# Highly Efficient Multicast over Surface Wave in Hybrid Wireless-Optical On-Chip Networks for IoT HPC

Authors: Shengyan Zhu; Caiqiu Zhou; Yongjian Wang
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

As an ideal platform for Internet of Things (IoT) High Performance Computing (HPC), the Network-on-Chip (NoC) implements the parallelized task processing of Intellectual Property (IP) cores. However, the data interaction of IoT HPC has increased exponentially, resulting in highly consumed energy and bandwidth of the electrical NoC. This problem can be solved by the Optical NoC (ONoC), but the flexibility should be further improved for the multicast message transmission. We design a novel hybrid wireless-optical on-chip network with an effective routing mechanism for the message multicast transmission of IoT HPC. We utilize the wireless single-hop transmission to reduce on-chip communication distance and to forward multicast messages. For the high attenuation on-chip wireless signal, we design an on-chip surface waveguide structure for the surface wave as a more reliable wireless transmission medium. A flexible routing mechanism is also proposed to ensure efficient coordination between optical and wireless layers, thus relieving the pressure of the single-layer message transmission. The simulation results show that, compared with the traditional ONoC using mesh topology, our scheme performs better in terms of average delay, average energy consumption, and network throughput.


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## Body

## 1. Introduction

At present, the people has entered the era of the interconnected all things with information computing as the center, and the urgent demand of High Performance Computing (HPC) in Internet of Things (IoT) has made the number of IP cores integrated on a single chip sharply increase. The multicore chip for HPC IoT has become the key development direction mainly divided into three stages: System-on-Chip (SoC), Network-on-Chip (NoC), and Optical NoC (ONoC) [1–4]. As the system scale expands, the global synchronization required by SoCs will be difficult to realize. In NoCs, IP cores are connected by the network topology, and the information exchange is performed by packet switching and routing. However, the energy consumption of the electrical interconnection will inevitably become high. Moreover, the noise caused by signal crosstalk and parasitic capacitance also has a serious impact on the NoC performance, and the limited bandwidth provisioning and high link delay become gradually serious [5–8]. Compared with NoCs, ONoCs can provide the higher bandwidth, the lower energy consumption, and the smaller delay.IoT HPC applications tend to be highly parallelized, thus generating a large amount of interactive data in which multicast messages are relatively high. As shown in Figure1, the current ONoC research mainly focuses on network architecture, optical router, routing mechanism, and thermal modeling, mostly to enhance unicast message transmission [9–12], but few studies on multicast. Featuring the message multicast as multiple repeated unicast transmissions undoubtedly increases the waste of on-chip resources [13–15]. In addition, the ONoC node repeatedly sends the same copy but other messages within the node remain in the waiting state, resulting in a large delay. In this paper, we improve the message multicast from two aspects: network architecture and routing mechanism. In terms of network architecture, ONoC mostly adopts photo electric scheme divided into electrical control layer and optical transmission layer. As shown in Figure 2(a), during the (1) stage, the source node sends a control signal to the destination via one-by-one transmission on the electrical control layer for lightpath reservation. In the (2) stage, the message is delivered to the destination along the reserved lightpath on the optical transmission layer. Since a multicast message has multiple destinations, a number of generated control packets and reserved lightpaths increase sharply, and the optical transmission efficiency is very limited by the delay of the electrical control layer. For this end, we propose a novel hybrid wireless-optical on-chip network architecture in Figure 2(b). The wireless transceiver module is integrated on the electrical control unit of nodes, and the wireless transmission layer is formed on the top of the electrical control layer. Using the advantage of long-range, single-hop, and multidirectional wireless delivery of messages, we can reduce the on-chip communication distance and mitigate the pressure of the optical transmission layer. Regarding the routing mechanism in Figure 2(b), the message at the source wireless node can be single-hop transmitted to the relay nearest to the destination, which involves the coordination of wireless and optical transmission layers. The main contributions of the paper are summarized as follows:
(i)
The novel hybrid wireless-optical on-chip network architecture is designed for IoT HPC. The wireless transceiver module is integrated on the electrical control unit of some nodes in the mesh-based ONoC, which effectively shortens the on-chip communication distance. A surface structure is designed on the wireless transmission layer to support the message multicast. Compared with the air-based wireless multicast, our solution has the lower power loss and the higher reliability. To better utilize the wireless fan-out for the enhancement of message multicast, we propose a coding mechanism realizing multiplexed signal transmission on the same complete channel(ii)
We design a flexible routing mechanism fully uses the advantages of surface wave while alleviating the excessive single-layer transmission pressure through the efficient cooperation between wireless and optical layers. A novel multicast routing algorithm is also proposed based on the node-location distribution, and it can select the appropriate multicast-tree and dimension-order routing strategy to calculate the forwarding path with reduced routing hops. Especially for the10×10 topological scale, the improvement rate can reach 50% for the reduction of routing hops(iii)
The simulation results show that the surface waveguide designed in this paper can bind most of the light waves to be transmitted at its boundary with air. In addition, the attenuation of the Zenneck surface wave is significantly improved compared with the electromagnetic wave transmitted in the air, and the improvement ratio is up to 85%. Over other benchmark schemes, the improvement rate of the average delay can reach 30% and 25% for the average energy consumptionFigure 1
Proportional distribution of researches in different ONoC directions.Figure 2
(a) Traditional ONoC. (b) Our hybrid wireless-optical on-chip network.
(a)(b)The structure of the rest of the paper is organized as follows: in Section2, we mainly describe the hybrid wireless-optical on-chip network architecture. In Section 3, we describe the routing algorithm in detail for our hybrid wireless-optical on-chip network. In Section 4, we give simulation results and performance analysis.


