architecture based on subtree scheme for elastic optical networks 
年度：  2022 
類別： 
期刊論文
Optical Switching and Networking

摘要：  Elastic optical networks (EONs) are a promising solution for future highspeed optical communication, and multicasting in EONs can efficiently support many emerging services. Different schemes, such as path, tree and subtree schemes, serve multicast services. In this paper, we consider a threestage wavelengthspacewavelength (WSW) node architecture, which adopts wavelength switches in the first and last stages and space switches in the middle stage, and uses the path scheme to accommodate multicast requests, as proposed in an earlier work for elastic optical networks. We also enhance the WSW architecture to serve multicast requests in a more spectrumefficient way, namely, using the subtree scheme, by making each switch support multicast capacity, and we term the resulting architecture MWSW. To the best of our knowledge, this is the first study of the WSW architecture using the subtree scheme to support multicast capacity. We prove the sufficient and necessary conditions, in terms of the number of middle switches, of the MWSW architecture for being strictly nonblocking (SNB) and widesense nonblocking (WSNB) under the two routing algorithms proposed in this paper. Our results show that the number of middle switches required for the architecture to be WSNB under each of the two proposed routing algorithms is much less than the number of middle switches required for SNB, especially when the SNB results meet the boundary condition. 
關鍵字：  Strictly nonblocking networks, widesense nonblocking networks, elastic optical networks, multicast. 
著作名稱：  Designing nonblocking networks with a general topology 
年度：  2022 
類別： 
期刊論文
IEEE Access

摘要：  Conventional theory for designing strictly nonblocking networks, such as crossbars or Clos networks, assumes that these networks have a centralized topology. Many new applications, however, require networks to have a distributed topology, like 2D mesh or torus. In this paper, we present a new theoretical framework for designing such nonblocking networks. The framework is based on a linear programming formulation originally proposed for solving the hosemodel traffic routing problem. The main difference, however, is that the link bandwidths in our problem must be discrete. This makes the problem much more challenging. We show how to apply the developed theorems to tackle the problem of designing bufferless NoCs (networksonchip). The proposed bufferless NoCs are deadlock/livelockfree and consume significantly less power than their buffered counterparts. We also present a multislice technique to reduce node capacity variations. This can make the proposed NoC architecture more cost efficient in a VLSI (very largescale integration) implementation. In addition, we offer a detailed delay/throughput performance evaluation of the proposed bufferless NoC in the paper. 
關鍵字：  Nonblocking networks, Networksonchip (NoCs), Bufferless, Hose model. 
著作名稱：  Repackable Log2(N, m, p) Networks and WideSense Nonblocking Log2(8, 0, p) Networks 
年度：  2018 
類別： 
期刊論文
Journal of Interconnection Networks

摘要：  The repackable Log2(N, 0, p) network, wherein repacking activities are required during departures but not upon arrivals, was proposed by Lin and Lea in a study on multiLog2N networks. Due to their complexity, Log2(N, m, p) networks are considerably more difficult to analyze compared with Log2(N, 0, p) networks. In this paper, we successfully extend the repackable Log2(N, 0, p) networks to Log2(N, m, p) networks. In addition, the proposed
routing algorithm is shown to be an optimal algorithm according to the total number of planes required. Furthermore, an analysis tool is proposed for studying repackable Log2(N, m, p) networks and is applied to show that each widesense nonblocking Log2(8, 0, p) network requires the same total number of planes as a strictly nonblocking network under any possible routing strategy. 
關鍵字：  Log2(N, m, p) networks; repackable networks; widesense nonblocking networks. 
著作名稱：  Rearrangeable and Repackable SWS Elastic Optical Networks for Connections with Limited Bandwidths 
年度：  2020 
類別： 
期刊論文
Applied Sciences

摘要：  Elastic optical networks flexibly allocate bandwidth to a connection for improving utilization efficiency. The paper considers an optical node architecture that is similar to a threestage Clos network for elastic optical networks. The architecture, which employs space switching in the first and the third stages and wavelength switching in the second stage, is called an SWS switching fabric. In this paper, we propose a graphtheoretic approach and different routing algorithms to derive the sufficient conditions under which an SWS switching fabric will be rearrangeable nonblocking and repackable nonblocking. The proposed rearrangeable and repackable nonblocking SWS switching fabrics for connections with limited bandwidths consume around half the number of middle wavelength switches compared to strictly nonblocking SWS switching fabrics. 
關鍵字：  Elastic optical network; rearrangeable nonblocking; spacewavelengthspace switching fabric; repackable nonblocking 
著作名稱：  Rearrangeable Nonblocking Conditions for Four Elastic Optical Data Center Networks 
年度：  2020 
類別： 
期刊論文
Applied Sciences

摘要：  Four variants of elastic optical data center network (DCN) architectures based on optical circuit switching were proposed in an earlier study. The necessary and sufficient values of frequency slot units (FSUs) per fiber required for these four DCNs in the sense of there being strictly nonblocking (SNB) were derived, but no results in the sense of being rearrangeable nonblocking (RNB) were presented. In reality, only limited bandwidths are available, and reducing the value of FSUs per fiber has become a critical task to realize nonblocking optical DCN architectures in practice. In this paper, we derive the sufficient value of FSUs per fiber required for the four DCNs to be RNB by two multigraph approaches. Our results show that the proposed RNB conditions in terms of FSUs per fiber for a certain two of the four DCNs reduce their SNB results down to at least half for most cases, and even down to onethird. 
關鍵字：  data center networks; elastic optical networks; rearrangeable nonblocking (RNB); edgecoloring 
著作名稱：  Rearrangeable WSW Elastic Optical Networks Generated by Graph Approaches: Erratum 
年度：  2019 
類別： 
期刊論文
IEEE/OSA J. Opt. Commun. Netw.

