Simple regenerating codes: Network Coding for Cloud Storage
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The document presents Simple Regenerating Codes (SRC) for efficient data repair in cloud storage systems. SRC combines MDS codes for reliability with XOR operations to allow repair using minimal bandwidth and disk I/O. Simulations show SRC reduces storage costs compared to replication and maintains high reliability while improving repair scalability through reduced repair bandwidth and disk accesses.
![Introduction
Background
◦ Recovery
rare exception -> regular operation
GFS[1]:
Hundreds or even thousands of machines
Inexpensive commodity parts
High concurrency/IO
◦ High failure tolerance, both for
High availability and to prevent data loss
[1] S. Ghemawat, H. Gobioff, and S.-T. Leung, “The Google file system,” in
SOSP ’03: Proc. of the 19th ACM Symposium on Operating Systems
Principles, 2003.](https://image.slidesharecdn.com/simpleregeneratingcodes-120410203719-phpapp02/85/Simple-regenerating-codes-Network-Coding-for-Cloud-Storage-9-320.jpg)
![Introduction
Erasure coding vs. Replica[3]erasure code
(4,2) MDS
Replication (any 2 suffice to recover)
File or A A
data A
object
A B
vs
B
B A+B
B A+2B
[3]A. G. Dimakis, P. G. Godfrey, Y. Wu, M. J. Wainwright, and K. Ramchandran,“Network
coding for distributed storage systems,” in IEEE Trans. on Inform. Theory, vol. 56, pp.](https://image.slidesharecdn.com/simpleregeneratingcodes-120410203719-phpapp02/85/Simple-regenerating-codes-Network-Coding-for-Cloud-Storage-12-320.jpg)
![Introduction
Erasure coding vs. Replica[3]erasure code
(4,2) MDS
Replication (any 2 suffice to recover)
File or A A
data A
object
A B
Erasure coding is introducing redundancy in an optimal way.
vs
B Very useful in practice
i.e. Reed-Solomon codes, Fountain Codes, (LT and Raptor)…
B A+B
B A+2B
[3]A. G. Dimakis, P. G. Godfrey, Y. Wu, M. J. Wainwright, and K. Ramchandran,“Network
coding for distributed storage systems,” in IEEE Trans. on Inform. Theory, vol. 56, pp.](https://image.slidesharecdn.com/simpleregeneratingcodes-120410203719-phpapp02/85/Simple-regenerating-codes-Network-Coding-for-Cloud-Storage-13-320.jpg)
![SRC
Object
Requirement I: (n, k) property
MDS[2]
[2] Alexandros G. Dimakis, Kannan Ramchandran, Yunnan
Wu, Changho Suh:
A Survey on Network Codes for Distributed Storage. in Proceedings of the](https://image.slidesharecdn.com/simpleregeneratingcodes-120410203719-phpapp02/85/Simple-regenerating-codes-Network-Coding-for-Cloud-Storage-17-320.jpg)
![SRC
Requirement II: efficient exact repair
◦ Efficient: Low complexity
◦ Exact repair (vs. functional repair)[3] :
1. [demands]Data have to stay in systematic
form
2. [complexity]Updating repairing-decoding
rules-> additional overhead
3. [security] dynamic repairing-and-decoding
rules observed by eavesdroppers ->
information leakage
[2] Changho Suh, Kannan Ramchandran: Exact Regeneration Codes
for Distributed Storage Repair Using Interference Alignment. in IEEE
TRANSACTIONS ON INFORMATION THEORY, VOL. 57, NO. 3, MARCH](https://image.slidesharecdn.com/simpleregeneratingcodes-120410203719-phpapp02/85/Simple-regenerating-codes-Network-Coding-for-Cloud-Storage-19-320.jpg)
Simple regenerating codes: Network Coding for Cloud Storage
- 1. Simple Regenerating Codes: Network Coding for Cloud Storage Dimitris S. Papailiopoulos, Jianqiang Luo, Alexandros G. Dimakis, Cheng Huang, and Jin Li INFOCOM 2012 Presented by Tangkai
- 2. Index About the author Introduction SRC Simulations Conclusion
- 3. About the author Jianqiang Luo ◦ Experience Senior Software Engineer @ EMC Received PhD, Wayne State University Intern @ Microsoft, Data Domain Team Leader @ Actuate Received MS, SJTU ◦ Specialties Working on distributed storage systems during PhD Performance profiling.
