1. Related Works of Data Persistence in WSN htchiu 1

2. Outline Fountain codes – LT codes Wireless sensor network – Random geometric graph model Related works – Growth codes, ACM Sigcomm 2006 – EDFC, INFOCOM 2007 – LTCDS-I, IPSN 2008 – Ratless packet approach, IEEE Journal on Selected Areas in Communications 2010 summary 2

3. Fountain codes D.J.C MacKay IEE Proc.-Commun., Vol. 152, No. 6, December 2005 3

4. Concept 4

5. Application One-to-many data delivery problem – Multicast – Broadcast P2P Robust distributed storage 5

6. LT Codes Michael Luby Proceedings of the 43 rd Annual IEEE Symposium on Foundations of Computer Science (FOCS’02 ) 6

7. Introduction 7

8. LT codes: Encoding 8 0 0100 1 Degree d = 2 value = 0 XOR 0 1.Choose d from a good degree distribution. 2.Choose d neighbors uniformly at random. 3.XOR

9. LT codes: Decoding Message Passing (Back substitution) Gaussian Elimination 9

10. Balls-and-Bins 10

11. All-At-Once distribution 11

12. All-At-Once distribution 12

13. Ideal Soliton Distribution 13 fragile

14. Robust Soliton Distribution  (d) = (  (d) +  (d)) /  where 14

15. Wireless Sensor Network 15

16. WSN To monitor physical and environmental conditions. – temperature, pressure, war zone, earthquake The sensors are energy constrained, unreliable, and computation limited. Collect data from sensors using – Push model (sink) – Pull model (mobile collector) 16

17. Data persistence in WSN The sensors are prone to fail due to running down of battery or external factors. How to increase data persistence in sensor networks? – Encoding data in distributed fashion 17

18. Data persistence in WSN Method – Simple replication – Erasure codes such as RS code, LT codes – Growth codes 18

19. Network Model 19

20. Random Geometric Graph [1] 20

21. Connectivity of RGG [2] 21

22. Related Works 22

23. Growth Codes: Maximizing Sensor Network Data Persistence Abhinav Kamra, Vishal Misra, Dan Rubenstein Department of Computer Science, Columbia University 23 Jon Feldman Google Labs ACM Sigcomm 2006

24. Growth codes 24 Degree of a codeword “grows” with time At each timepoint codeword of a specific degree has the most utility for a decoder (on average) This “most useful” degree grows monotonically with time R: Number of decoded symbols sink has R1R1 R3R3 R2R2 R4R4 d=1 d=2d=3d=4 Time -> http://www.powercam.cc/slide/17704

25. Growth codes The neighbor nodes of the sink have communication overloaded problem. 25

26. Data Persistence in Large-scale Sensor Networks with Decentralized Fountain Codes Yunfeng Lin, Ben Liang, Baochun Li Department of Electrical and Computer Engineering, University of Toronto 26 INFOCOM 2007

27. Introduction The first paper study on distributed implementation of fountain codes through stateless random walk. No sink is available.(but mobile collector.) 27

28. Random Walk A random walk with length L will stops at a node. If the length L of random walk is sufficiently long, then the distribution will achieve steady state. 28

29. IDEA 29

30. Probabilistic Forwarding Table computed by Metropolis algorithm based on the required steady-state distribution of the random walks, which in turn is derived from the initially assigned RSD. 30

31. Algorithm Step 1 : Degree generation – Choose degree independently from RSD. Step 2 : Compute steady-state distribution Step 3 : Compute probabilistic forwarding table – By the Metropolis algorithm Step 4 : Compute the number of random walk – b Step 5 : Block dissemination – Each node disseminate b copies of its source block with its node ID by b random walks based on the probabilistic forwarding table. Step 6: Encoding 31

32. Transmission Cost 32

33. Transmission cost KNb 1000200011.2222.44 100002000015.9931.9842.49 33

34. Experiments Random Geometric Graph K = 10000, N =20000, r = 0.033 The average number of neighbors for each node is 21. Decoding ration = 1.05 EDFC achieves the same decoding performance of the original centralized fountain codes. 34

35. Disadvantage 35

36. Fountain Codes Based Distributed Storage Algorithms for Large-Scale Wireless Sensor Networks Salah A.Aly, Zhenning Kong, Emina Soljanin 2008 International Conference on Information Processing in Sensor Networks 36

37. Introduction Simple random walk without trapping – Choose one of neighbors to send a packet. – To avoid local-cluster effect, let each node accept a packet equiprobably. – Visit each node in the network at least once. Little global information – N, K – LTCDS-II does not need any information in expense of transmission cost. 37

38. Cover Time 38

39. Algorithm 39

40. K = 40 40

41. Transmission Cost 41

42. 42

43. η = 1.8 η = 1.6 Ideal Soliton Distribution 43

44. disadvantage Large transmission cost High decoding ratio Only evaluate the performance of small and medium number of k. 44

45. Rateless Packet Approach for Data Gathering in Wireless Sensor Networks Dejan Vukobratovic, Cedomir Stefanovic, Vladimir Crnojevic, Francesco Chiti, and Romano Fantacci 45 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 7, SEPTEMBER 2010.

46. Introduction Node-centric Packet-centric 46

47. Random walk 47

48. Mixing time 48

49. Performance 49

50. Performance 50

51. Transmission cost 51

52. Summary 52

53. Challenge How to disseminate data efficiently and scalably is a challenge in large-scale wireless sensor network, since the randomness of the network topology. How to find a practical dissemination method to guarantee Robust Soliton distribution subject to a resource constrained sensor network? 53

54. Reference [1] http://www.lsi.upc.edu/~diaz/RGG_HK.pdfhttp://www.lsi.upc.edu/~diaz/RGG_HK.pdf [2] Vivek Mhatre, Catherine Rosenberg, Design guidelines for wireless sensor networks: communication, clustering and aggregation, Ad Hoc Networks, Volume 2, Issue 1, January 2004, Pages 45-63, ISSN 1570-8705, 10.1016/S1570-8705(03)00047-7. [3] A. Sinclair, and M. Jerrum, “Approximate counting, uniform generation and rapidly mixing Markov chains,” Information and Computation, vol. 82, pp. 93–133, 1989. [4] S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, “Mixing Times for Random Walk on Geometric Random Graphs,” Proc. SIAM ANALCO Workshop, 2005 [5] P. Gupta and P. R. Kumar, “The Capacity of Wireless Networks,” IEEE Trans. Info. Theory, vol. 46, No. 2, pp. 388–404, March 2000. [6] C. Avin and G. Ercal, “On the cover time and mixing time of random geometric graphs,” Theor. Comp. Science, vol. 380, pp. 2–22, 2007. [7]Improving the performance of LT codes on noisy channel with systematic connections and power allocations. 54