## 2. Design of Hybrid Wireless-Optical On-Chip Network Architecture

The hybrid wireless-optical on-chip network architecture has three layers, namely, optical transmission layer, electrical control layer, and wireless transmission layer.


### 2.1. Design of Optical Transmission Layer

As shown in Figure3, each node in the optical transmission layer is composed of an electrical control unit and a five-port optical router. Five ports of the router are east, west, south, north, and injection/ejection. The router structure mainly consists of microring resonators (MRs) and optical waveguides, and the local IP core is responsible for data generation and reception through injection and ejection ports, respectively. The routing function of the optical transmission layer is realized by judging whether the wavelength of the optical signal is equal to that of the MR or not. If equal, the optical signal is coupled into the opened MR; otherwise, it outputs from the through port of the closed MR. Opening and closing of MRs (all MRs are closed by default) is controlled by the local electrical control unit [16–19]. As shown in the table of Figure 3, the message forwarding between each pair of ports only needs to open a unique and different MR, or all the relevant MRs are closed (through case), avoiding communication conflicts and achieving none blocking.Figure 3
Optical transmission layer in our hybrid wireless-optical on-chip network.


### 2.2. Design of Electrical Control Layer

It is unrealistic to integrate the wireless transceiver module to the electrical control unit of all nodes due to channel resource constraints and on-chip integration complexity. In this paper, mesh topology is evenly divided into multiple partitions, and the wireless transceiver module is integrated on the node located at the center of the partition, thus constructing the corresponding wireless node. As an example of Figure4(a), the 10×10 mesh topology is divided into four 5×5 partitions. In each wireless node located at the center of the partition, the wireless transceiver module replaces the original IP core, and it is connected to the injection/ejection port of the local optical router, thus preserving the capability of optical transmission, which can be seen in Figure 4(b). To reduce the transmission attenuation, the wireless transceiver module operates Zenneck surface wave as a nonradiative guided electromagnetic wave transmitted on a specially designed surface. The surface waveguide structure is designed later by covering the dielectric coating on the metal plane. In addition to the surface waveguide, within the wireless transceiver module of Figure 4(b), an inverted quarter-wavelength dipole antenna is also used to couple the electromagnetic wave into the surface waveguide, thus supporting omnidirectional communication of multicast messages. After signal coupling, the surface wave conversion/transfer layer receives the Zenneck surface wave from the waveguide and transfers this wave to the transceiver (T/R) circuit integrated using flip chip technology and TSV (Through Si Vias). Here, the cost of surface wave conversion is not within the discussion scope of this paper. Finally, the T/R circuit sends the signal to the electrical control unit where it makes the Electrical-to-Optical (EO) conversion. Similarly, once making Optical-to-Electrical (OE) conversion, the T/R circuit sends the signal to the surface wave conversion/transfer layer where the converted Zenneck surface wave will go to another wireless node via the surface waveguide.Figure 4
Wireless transmission layer in our hybrid wireless-optical on-chip network. (a) Distribution of wireless nodes. (b) Internal structure of wireless nodes. (c) The surface waveguide structure. (d) Dipole wave emission source. (e) The field intensity distribution of dipole antenna. (f) The scattering matrix parameter S21 between the Zenneck surface wave and the electromagnetic wave transmitted in the air. (g) Transmission gain of surface waves at different transmission distances.