- 4. About the author Alexandros G. Dimakis ◦ Assistant Professor Dept of EE – Systems, USC ◦ Research interests: Communications, signal processing and networking. ◦ INFOCOM 2012 - 2 ◦ Erasure code MDS MSR MBR etc
- 5. About the author Cheng Huang ◦ Education Microsoft Research Ph.D. Washington University B.S. and M.S. EE Dept, SJTU ◦ Research interest cloud services, internet measurements, erasure correction codes, distributed storage systems, peer-to- peer streaming, networking and multimedia communications. ◦ INFOCOM 2011 Public DNS System and Global Traffic Management Estimating the Performance of Hypothetical Cloud Service Deployments: A Measurement-Based Approach
- 6. About the author Jin Li ◦ Experience Microsoft Research BS/MS/PhD THU (within 7 years) 计算机普及要从娃娃抓起 ◦ Title IEEE Fellow GLOBECOM/ICME/ACM MM Chair
- 7. Index About the author Introduction SRC Simulations Conclusion
- 8. Introduction Background ◦ We have come into BIG DATA ERA! Digital Universe 1.8 ZB (=1.8e9 TB) Several PBs photo stored on Facebook 14.1PB data stored on Taobao (2010) ◦ Data security is IMPORTANT Free from unwanted actions of unauthorized users. Free from data loss caused by destructive forces
- 9. Introduction Background ◦ Recovery rare exception -> regular operation GFS[1]: Hundreds or even thousands of machines Inexpensive commodity parts High concurrency/IO ◦ High failure tolerance, both for High availability and to prevent data loss [1] S. Ghemawat, H. Gobioff, and S.-T. Leung, “The Google file system,” in SOSP ’03: Proc. of the 19th ACM Symposium on Operating Systems Principles, 2003.
- 10. Introduction Background ◦ Erasure coding > replication 1. redundancy level, reliability 2. reliability, storage cost ◦ Some applications Cloud storage systems Archival storage Peer-to-peer storage systems
- 11. Introduction Erasure coding: MDS n=3 n=4 k=2 File or A A data A object A B B B B A+B A+B (3,2) MDS code, (single parity) A+2B used in RAID 5 (4,2) MDS code. Tolerates any 2 failures Used in RAID 6
- 12. Introduction Erasure coding vs. Replica[3]erasure code (4,2) MDS Replication (any 2 suffice to recover) File or A A data A object A B vs B B A+B B A+2B [3]A. G. Dimakis, P. G. Godfrey, Y. Wu, M. J. Wainwright, and K. Ramchandran,“Network coding for distributed storage systems,” in IEEE Trans. on Inform. Theory, vol. 56, pp.
- 13. Introduction Erasure coding vs. Replica[3]erasure code (4,2) MDS Replication (any 2 suffice to recover) File or A A data A object A B Erasure coding is introducing redundancy in an optimal way. vs B Very useful in practice i.e. Reed-Solomon codes, Fountain Codes, (LT and Raptor)… B A+B B A+2B [3]A. G. Dimakis, P. G. Godfrey, Y. Wu, M. J. Wainwright, and K. Ramchandran,“Network coding for distributed storage systems,” in IEEE Trans. on Inform. Theory, vol. 56, pp.
- 14. Introduction Metrics ◦ Storage per node (α) ◦ Repair Bandwidth per single node repair (γ) ◦ Disk Accesses per single node repair (d) ◦ Effective Coding Rate (R) Contribution ◦ High R, Small d ◦ Low repair computation complexity
- 15. Index About the author Introduction SRC Simulations Conclusion
- 16. SRC SRC: Simple Regenerating Codes ◦ Regenerating Codes address the issue of rebuilding (also called repairing) lost encoded fragments from existing encoded fragments. This issue arises in distributed storage systems where communication to maintain encoded redundancy is a problem.
