Making Path Selection Bright: A Routing Algorithm for On-Chip Benes Networks
Abstract
:1. Introduction
- The concept of IL fairness is applied to Benes networks. When fewer ports exist, the optimal routing algorithm (ORA) is proposed to reduce the imbalance at the receiver.
- As the number of ports increases, a greedy algorithm (GRA) is proposed to suppress the PDR, which allows the signal to propagate under one and only one first-order XTL.
- A cooperative ETS algorithm combining ORA and GRA improves ER performance by balancing maximum IL and XTL of the longest path.
2. Network Topology
2.1. Problem Statement
2.2. Mathematical Model
2.2.1. Model Parameters
2.2.2. Auxiliary Graphs
2.2.3. MODEL and Constraints
2.3. Algorithm and Constraints
3. Numerical Results
3.1. Two-Port Switching Element
3.2. ORA Scheme
3.3. Routing Table for Four-Port Benes
3.4. Ratio of the Optimal to Near-Optimal Algorithm
3.5. Routing Table for Eight-Port Benes
3.6. Routing Table for 32-Port Benes
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
BW | Bandwidth |
CDF | Cumulative Distribution Function |
ER | Extinction Ratio |
ETS | Efficient Two-Step Algorithm |
GRA | Greedy Algorithm |
IL | Insertion loss |
ORA | Optimal Routing Algorithm |
PDR | Power Dynamic Range |
XTL | Crosstalk |
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Parameters | Values |
---|---|
Coupling efficient | |
Group refractive/Effective refractive index | 2.6/2.6 |
Free spectrum range (FSR) | 26 nm |
Maximum attenuation | 3 dB/cm |
The perimeter of the ring (On state) | 4/12 µm |
The perimeter of the ring (Off state) | 3.48/10.45 µm |
References | Solutions | Power Imbalances | Physical Indicators | Time Complexity |
---|---|---|---|---|
Looping Algorithm [21] | Always | High | Not given | O() |
Work Efficient Algorithm [23] | Sometimes | Low | Not given | O() |
Lee’s Algorithm [17] | Always | Low | MLSE | O() |
This Work | Always | Low | Without MLSE | min(O(, O()) |
Key Indicators | [14] | Our Previous Work [3,4] | This Work |
---|---|---|---|
Port number | 64 | 32 | 32 |
Data rate | 25 | 25 | 25/50 |
Link power budget | −15 dBm | −10.9 dBm | −10.9 dBm |
Power imbalance | 1.5 dB to 95 dB | 1.5 dB to 45 dB | 5 dB to 36 dB |
Eye width | Almost closed | 1.7 nm−110 nm | 2.4 nm−60 nm |
Number of the first-order XTLs | n | n | 1 or p |
BER | |||
WDM | 16 | 8 | 8 |
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Zhao, L.; Li, Z.; Ma, T. Making Path Selection Bright: A Routing Algorithm for On-Chip Benes Networks. Electronics 2024, 13, 981. https://doi.org/10.3390/electronics13050981
Zhao L, Li Z, Ma T. Making Path Selection Bright: A Routing Algorithm for On-Chip Benes Networks. Electronics. 2024; 13(5):981. https://doi.org/10.3390/electronics13050981
Chicago/Turabian StyleZhao, Li, Zhiwei Li, and Tianming Ma. 2024. "Making Path Selection Bright: A Routing Algorithm for On-Chip Benes Networks" Electronics 13, no. 5: 981. https://doi.org/10.3390/electronics13050981
APA StyleZhao, L., Li, Z., & Ma, T. (2024). Making Path Selection Bright: A Routing Algorithm for On-Chip Benes Networks. Electronics, 13(5), 981. https://doi.org/10.3390/electronics13050981