Related Works of Data Persistence in WSN

htchiu

1

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

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

0 1 0 0 1

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 RubensteinDepartment of Computer Science, Columbia University

Jon FeldmanGoogle Labs

ACM Sigcomm 2006

24

Growth codes

•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

R1 R3R2 R4

d=1 d=2 d=3 d=4

Time ->

http://www.powercam.cc/slide/17704

25

Growth codes

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

Data Persistence in Large-scale Sensor Networkswith Decentralized Fountain Codes

Yunfeng Lin, Ben Liang, Baochun LiDepartment of Electrical and Computer Engineering, University of Toronto

26INFOCOM 2007

Introduction

• The first paper study on distributed implementation of fountain codes through stateless random walk.

• No sink is available.(but mobile collector.)

27

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

IDEA

𝜋 𝑖>𝜋 𝑗 𝑅 (𝑖)>𝑅( 𝑗)

: the steady state of node i.: the number of received packets of node id: the degree chosen from RSD of node i

d

29

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.

𝜋𝑑=𝑥𝑑𝑑𝑏𝐾

To Guarantee the RSD, disseminate more than d source blocks on each node each node receives source blocks on average.

30

AlgorithmStep 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

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 .

32

Transmission costK N /K b

1000 2000 11.22 22.44

10000 20000 15.99 31.98 42.49

Transmission cost is huge!

Total transmission =

33

Experiments• Random Geometric Graph• K = 10000, N =20000, r = 0.033• The average number of neighbors for each node is 21.

Decoding ration = 1.05EDFC achieves the same decoding performance of the original centralized fountain codes.

34

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.– ()

35

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

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

Cover Time

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

38

Algorithm

39

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

40

Transmission Cost

• Transmission cost huge due to the cover time.– It seems larger than the EDFC proposed by Lin et

al[11]. ( K(bL) )

41

Ideal Soliton distributionFiled = 5*5 5

42

η = 1.8η = 1.6

Ideal Soliton Distribution

43

disadvantage

• Large transmission cost• High decoding ratio• Only evaluate the performance of small and

medium number of k.

44

Rateless Packet Approach for Data Gathering in Wireless Sensor Networks

Dejan Vukobratovic, Cedomir Stefanovic, Vladimir Crnojevic, Francesco Chiti, and Romano Fantacci

45IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 7, SEPTEMBER 2010.

Introduction

• Node-centric• Packet-centric

46

𝜏=𝐶𝑙𝑜𝑔𝑁

Random walk• Non uniform stationary distribution– Simple random walk

• Uniform stationary distribution–

– 47

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]

48

Slow mixing time that scale as .

Performance

49

Performance

50

Transmission cost

51

Summary

52

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.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.