- 17. SRC Object Requirement I: (n, k) property MDS[2] [2] Alexandros G. Dimakis, Kannan Ramchandran, Yunnan Wu, Changho Suh: A Survey on Network Codes for Distributed Storage. in Proceedings of the
- 18. SRC ◦ MDS
- 19. SRC Requirement II: efficient exact repair ◦ Efficient: Low complexity ◦ Exact repair (vs. functional repair)[3] : 1. [demands]Data have to stay in systematic form 2. [complexity]Updating repairing-decoding rules-> additional overhead 3. [security] dynamic repairing-and-decoding rules observed by eavesdroppers -> information leakage [2] Changho Suh, Kannan Ramchandran: Exact Regeneration Codes for Distributed Storage Repair Using Interference Alignment. in IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 57, NO. 3, MARCH
- 20. SRC Solution ◦ MDS codes are used to provide reliability to meets Requirement I ◦ simple XORs applied over the MDS coded packets provide efficient exact repair to meets Requirement II
- 21. SRC Construction
- 22. SRC Repair
- 23. (n,k,2)-SRC Code Construction ◦ File f , of size M = 2k ◦ Split into 2 parts ◦ 1. 2 independent (n,k)-MDS encoding ◦ 2. Generating a parity sum vector using XOR
- 24. (n,k,2)-SRC Distribution ◦ 3n chunks in n storage nodes
- 25. (n,k,2)-SRC Repair
- 26. (n,k,f)-SRC General Code Construction ◦ File f , of size M = fk ◦ Cut into f parts ◦ 1. f independent (n,k)-MDS encoding ◦ 2. Generating a parity sum vector using XOR
- 27. (n,k,f)-SRC Distribution ◦ (f+1)n chunks in n storage nodes
- 28. (n,k,f)-SRC Repair
- 29. (n,k,f)-SRC Theorem ◦ Effective Coding Rate (R) SRC is a fraction f/f+1 of the coding rate of an (n, k) MDS code, hence is upper bounded
- 30. (n,k,f)-SRC Theorem ◦ Effective Coding Rate (R)
- 31. (n,k,f)-SRC Theorem ◦ Storage per node (α) ◦ Repair Bandwidth per single node repair (γ) ◦ Disk Accesses per single node repair (d) Seek time
- 32. (n,k,f)-SRC Theorem ◦ Disk Accesses per single node repair (d) Starting with f disk accesses for the first chunk repair
- 33. (n,k,f)-SRC Theorem ◦ Disk Accesses per single node repair (d) each additional chunk repair requires an additional disk access
- 34. (n,k,f)-SRC Comparasion
- 35. (n,k,f)-SRC Asymptotics of the SRC -> MDS ◦ let the degree of parities f grow as a function of k ◦ Repair Bandwidth per single node repair (γ) ◦ Effective Coding Rate (R)
- 36. Index About the author Introduction SRC Simulations Conclusion
- 37. Simulations Simulator Introduction ◦ One master, other storage server. ◦ Chunks form the smallest accessible data units and in our system are set to be 64MB Simulator Validation ◦ 16 machines ◦ 1Gbps network. ◦ 410GB data per machine ◦ Approximately 6400 chunks
- 38. Simulations Simulator Validation ◦ matches very well, when the percentile is below 95
- 39. Simulations Storage Cost Analysis ◦ 3-way replication as baseline
- 40. Simulations Repair Performance ◦ Calculated on time ◦ Highlights: Scalability
- 41. Simulations Degraded Read Performance ◦ The only difference is after a chunk is repaired, we do not write it back.
- 42. Simulations Data Reliability Analysis ◦ simple Markov model to estimate the reliability ◦ 5 years /1PB data / ◦ 30 min for replica / 15 min for SRC
- 43. Simulations Data Reliability Analysis Several order of magnitude of reliablity Scalability
- 44. Index About the author Introduction SRC Simulations Conclusion
- 45. Conclusions Highlight ◦ R-S Low IO/bandwidth -> scalability ◦ replica High reliability Decent repair/degraded read performance
- 46. Critical Thinking Simulation （n, k）as n grows, erasure performance is weaker Compare ◦ MSR? ◦ Exact? ◦ Implementation - > Simulation