1 An Update Model for Network Coding in Cloud Storage Systems th Annual Allerton Conference on Communication, Control, and Computing Mohammad Reza Zakerinasab Mea Wang Department of Computer Science University of Calgary

2 Outline ﻪIntroduction ﻪRelated Works ﻪProposed System ﻪDifferential Update Model ﻪEvaluation ﻪConclusion

Network Coding (1/2) ﻪThere are different mechanisms for arranging file copies among storage nodes or devices ﻩstandard RAID architectures ﻩerasure code ﻩnetwork coding ﻪThe network coding in cloud storage systems allows storage nodes to collectively host multiple copies of a file. 3

Network Coding (2/2) ﻪIn a network-coding-assisted cloud storage system ﻩa file is divided into n blocks ﻯencoded using random coefficients. ﻩencoded blocks are distributed in the Cloud. ﻯdecoded the n encoded blocks from any subset of the storage nodes. 4

5 Problem Definition ﻪExisting works have been focusing on mechanisms for preserving the level of redundancy. ﻪHowever, the most frequent operations maintaining coded information in the system up to date performed on files. ﻩfile updates ﻪAny change in the file will impact all coded blocks in the system. ﻩreplace all traces of the file

Application ﻪGoogleDocs : online collaborative office suites, let users create, edit and publish a document collaboratively from around the world. ﻪWhen a file is updated, even changing a single byte can outdate all coded blocks in the system. ﻩre-computations ﻩre-deliveries 6

7 Problems ﻪRe-computing coded blocks is very CPU intensive. ﻪReplacing all the coded blocks consumes large amount of bandwidth.

Proposed Model ﻪSending only the modified parts with a minimum possible overhead. ﻪThe mathematical model of Differential Update Mechanism (DUM) was presented by this paper. ﻩupdate algorithms can be performed on all nodes. ﻪThe simulation results show that the proposed DUM saving a significant bandwidth in a cloud storage system. 8

9 Outline ﻪIntroduction ﻪRelated Works ﻪProposed System ﻪDifferential Update Model ﻪEvaluation ﻪConclusion

Related Works (1/2) ﻪCommercial cloud storage systems, such as Microsoft Azure [8] and Google Cloud [9], utilize source erasure codes. ﻪNetwork coding was originally proposed in information theory in 2000 [1]. ﻪIn contrast to source erasure codes, network coding applies coding at intermediate relay nodes throughout the network. 10

Related Works (2/2) ﻪThe benefits for coding at intermediate nodes include ﻩhigh throughput [1], [3] ﻩefficient routing algorithm design [17] ﻩenergy savings in wireless networking [18] ﻩsecurity [19] ﻪThe closest related works of update problem are on the repair problem ﻩprovide mechanisms for one or more nodes fail [25]. ﻩpreserve the level of redundancy. 11

Reference ﻪ[1] R. Ahlswede, N. Cai, S. R. Li, and R. W. Yeung, “Network Information Flow,” IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1204– 1216, July ﻪ[3] R. Koetter and M. Medard, “An Algebraic Approach to Network Coding,” IEEE/ACM Transactions on Networking, vol. 11, no. 5, pp. 782–795, October ﻪ[8] B. Calder, J. Wang, A. Ogus, N. Nilakantan, A. Skjolsvold, S. McKelvie, Y. Xu, S. Srivastav, J. Wu, H. Simitci, J. Haridas, C. Uddaraju, H. Khatri, A. Edwards, V. Bedekar, S. Mainali, R. Abbasi, A. Agarwal, M. F. ul Haq, M. I. ul Haq, D. Bhardwaj, S. Dayanand, A. Adusumilli, M. McNett, S. Sankaran, K. Manivannan,, and L. Rigas, “Windows Azure Storage: A Highly Available Cloud Storage Service with Strong Consistency,” in Proc. of the 23rd ACM Symposium on Operating Systems Principles (SOSP), Cascais, Portugal, October , pp. 143–

Reference ﻪ[9] D. Ford, F. Labelle, F. I. Popovici, M. Stokely, V.-A. Truong, L. Barroso, C. Grimes, and S. Quinlan, “Availability in Globally Distributed Storage Systems,” in Proc. of the 9th USENIX Symposium on Operating Systems Design and Implementation (OSDI), Vancouver, BC, October , pp. 1– 14. ﻪ[17] D. S. Lun, N. Ratnakar, R. Koetter, M. Medard, E. Ahmed, and H. Lee, “Achieving Minimum Cost Multicast: A Decentralized Approach Based on Network Coding,” in Proc. of the 24th Conference of the IEEE Communications Society (INFOCOM), Miami, FL, March , pp. 1607–1617. ﻪ[18] H. Rahul, W. Hu, D. Katabi, M. Medard, and J. Crowcroft, “XORs in the Air: Practical Wireless Network Coding,” IEEE/ACM Transactions on Networking, vol. 16, no. 3, pp. 497–510, June ﻪ[19] C. Gkantsidis and P. Rodriguez, “Cooperative Security for Network Coding File Distribution,” in Proc. of the 25th Conference of the IEEE Communications Society (INFOCOM), Barcelona, Spain, April , pp. 1–13. 13

