Latency Performance of Encoding with Random Linear Network Coding
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This document summarizes research on the latency performance of encoding with random linear network coding (RLNC). It finds that doubling the generation or symbol size increases latency by approximately 2x for a full vector encoding algorithm. Switching to an on-the-fly encoding algorithm provides more moderate latency gains of 1.41x for generation size 8, 1.62x for size 16, and 1.75x for size 32. Future work could confirm these results on different CPU architectures, further investigate results from 1kB to 1MB data sizes, and evaluate if multi-threading can decrease encoding latency.
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Latency Performance of Encoding with Random Linear Network Coding
- 1. Latency Performance of Encoding with Random Linear Network Coding Lars Nielsen 1,2,3 René Rydhof Hansen 1 Daniel E. Lucani 2,3 May 3, 2018 1Department Of Computer Science (Cassiopeia), Aalborg University 2Department of Engineering, Aarhus University 3Chocolate Cloud ApS
- 2. Problem • User experience is affected by long encoding latency • Large management overhead, with multiple generation • What happens if we change the NC configuration? • For what data size, is a single generation plausible? 1
- 3. Problem • Can we confirm theory? • Is it possible to predict changes to latency, based on NC configuration? Nistor et al. 2011, 2012 Focus: Latency of coefficient generation from a Finite Field. A. Paramanathan et al. 2013 and C. W. Sørensen et al. 2016 Focus: Energy consumption. 2
- 4. Network Coding • A technique to improve the reliability, robustness, and security of networks • It is a subset of erasure correcting code • Random Linear Network Coding (RLNC), is a subset of Network Coding • Companies and research have started to apply Network Coding in data storage 3
- 7. Network Coding Encoding • For each generation, a symbol matrix is constructed • Each symbol represent a linear equation • Coefficients are randomly drawn from a GF(2q) C × S = CS 5
- 8. On-The-Fly c1,1 c1,2 01,3 · · · 01,g · Symbol1 Symbol2 0 ... 0g+r = first coded symbol 6
- 9. On-The-Fly c1,1 c1,2 01,3 · · · 01,g c2,1 c2,2 c2,3 · · · 02,g · Symbol1 Symbol2 Symbol3 0 ... 0g+r = second coded symbol 6
- 10. On-The-Fly c1,1 c1,2 01,3 · · · 01,g c2,1 c2,2 c2,3 · · · 02,g ... cg+r,1 cg+r,2 · · · cg+r,g · Symbol1 Symbol2 Symbol3 ... Symbolg = g+r coded symbol 6
- 11. Experiment Full Vector f (g, k) = α · g · k(g + r) + β · k · (g − 1)(g + r) On-The-Fly h(g, k) = (α + β) · k · g−1 i=0 i + r · k · (α · g + β · (g − 1)) = (α+β)·k·g·(g−1) 2 + r · k · (α · g + β · (g − 1)) g = generation size, k = symbol size, r = amount of redundancy symbols, α = cost of product operation and β = cost of addition operation 7
- 12. Experiment Expectations Algorithm / g 8 - 16 Result 16 - 32 Result Full Vector 2.06x 2.03x On-The-Fly 2.14x 2.06x Data Sizes Expected Latency increase Result 1kB - 1 MB 103x 1 - 10 MB 10x 10 - 20 MB 2x 2n MB ∼ 2x g ∆L Result 8 2.14x 16 2.06x 32 2.03x 8
- 13. How the experiment was conducted • The benchmark is implemented in C++ and uses Kodo • Using multiple configuration for generation size and symbol size • Data is generated following Monte Carlo simulation • We use high granularity clock for recording start/stop of encoding • For each experiment configuration 1000 experiments have been performed The source code, configurations, and results are available on GitHub under the MIT software license github.com/looopTools/sw9-source 9
- 14. For the Full Vector Algorithm 1kB 1MB 10MB 20MB 32MB 64MB 128MB 256MB 512MB Data size 10−2 10−1 100 101 102 103 Latencyinms 10
- 15. For the Full Vector Algorithm Data Sizes Expected Latency increase Result 1kB - 1 MB 103x ∼ 102x 1 - 10 MB 10x 13x 10 - 20 MB 2x 2x 2n MB ∼ 2x 1.92x − 2.41x, av- erage 2.16x 1kB 1MB 10MB 20MB 32MB 64MB 128MB 256MB 512MB Data size 10−2 10−1 100 101 102 103 Latencyinms 11
- 16. For the Full Vector Algorithm 1kB 1MB 10MB 20MB 32MB 64MB 128MB 256MB 512MB Data size 10−2 10−1 100 101 102 103 Latencyinms G=8 G=16 G=32 12
- 17. For the Full Vector Algorithm Algorithm / g 8 - 16 Result 16 - 32 Result Full Vector 2.06x 1.75x 2.03x 1.82x 1kB 1MB 10MB 20MB 32MB 64MB 128MB 256MB 512MB Data size 10−2 10−1 100 101 102 103 Latencyinms G=8 G=16 G=32 13
- 18. Comparison of the On-The-Fly and Full Vector algorithms 1kB 1MB 10MB 20MB 32MB 64MB 128MB 256MB 512MB Data size 10−2 10−1 100 101 102 103 Latencyinms FV G=8 FV G=16 FV G=32 OTF G=8 OTF G=16 OTF G=32 14
- 19. Comparison of the On-The-Fly and Full Vector algorithms g ∆L Result 8 2.14x 1.41x 16 2.06x 1.62x 32 2.03x 1.75x 1kB 1MB 10MB 20MB 32MB 64MB 128MB 256MB 512MB Data size 10−2 10−1 100 101 102 103 Latencyinms FV G=8 FV G=16 FV G=32 OTF G=8 OTF G=16 OTF G=32 15
- 20. Conclusion Future Work Conclusion • ∼ 2x increase to latency, when doubling generation- or symbol size • Gain of switching to On-The-Fly is more moderate than expected • 1.41x for g = 8 • 1.62x for g = 16 • 1.75x for g = 32 Future Work • Confirm results on additional CPU architectures • Further investigate the 1kB to 1MB results • Can multi-threading be used to decrease latency? 16