### 2.3. Design of Wireless Transmission Layer

As the most important part of the wireless transceiver module, the surface waveguide is designed with the appropriate impedance Xs by selecting suitable materials and dimensions, in order to achieve surface wave communication on the chip. To generate the TM surface wave signal, we use SiO2 as dielectric material and Cu as metal conductor thin layer. According to Equation (1), given the surface wave signal frequency f, the value of Xs becomes larger with the increasing of l defined as the SiO2 thickness. As Xs becomes larger, there will be more light waves bound to the surface waveguide for improving transmission efficiency. However, Xs cannot be too high because a big l could cause the electromagnetic wave to be coupled into SiO2 rather than the junction of air and SiO2. In summary, we set the thickness of SiO2 to 0.25 mm and cover it on a 0.01 mm Cu layer; then, the 80Ω‐320Ω surface reactance can be realized within the signal frequency range of 20-80 GHz, as shown in Figure 4(c).
(1)Xs=2πfμ0εr−1εrl+14πμ0σ.High Frequency Structure Simulator (HFSS) is used to verify the effectiveness of the above surface waveguide. By using the dipole antenna of Figure4(d) as the signal excitation source, the field intensity distribution shown in Figure 4(e) is obtained. It can be seen that the surface waveguide designed in this paper can bind most of the light waves on its boundary with air. Furthermore, in Figure 4(f), we compare the scattering matrix parameter S21 between the Zenneck surface wave and the electromagnetic wave transmitted in the air. Obviously, the signal attenuation in the air is much larger than that of the Zenneck surface wave. In Figure 4(g), by changing the distance between the sending and receiving ends, we measure the voltage gain of electromagnetic waves propagating on the Zenneck surface, which well demonstrates the low power loss of our solution.Finally, the four wireless nodes in Figure4(a) are connected together through wireless links attached to the surface waveguide, thus forming the wireless transmission layer on the top of the electrical control layer. On the wireless transmission layer, multiple wireless nodes may simultaneously send messages to somewhere. Under this case, to avoid communication conflicting and interfering within the common wireless channel, we assign a unique Walsh sequence code to each wireless node. In Figure 5(a), after using Walsh codes to perform XOR operations with sending messages, we can achieve the superposition of encoding signals on the common wireless channel. For example, wireless node 1 sends message 1, and Walsh code is 10101010, while wireless node 2 sends message 0 and Walsh code is 01100110. After performing XOR operations, their sending messages are coded as 01010101 and 01100110, and the received data is 02110211 after superposition by the same channel. In Figure 5(b), at the receiving end, according to the order of the Walsh code, we execute the word-by-word judgment: if the current bit Walsh code word is 1, the corresponding bit number of the received data is accumulated to the negative accumulator, and conversely, to the positive accumulator. We then compare positive and negative accumulator results, and if the negative accumulator is small, the final received message is 1, otherwise 0. For example, the first, third, fifth, and seventh bits of the Walsh code 10101010 are 1; then, the received first, third, fifth, and seventh digits of the data 02110211 are {0,1,0,1}, which means the negative cumulative result is 2; the second, fourth, sixth, and eighth bits of the Walsh code 10101010 are 0; then, the received second, fourth, sixth, and eighth digits of the data 02110211 are {2,1,2,1}, which means the positive cumulative is 6. Because the negative cumulative result is small, the received message from wireless node 1 is 1, which is successfully decoded.Figure 5
Walsh coding for wireless transmission layer in our hybrid wireless-optical on-chip network. (a) The module of Walsh encoding. (b) The module of Walsh decoding.
(a)(b)


## 2.1. Design of Optical Transmission Layer

As shown in Figure3, each node in the optical transmission layer is composed of an electrical control unit and a five-port optical router. Five ports of the router are east, west, south, north, and injection/ejection. The router structure mainly consists of microring resonators (MRs) and optical waveguides, and the local IP core is responsible for data generation and reception through injection and ejection ports, respectively. The routing function of the optical transmission layer is realized by judging whether the wavelength of the optical signal is equal to that of the MR or not. If equal, the optical signal is coupled into the opened MR; otherwise, it outputs from the through port of the closed MR. Opening and closing of MRs (all MRs are closed by default) is controlled by the local electrical control unit [16–19]. As shown in the table of Figure 3, the message forwarding between each pair of ports only needs to open a unique and different MR, or all the relevant MRs are closed (through case), avoiding communication conflicts and achieving none blocking.Figure 3
Optical transmission layer in our hybrid wireless-optical on-chip network.


## 2.2. Design of Electrical Control Layer

It is unrealistic to integrate the wireless transceiver module to the electrical control unit of all nodes due to channel resource constraints and on-chip integration complexity. In this paper, mesh topology is evenly divided into multiple partitions, and the wireless transceiver module is integrated on the node located at the center of the partition, thus constructing the corresponding wireless node. As an example of Figure4(a), the 10×10 mesh topology is divided into four 5×5 partitions. In each wireless node located at the center of the partition, the wireless transceiver module replaces the original IP core, and it is connected to the injection/ejection port of the local optical router, thus preserving the capability of optical transmission, which can be seen in Figure 4(b). To reduce the transmission attenuation, the wireless transceiver module operates Zenneck surface wave as a nonradiative guided electromagnetic wave transmitted on a specially designed surface. The surface waveguide structure is designed later by covering the dielectric coating on the metal plane. In addition to the surface waveguide, within the wireless transceiver module of Figure 4(b), an inverted quarter-wavelength dipole antenna is also used to couple the electromagnetic wave into the surface waveguide, thus supporting omnidirectional communication of multicast messages. After signal coupling, the surface wave conversion/transfer layer receives the Zenneck surface wave from the waveguide and transfers this wave to the transceiver (T/R) circuit integrated using flip chip technology and TSV (Through Si Vias). Here, the cost of surface wave conversion is not within the discussion scope of this paper. Finally, the T/R circuit sends the signal to the electrical control unit where it makes the Electrical-to-Optical (EO) conversion. Similarly, once making Optical-to-Electrical (OE) conversion, the T/R circuit sends the signal to the surface wave conversion/transfer layer where the converted Zenneck surface wave will go to another wireless node via the surface waveguide.Figure 4
Wireless transmission layer in our hybrid wireless-optical on-chip network. (a) Distribution of wireless nodes. (b) Internal structure of wireless nodes. (c) The surface waveguide structure. (d) Dipole wave emission source. (e) The field intensity distribution of dipole antenna. (f) The scattering matrix parameter S21 between the Zenneck surface wave and the electromagnetic wave transmitted in the air. (g) Transmission gain of surface waves at different transmission distances.