14 Outline ﻪIntroduction ﻪRelated Works ﻪProposed System ﻪDifferential Update Model ﻪEvaluation ﻪConclusion

Modeling the Storage Cloud System 15 Storage Cloud End Hosts

Modeling the Storage Cloud System 16

Network Coding in the Storage Cloud System ﻪWith randomized network coding, a file is divided into n original blocks B = [b 1, b 2, …, b n ], where b i has a fixed number of bytes s. ﻪEncoding a new block c i ﻩthe source node first independently and randomly chooses a set of coding coefficients ε i = [ε i,1, ε i,2, …, ε i,n ] in the Galois field GF(2 8 ). ﻯ. 17 …… B = b 1, b 2, b 3,..…. b j c 1, c 2, c 3,......, c R*n b1,b2,b3,..bnb1,b2,b3,..bn

Network Coding in the Storage Cloud System 18

The Update Problem 19

20 Outline ﻪIntroduction ﻪRelated Works ﻪProposed System ﻪDifferential Update Model ﻪEvaluation ﻪConclusion

Differential Update Model (DUM) ﻪThey believe that the update problem is just as essential as the repair problem. ﻪThey propose the DUM to update coded blocks by delivering only the blocks that are affected by the updates. ﻩavoids transmissions of the entire file for each update. 21

Updating Coded Blocks 22

Updating Coded Blocks 23

Updating Storage Nodes ﻪA significant amount of bandwidth can be saved since most updates will affect only a smaller portion of a file. ﻪRecover Δ from Δ’ ﻩreconstructed by inserting the zero δ-vectors into Δ’ according to the update vector u. 24

Updating Storage Nodes ﻪSend the non-zero rows of Δ’ = [δ 1, δ 2, δ 3, …, δ n’ ] ﻪUpdate vector u v+1 = [u v+1,1, u v+1,2,..., u v+1,n ] ﻩ. ﻪEncode the matrix Δ’, ﻪDecode the matrix Δ’, 25

Updating Storage Nodes 26

Updating Target Nodes 27

Aggregating Updates Across Multiple Versions (1/4) 28

Aggregating Updates Across Multiple Versions (2/4) ﻪA coded block in version v may be expressed in terms of the coded blocks of version 0 and the summation of coded δ-blocks from version 0 to version m. 29

Aggregating Updates Across Multiple Versions (3/4) ﻪTo support such an aggregated update, the update table that stores ﻩthe update vectors ﻩthe coded δ- blocks ﻪIf a storage node misses one or more updates, then find the first non-empty entry following the empty entries. ﻩthe aggregated Δ’ containing changes across the missing versions. 30

Aggregating Updates Across Multiple Versions (4/4) ﻪComputational overhead ﻩgeneration of the aggregated update vector ﻯ. ﻩgeneration of n’ aggregated coded δ-vectors ﻯ. 31

32 Outline ﻪIntroduction ﻪRelated Works ﻪProposed System ﻪDifferential Update Model ﻪEvaluation ﻪConclusion

Numerical Analysis 33

Experiment Results (1/7) ﻪThe number of blocks n should be no more than 100 to ensure that network coding operates at a rate faster than a typical transmission rate in a network. ﻪWe compare the performance of conventional network coding update (NC) and DUM. 34

Experiment Results (2/7) ﻪBandwidth usages 35

Experiment Results (3/7) ﻪBandwidth usage and Computational cost 36

Experiment Results (4/7) ﻪComputational cost on storage nodes dominates the overall cost. 37

Experiment Results (5/7) ﻪAggregated updates 38

Experiment Results (6/7) ﻪUpdate affects 39

Experiment Results (7/7) ﻪSimulation study ﻪDiff [31], bsDiff [32] 40 [31] J. W. Hunt and M. D. McIlroy, “An Algorithm for Differential File Comparison,” Bell Laboratories 41, Computing Science Technical Report, June [32] C. Percival, “Matching with Mismatches and Assorted Applications,” Ph.D. dissertation, Wadham College, University of Oxford, 2006.

41 Outline ﻪIntroduction ﻪRelated Works ﻪProposed System ﻪDifferential Update Model ﻪEvaluation ﻪConclusion

Conclusion ﻪDUM saves both the communication and computational costs, unless the update affects almost the entire file ﻪDUM conserves CPU cycles for large files and when the data is more scattered in the Cloud. ﻪThis paper only considered n’ is smaller than n, what’s happened if n’ is large than n ? 42