Related Works of Data Persistence in WSN

1. Related Works of Data Persistence in WSN htchiu

2. Outline • Fountain codes • LT codes • Wireless sensor network • Random geometric graph model • Related works • Growth codes, ACM Sigcomm2006 • EDFC, INFOCOM 2007 • LTCDS-I, IPSN 2008 • Ratless packet approach, IEEE Journal on Selected Areas in Communications 2010 • summary

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

4. Concept

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

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

7. Introduction • The first realization of practical fountain codes that are near-optimal. • k original symbols can be recovered from • encoding symbols with high probability . • Complexity

8. LT codes: Encoding 0 1 0 0 1 0 Degree d = 2value = 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

10. Balls-and-Bins

11. All-At-Once distribution

12. All-At-Once distribution • The sum of edges is • GOOD! • The number of encoding symbols needed to recover all k input symbols is • Unacceptable!!

13. Ideal Soliton Distribution fragile

14. Robust Soliton Distribution • m(d) = (r(d) + t(d)) / b where

15. Wireless Sensor Network

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)

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

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

19. Network Model

20. Random Geometric Graph[1] • : Choose a sequence of independent and uniformly distributed points on , given a fixed r(n)>0, connect two points if their -distance is at most r.

21. Connectivity of RGG[2] When N sensor nodes are distributed over an area , then

22. Related Works

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

24. d=2 d=3 d=4 d=1 R1 R2 R3 R4 Time -> Growth codes • Degree of a codeword “grows” with time • At each timepointcodeword 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 http://www.powercam.cc/slide/17704

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

26. Data Persistence in Large-scale Sensor Networkswith Decentralized Fountain Codes Yunfeng Lin, Ben Liang, Baochun Li Department of Electrical and Computer Engineering, University of Toronto • 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.)

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.

29. IDEA d : the steady state of node i. : the number of received packets of node i d: the degree chosen from RSD of node i

30. Probabilistic Forwarding Table • computed by Metropolis algorithm based on the required steady-state distributionof the random walks, which in turn is derived from the initially assigned RSD. • To Guarantee the RSD, • disseminate more than d source blocks on each node • each node receives source blocks on average.

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

32. Transmission Cost • The product of the number of random walks and the length of random walks(). • To minimize the dissemination cost, which is governed by .

33. Transmission cost Transmission cost is huge! Total transmission =

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.

35. Disadvantage • Global information • K, N, maximum node degree • is not a constant. • Memory cost • Each node should maintain received packets. • Probabilistic forwarding table • Transmission cost • Since a random walk stops at a node. • ()

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

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.

38. Cover Time • Lemma 5 (Avin and Ercal [3]). If a random geometric graph with n nodes is a connected graph with high probability, then

39. Algorithm

40. K = 40 K = 40, c = 0.1, = 0.5

41. Transmission Cost • Transmission cost huge due to the cover time. • It seems larger than the EDFC proposed by Lin et al[11]. ( K(bL) )

42. Ideal Soliton distribution Filed = 5*5 5

43. Ideal Soliton Distribution η = 1.8 η = 1.6

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

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

46. Introduction • Node-centric • Packet-centric

47. Random walk • Non uniform stationary distribution • Simple random walk • Uniform stationary distribution

48. Mixing time • The mixing time is related to transition probability P. • [3] • At G(n , r), affected by the radius r. • [4] • Critical connectivity radius of G(N, r) • [5] • Rapid mixing • [6] Slow mixing time that scale as .

49. Performance

50. Performance