## 2.3. Design of Wireless Transmission Layer

As the most important part of the wireless transceiver module, the surface waveguide is designed with the appropriate impedance Xs by selecting suitable materials and dimensions, in order to achieve surface wave communication on the chip. To generate the TM surface wave signal, we use SiO2 as dielectric material and Cu as metal conductor thin layer. According to Equation (1), given the surface wave signal frequency f, the value of Xs becomes larger with the increasing of l defined as the SiO2 thickness. As Xs becomes larger, there will be more light waves bound to the surface waveguide for improving transmission efficiency. However, Xs cannot be too high because a big l could cause the electromagnetic wave to be coupled into SiO2 rather than the junction of air and SiO2. In summary, we set the thickness of SiO2 to 0.25 mm and cover it on a 0.01 mm Cu layer; then, the 80Ω‐320Ω surface reactance can be realized within the signal frequency range of 20-80 GHz, as shown in Figure 4(c).
(1)Xs=2πfμ0εr−1εrl+14πμ0σ.High Frequency Structure Simulator (HFSS) is used to verify the effectiveness of the above surface waveguide. By using the dipole antenna of Figure4(d) as the signal excitation source, the field intensity distribution shown in Figure 4(e) is obtained. It can be seen that the surface waveguide designed in this paper can bind most of the light waves on its boundary with air. Furthermore, in Figure 4(f), we compare the scattering matrix parameter S21 between the Zenneck surface wave and the electromagnetic wave transmitted in the air. Obviously, the signal attenuation in the air is much larger than that of the Zenneck surface wave. In Figure 4(g), by changing the distance between the sending and receiving ends, we measure the voltage gain of electromagnetic waves propagating on the Zenneck surface, which well demonstrates the low power loss of our solution.Finally, the four wireless nodes in Figure4(a) are connected together through wireless links attached to the surface waveguide, thus forming the wireless transmission layer on the top of the electrical control layer. On the wireless transmission layer, multiple wireless nodes may simultaneously send messages to somewhere. Under this case, to avoid communication conflicting and interfering within the common wireless channel, we assign a unique Walsh sequence code to each wireless node. In Figure 5(a), after using Walsh codes to perform XOR operations with sending messages, we can achieve the superposition of encoding signals on the common wireless channel. For example, wireless node 1 sends message 1, and Walsh code is 10101010, while wireless node 2 sends message 0 and Walsh code is 01100110. After performing XOR operations, their sending messages are coded as 01010101 and 01100110, and the received data is 02110211 after superposition by the same channel. In Figure 5(b), at the receiving end, according to the order of the Walsh code, we execute the word-by-word judgment: if the current bit Walsh code word is 1, the corresponding bit number of the received data is accumulated to the negative accumulator, and conversely, to the positive accumulator. We then compare positive and negative accumulator results, and if the negative accumulator is small, the final received message is 1, otherwise 0. For example, the first, third, fifth, and seventh bits of the Walsh code 10101010 are 1; then, the received first, third, fifth, and seventh digits of the data 02110211 are {0,1,0,1}, which means the negative cumulative result is 2; the second, fourth, sixth, and eighth bits of the Walsh code 10101010 are 0; then, the received second, fourth, sixth, and eighth digits of the data 02110211 are {2,1,2,1}, which means the positive cumulative is 6. Because the negative cumulative result is small, the received message from wireless node 1 is 1, which is successfully decoded.Figure 5
Walsh coding for wireless transmission layer in our hybrid wireless-optical on-chip network. (a) The module of Walsh encoding. (b) The module of Walsh decoding.
(a)(b)


## 3. Design of Multicast Routing Algorithm

There are optical and wireless transmission layers in the hybrid wireless-optical on-chip network. The wireless transmission layer has the characteristics of long-distance single-hop transmission and natural fan out, so it is the preferred choice of message multicast to replace the multihop optical transmission. The optical transmission layer can share the pressure of the wireless transmission layer and avoid insufficient provisioning of wireless channel resources. For this end, we design a flexible routing scheme to ensure the highly efficient coordination between wireless and optical transmission layers.