摘要：  We correct the results for WSW2 networks with limited input/output fibers derived in the paper [J. Opt. Commun. Netw., vol. 10, no. 8, pp. 675685]. The revised results show that when the number of input/output switches is less than the maximum number of frequency slot units (FSUs) occupied by a single connection, a rearrangeable nonblocking (RNB) WSW2 network with limited input/output fibers 1) consumes fewer middle switches than a WSW2 network with limited connection rates, and 2) reduces the strictly nonblocking (SNB) result down to at least half. 
關鍵字：  Elastic optical networks, optical switching fabrics, rearrangeable nonblocking (RNB), edgecoloring. 
著作名稱：  Generalization of an Optical ASA Switch 
年度：  2019 
類別： 
期刊論文
Applied Sciences

摘要：  An arrayed waveguide grating (AWG) is a kind of passive wavelength router, and it is the most promising technology for developing large optical switches. However, AWGs have poor scalability, and using small AWGs to construct a large switch has been done in many prior works. A novel AWGbased switch called ASA (AWG, space switching, AWG) that does not use wavelength converters has been proposed. It can expand the switch size from N to N^2 by using N×N AWGs. In this paper, we generalize the ASA switch by using only N×N AWGs, N×N space switches and N wavelengths such that the switch size is expanded to N^t for any positive integer t. Since each port of an N×N AWG can transmit up to N wavelengths simultaneously, the total capacity of the generalized ASA switch is extended to be close to N^(t+1) × the bandwidth of a wavelength channel, provided that inputs which are located in the same port position of each input AWG are destined to distinct outputs. 
關鍵字：  arrayedwaveguide grating (AWG); optical networks; rearrangeable nonblocking; wavelengthdivisionmultiplexing (WDM) 
著作名稱：  A unifying approach to nonblocking Closlike networks with k multiplexing levels 
年度：  2019 
類別： 
期刊論文
Optical Switching and Networking

摘要：  Many multiplexing technologies have been proposed to meet the need for high network capacity. One can foresee that transmission systems with many multiplexing levels will be used in telecommunication networks in the future, and the need for switching connections to pass through multiplexed fiber links will rise accordingly. One Closlike network with k multiplexing levels was proposed in an earlier work, and the work proved only the strictly nonblocking (SNB) conditions. In this paper, we propose a unifying method to prove not only the SNB condition, but also rearrangeable, repackable and widesense nonblocking conditions for the Closlike network with k multiplexing levels. Note that the proposed new proof for the SNB condition is more compact than that given in the earlier work. 
關鍵字：  Clos networksStrictly nonblocking networksRearrangeable nonblocking networksRepackable nonblocking networksWidesense nonblocking networks 
著作名稱：  New Upper Bound for a Rearrangeable Nonblocking WSW Architecture 
年度：  2019 
類別： 
期刊論文
IET Communications

摘要：  An optical network based on elastic optical switches allows requests using different spectrum widths to improve utilization efficiency. The paper considers one threestage WSW (waveband switchingspace switchingwaveband switching) optical node architecture for elastic optical networks. A sufficient condition for a rearrangeable nonblocking (RNB) WSW architecture with limited input/output links has been derived in an earlier work. In this paper, we improve the upper bound by adopting a new interstage link partition scheme associated with a tricky routing algorithm. Suppose a WSW architecture has r input/output links each of which has n frequency slot units (FSUs). Compared with earlier results, the results of the proposed scheme show that s 1 (or 3s 4) FSUs per interstage link can be reduced for even (or odd) min{r, n}, where s min{r/2, n/2}. The reduction gain is at least 3.5% (or 10%) for even (or odd) min{r, n} if r n 26, even achieving 23.3% for limited odd r n. 
關鍵字：  Elastic optical networks, optical switching fabrics, photonic switching systems, rearrangeable nonblocking (RNB). 
著作名稱：  Rearrangeable WSW Elastic Optical Networks Generated by Graph Approaches 
年度：  2018 
類別： 
期刊論文
IEEE/OSA J. Opt. Commun. Netw.

摘要：  In elastic optical networks, a connection uses different spectrum widths that spread over adjacent frequency slot units (FSUs) to improve utilization efficiency. A threestage wavelengthspacewavelength (WSW) optical node architecture for elastic optical networks employs wavelength switching in the first and third stages and space switching in the second stage. This paper considers twoWSWarchitectures, calledWSW1andWSW2networks. In an earlier study, a matrix decomposition approach was used to derive a condition that was sufficient for rearrangeable nonblocking (RNB), but only for a WSW1 network with a limited number of connection rates. In this paper, instead of using a matrix decomposition approach, we use a graph approach to derive the same result. Furthermore, we adopt different graph approaches to derive two sufficient conditions, which benefit limited connection rates and limited input/output fibers of an RNB WSW1 (or WSW2) network. Specifically, the former is better than the latter if the number of connection rates is less than the minimum ceiling value of half the number of 1) input/output switches and 2) FSUs in each input and output fiber, and vice versa if the number of input/output switches is less than the minimum value of 1) twice the maximum FSUs occupied by a single connection and 2) FSUs in each input and output fiber. Note that limited input/output switches lead to limited input/output fibers. The graph approaches proposed in this paper can be applied to various other elastic optical networks for further study. 
關鍵字：  Edgecoloring; Elastic optical networks; Optical switching fabrics; Rearrangeable nonblocking (RNB). 