### 3.1. Adaptive Selection of Transmission Layers

We choose whether to use the optical transmission layer alone or to use the wireless-optical hybrid transport by setting the following rules:Rule 1: for each unicast message, the wireless-optical hybrid transport is selected only if the current congestion flag bit is 0, and the Manhattan distance from the source node to the destination node is greater than the threshold. Here, the Manhattan distance is the sum of the XY axis distances between the two nodes, as an example of Figure 4(a), while the congestion flag bits 0, 1, and 2, respectively, indicate that the wireless node buffer occupancy is idle, mild use, and heavy use.Rule 2: for a multicast message whose destination and source nodes are not in the same partition, when the congestion flag bit is less than 2, the wireless-optical hybrid transport will be selected.Rule 3: for cases where rules 1 and 2 are not satisfied, we use the optical transmission layer alone.Rule 4: the priority of multicast messages is higher than that of unicast messages.


### 3.2. Intrapartition Multicast Routing Based on Node Distribution

According to rule 3 as elaborated in Section3.1, the multicast routing within the partition will only select the optical transmission layer, and the XY multicast-tree and dimension ordered routing strategy is widely used. As an example of Figure 6(a), the message is transmitted along the row (X-axes) where the source node is located. When arriving at the column where one of the destinations is located, the message is copied, and the copied message is transmitted along the Y-axes to the destination, while the original message continues to be transmitted along the X-axes until all messages are sent to specified destinations. Since the destination is far from the row of the source node and most of the destinations are in different columns, the forwarding path of the multicast message will cover almost the entire network in Figure 6(a). For this case, the effect will be significantly improved if it is changed to YX multicast-tree and dimension-order routing strategy in Figure 6(b). However, if the destination is far away from the column of the source node and most of the destinations are distributed in different rows, the YX routing strategy will also encounter the problem that the forwarding path covers almost the entire network. Therefore, we make a reasonable choice of XY and YX routing strategies based on the distribution of the source node and destinations of the multicast message. The node distribution is determined according to the weights shown in Equations (2) and (3). Here, DEST is the collection of all destinations of the multicast message, xi is the X-axis coordinate of the ith destination node, xsrc is the X-axis coordinate of the source node, yi is the Y-axis coordinate of the ith destination node, and ysrc is the Y-axis coordinate of the source node.
(2)Weightx=∑i∈DESTxi−xsrc,(3)Weighty=∑i∈DESTyi−ysrc.Figure 6
Illustration of existing multicast-tree and dimension-order routing. (a) TheXY multicast-tree and dimension ordered routing strategy. (b) The YX multicast-tree and dimension ordered routing strategy.
(a)(b)IfWeightx>Weighty, we use YX multicast-tree and dimension-order routing strategy; conversely, we use XY routing strategy.


### 3.3. Overall Algorithm Description

At the source node of the multicast message, we firstly flexibly select transmission layers as described in Section3.1, in order to determine whether the message requires the wireless transmission layer or not. If the wireless transmission layer is selected, 1 is the value of the WI field in the message header; otherwise, it is 0. Next, the multicast-tree and dimension-order routing policy for this message is determined by the weight comparison described in Section 3.2. If the YX routing policy is used, 1 is the value of the RS field in the message header; otherwise, it is 0. After determining the two field values, at each node along the forwarding path (including the source node), (1) we select the appropriate routing policy based on the RS field value, to calculate the output port of the local optical router for the message (copy). For example, in Figure 6(b), the node (4,0) determines that the message, and its copies enter from the local north port and go to the output east port based on the YX routing policy; then, the forwarding path insides the node (4,0) is shown in Figure 3 where north-to-east only needs to open MR13; (2) we determine whether the wireless transmission layer is required or not according to the WI field value. If the WI field value is 0, then (1) is directly executed. If the WI field value is 1, the routing policy of the corresponding field is used to calculate the output port of the local optical router, and the corresponding microforwarding path is obtained at the same time for the message (copy). Here, the wireless node within the same partition is also included into destinations. After receiving the message (copy), the wireless node needs to set the WI-field value as 0 to prevent the message (copy) from using the wireless link again to cause a cyclic deadlock. We then execute the weight comparison described in Section 3.2 to determine the routing policy within the partition and execute (1) based on the updated RS-field value. Here, this wireless node is the source node.To show the advantages of the above routing algorithm more intuitively, we give the example in Figure7. The left part shows the forwarding path obtained using the XY multicast-tree and dimension-order routing algorithm based on the traditional ONoC architecture. The right part shows the forwarding path obtained by our routing algorithm in the hybrid wireless-optical on-chip network architecture, owning average routing hops with the improvement rate of 50%. It is not difficult to see that this improvement rate will be further improved as the network size is further expanded.Figure 7
Example of comparing the number of routing hops between our and existing solutions. (a) The forwarding path obtained using theXY multicast-tree and dimension-order routing algorithm. (b) The forwarding path obtained by our routing algorithm.
(a)(b)


## 3.1. Adaptive Selection of Transmission Layers

We choose whether to use the optical transmission layer alone or to use the wireless-optical hybrid transport by setting the following rules:Rule 1: for each unicast message, the wireless-optical hybrid transport is selected only if the current congestion flag bit is 0, and the Manhattan distance from the source node to the destination node is greater than the threshold. Here, the Manhattan distance is the sum of the XY axis distances between the two nodes, as an example of Figure 4(a), while the congestion flag bits 0, 1, and 2, respectively, indicate that the wireless node buffer occupancy is idle, mild use, and heavy use.Rule 2: for a multicast message whose destination and source nodes are not in the same partition, when the congestion flag bit is less than 2, the wireless-optical hybrid transport will be selected.Rule 3: for cases where rules 1 and 2 are not satisfied, we use the optical transmission layer alone.Rule 4: the priority of multicast messages is higher than that of unicast messages.


## 3.2. Intrapartition Multicast Routing Based on Node Distribution

According to rule 3 as elaborated in Section3.1, the multicast routing within the partition will only select the optical transmission layer, and the XY multicast-tree and dimension ordered routing strategy is widely used. As an example of Figure 6(a), the message is transmitted along the row (X-axes) where the source node is located. When arriving at the column where one of the destinations is located, the message is copied, and the copied message is transmitted along the Y-axes to the destination, while the original message continues to be transmitted along the X-axes until all messages are sent to specified destinations. Since the destination is far from the row of the source node and most of the destinations are in different columns, the forwarding path of the multicast message will cover almost the entire network in Figure 6(a). For this case, the effect will be significantly improved if it is changed to YX multicast-tree and dimension-order routing strategy in Figure 6(b). However, if the destination is far away from the column of the source node and most of the destinations are distributed in different rows, the YX routing strategy will also encounter the problem that the forwarding path covers almost the entire network. Therefore, we make a reasonable choice of XY and YX routing strategies based on the distribution of the source node and destinations of the multicast message. The node distribution is determined according to the weights shown in Equations (2) and (3). Here, DEST is the collection of all destinations of the multicast message, xi is the X-axis coordinate of the ith destination node, xsrc is the X-axis coordinate of the source node, yi is the Y-axis coordinate of the ith destination node, and ysrc is the Y-axis coordinate of the source node.
(2)Weightx=∑i∈DESTxi−xsrc,(3)Weighty=∑i∈DESTyi−ysrc.Figure 6
Illustration of existing multicast-tree and dimension-order routing. (a) TheXY multicast-tree and dimension ordered routing strategy. (b) The YX multicast-tree and dimension ordered routing strategy.
(a)(b)IfWeightx>Weighty, we use YX multicast-tree and dimension-order routing strategy; conversely, we use XY routing strategy.


## 3.3. Overall Algorithm Description

At the source node of the multicast message, we firstly flexibly select transmission layers as described in Section3.1, in order to determine whether the message requires the wireless transmission layer or not. If the wireless transmission layer is selected, 1 is the value of the WI field in the message header; otherwise, it is 0. Next, the multicast-tree and dimension-order routing policy for this message is determined by the weight comparison described in Section 3.2. If the YX routing policy is used, 1 is the value of the RS field in the message header; otherwise, it is 0. After determining the two field values, at each node along the forwarding path (including the source node), (1) we select the appropriate routing policy based on the RS field value, to calculate the output port of the local optical router for the message (copy). For example, in Figure 6(b), the node (4,0) determines that the message, and its copies enter from the local north port and go to the output east port based on the YX routing policy; then, the forwarding path insides the node (4,0) is shown in Figure 3 where north-to-east only needs to open MR13; (2) we determine whether the wireless transmission layer is required or not according to the WI field value. If the WI field value is 0, then (1) is directly executed. If the WI field value is 1, the routing policy of the corresponding field is used to calculate the output port of the local optical router, and the corresponding microforwarding path is obtained at the same time for the message (copy). Here, the wireless node within the same partition is also included into destinations. After receiving the message (copy), the wireless node needs to set the WI-field value as 0 to prevent the message (copy) from using the wireless link again to cause a cyclic deadlock. We then execute the weight comparison described in Section 3.2 to determine the routing policy within the partition and execute (1) based on the updated RS-field value. Here, this wireless node is the source node.To show the advantages of the above routing algorithm more intuitively, we give the example in Figure7. The left part shows the forwarding path obtained using the XY multicast-tree and dimension-order routing algorithm based on the traditional ONoC architecture. The right part shows the forwarding path obtained by our routing algorithm in the hybrid wireless-optical on-chip network architecture, owning average routing hops with the improvement rate of 50%. It is not difficult to see that this improvement rate will be further improved as the network size is further expanded.Figure 7
Example of comparing the number of routing hops between our and existing solutions. (a) The forwarding path obtained using theXY multicast-tree and dimension-order routing algorithm. (b) The forwarding path obtained by our routing algorithm.
(a)(b)


## 4. Simulation Results and Analysis

We verify the advantages of the proposed scheme using the simulation platform based on Java language from the perspectives of network architecture and routing mechanism.


### 4.1. Performance Validation of Network Architecture

In this subsection, the superiority of our proposed network architecture is verified mainly in three performance matrices: average delay, average energy consumption, and throughput. In Table1, the first benchmark scheme considers a traditional ONoC architecture, while the second benchmark scheme utilizes millimeter wave wireless transmission and a MAC mechanism based on token ring although it adopts our new hybrid wireless-optical on-chip network architecture. In our scheme, the designed surface waveguide is used as the wireless transmission medium, and the MAC mechanism based on Walsh coding is taken into account.Table 1
Settings for benchmarks and our solution in tests of network architecture.
ParametersBenchmark-1Benchmark-2Our solutionTopology structureMesh ONoCHybrid wireless-optical on-chip networkHybrid wireless-optical on-chip networkTopology scale10×1010×1010×10Wireless transmission mediaNoneMillimeter waveSurface waveMAC mechanismNoneToken ringWalsh-coding MACRouting algorithmXYXYXYAs shown in Figure8, under three different traffic modes (the proportion of multicast messages is 0%,1%, and 5%), with the increasing proportion of multicast messages, the average delay and average energy consumption of each scheme both follow a rising trend, but benchmark-2 and our scheme obviously perform better than benchmark-1. This phenomenon shows that the proposed hybrid wireless-optical on-chip network architecture effectively enhances the multicast of messages. Furthermore, our scheme has the lower delay and energy consumption than those of benchmark-2 using token ring. The average delay decreases by 16.1%, while the average energy consumption decreases by 8.3%. The improvement of energy consumption is not obvious as delay. This is because, in the case of sending unicast messages, the natural fanout of wireless transmission generates more unnecessary energy consumption, although it significantly reduces delay.Figure 8
Simulation results of average delay given in (a) and energy consumption given in (b) among solutions under different traffic modes (tests of network architecture).
(a)(b)In Figure9, given the traffic mode 2, the simulation results of average delay and normalized network throughput owned by different schemes are shown under the variation of injection rate. With the increase of injection rate, the average delay increases gradually, and our solution always has the optimal delay under every injection rate. When the injection rate is 0.25, the normalized network throughput of benchmark-1 basically reaches saturation state, while the other two schemes show saturation trend when the injection rate is 0.4. After reaching saturation, the network throughput of our scheme is slightly higher because the Walsh coding MAC mechanism well improves the utilization of wireless channels.Figure 9
Simulation results of average delay given in (a) and normalized network throughput given in (b) among solutions under different injection rates (tests of network architecture).
(a)(b)


### 4.2. Performance Validation of Routing Algorithm

In this subsection, the routing mechanism is also verified in three performance matrices: average delay, average energy consumption, and throughput. The description of two benchmark schemes and our solution is shown in Table2.Table 2
Settings for benchmarks and our solution in routing tests.
ParametersBenchmark-1Benchmark-2Our solutionTopology structureMesh ONoCHybrid wireless-optical on-chip networkHybrid wireless-optical on-chip networkTopology scale10×1010×1010×10Wireless transmission mediaNoneSurface waveSurface waveMAC mechanismNoneWalsh-coding MACWalsh-coding MACTransmission layer assignmentNoneOur methodOur methodRouting algorithmXYXYHybridXY and YXFigure10 shows the simulation results of average delay and average energy consumption under different traffic modes. It can be seen that the average delay and average energy consumption increase gradually with the increasing proportion of multicast messages, and our solution performs best. Compared with benchmark-1, the average delay decreases by 54.5%, and the average energy consumption decreases by 42.6%. Compared with benchmark-2, the average delay decreases by 8.1%, and the average energy consumption decreases by 8.85%. This is mainly because our routing mechanism can provide ideal forwarding paths for multicast messages.Figure 10
Simulation results of average delay given in (a) and energy consumption given in (b) among solutions under different traffic modes (routing tests).
(a)(b)Given the traffic mode 2, Figure11 shows the simulation results of average delay and normalized network throughput at different injection rates. With the increase of injection rate, the average delay increases gradually, and our solution always performs best at every injection rate. When the injection rate is greater than 0.25, the average delay of our solution begins to show superiority. The normalized network throughput of our solution is slightly higher than that of benchmark-2, when reaching saturation state once the injection rate is greater than 0.4. The reason of this is that the proposed routing mechanism can simplify the forwarding path of multicast messages, thus occupying less optical links than benchmark-2.Figure 11
Simulation results of average delay given in (a) and normalized network throughput given in (b) among solutions under different injection rates (routing tests).
(a)(b)


## 4.1. Performance Validation of Network Architecture

In this subsection, the superiority of our proposed network architecture is verified mainly in three performance matrices: average delay, average energy consumption, and throughput. In Table1, the first benchmark scheme considers a traditional ONoC architecture, while the second benchmark scheme utilizes millimeter wave wireless transmission and a MAC mechanism based on token ring although it adopts our new hybrid wireless-optical on-chip network architecture. In our scheme, the designed surface waveguide is used as the wireless transmission medium, and the MAC mechanism based on Walsh coding is taken into account.Table 1
Settings for benchmarks and our solution in tests of network architecture.
ParametersBenchmark-1Benchmark-2Our solutionTopology structureMesh ONoCHybrid wireless-optical on-chip networkHybrid wireless-optical on-chip networkTopology scale10×1010×1010×10Wireless transmission mediaNoneMillimeter waveSurface waveMAC mechanismNoneToken ringWalsh-coding MACRouting algorithmXYXYXYAs shown in Figure8, under three different traffic modes (the proportion of multicast messages is 0%,1%, and 5%), with the increasing proportion of multicast messages, the average delay and average energy consumption of each scheme both follow a rising trend, but benchmark-2 and our scheme obviously perform better than benchmark-1. This phenomenon shows that the proposed hybrid wireless-optical on-chip network architecture effectively enhances the multicast of messages. Furthermore, our scheme has the lower delay and energy consumption than those of benchmark-2 using token ring. The average delay decreases by 16.1%, while the average energy consumption decreases by 8.3%. The improvement of energy consumption is not obvious as delay. This is because, in the case of sending unicast messages, the natural fanout of wireless transmission generates more unnecessary energy consumption, although it significantly reduces delay.Figure 8
Simulation results of average delay given in (a) and energy consumption given in (b) among solutions under different traffic modes (tests of network architecture).
(a)(b)In Figure9, given the traffic mode 2, the simulation results of average delay and normalized network throughput owned by different schemes are shown under the variation of injection rate. With the increase of injection rate, the average delay increases gradually, and our solution always has the optimal delay under every injection rate. When the injection rate is 0.25, the normalized network throughput of benchmark-1 basically reaches saturation state, while the other two schemes show saturation trend when the injection rate is 0.4. After reaching saturation, the network throughput of our scheme is slightly higher because the Walsh coding MAC mechanism well improves the utilization of wireless channels.Figure 9
Simulation results of average delay given in (a) and normalized network throughput given in (b) among solutions under different injection rates (tests of network architecture).
(a)(b)


## 4.2. Performance Validation of Routing Algorithm

In this subsection, the routing mechanism is also verified in three performance matrices: average delay, average energy consumption, and throughput. The description of two benchmark schemes and our solution is shown in Table2.Table 2
Settings for benchmarks and our solution in routing tests.
ParametersBenchmark-1Benchmark-2Our solutionTopology structureMesh ONoCHybrid wireless-optical on-chip networkHybrid wireless-optical on-chip networkTopology scale10×1010×1010×10Wireless transmission mediaNoneSurface waveSurface waveMAC mechanismNoneWalsh-coding MACWalsh-coding MACTransmission layer assignmentNoneOur methodOur methodRouting algorithmXYXYHybridXY and YXFigure10 shows the simulation results of average delay and average energy consumption under different traffic modes. It can be seen that the average delay and average energy consumption increase gradually with the increasing proportion of multicast messages, and our solution performs best. Compared with benchmark-1, the average delay decreases by 54.5%, and the average energy consumption decreases by 42.6%. Compared with benchmark-2, the average delay decreases by 8.1%, and the average energy consumption decreases by 8.85%. This is mainly because our routing mechanism can provide ideal forwarding paths for multicast messages.Figure 10
Simulation results of average delay given in (a) and energy consumption given in (b) among solutions under different traffic modes (routing tests).
(a)(b)Given the traffic mode 2, Figure11 shows the simulation results of average delay and normalized network throughput at different injection rates. With the increase of injection rate, the average delay increases gradually, and our solution always performs best at every injection rate. When the injection rate is greater than 0.25, the average delay of our solution begins to show superiority. The normalized network throughput of our solution is slightly higher than that of benchmark-2, when reaching saturation state once the injection rate is greater than 0.4. The reason of this is that the proposed routing mechanism can simplify the forwarding path of multicast messages, thus occupying less optical links than benchmark-2.Figure 11
Simulation results of average delay given in (a) and normalized network throughput given in (b) among solutions under different injection rates (routing tests).
(a)(b)


## 5. Conclusions

For the message multicast in IoT HPC, we have proposed a hybrid wireless-optical on-chip network added with a novel wireless transmission layer on the top of the electrical control layer. A surface waveguide structure suitable for Zenneck wave transmission has been designed, and a Walsh coding technique has maximized the fan-out advantages of the wireless. We have performed an efficient coordination between optical and wireless transmission layers through self-adaptive selection of multicast-tree and dimension-order routing strategies. The simulation results have shown that our solution obviously has the better performance than benchmark schemes in terms of average delay, average energy consumption, and network throughput. In the future work, the more extensive simulations will be done under different network scales considering various IoT HPC applications. Moreover, we integrate wireless nodes on the center of the partition, but sometimes, it may not be optimal, so the optimized design for the wireless-node location will be further discussed.



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*Source: 3882894-2022-05-06.xml*