1 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.

2 Outlines Introduction Distributed rateless coding using rateless packet Simulation results Conclusion

3 Introduction Node-centric distributed rateless coding schemes [6]-[10],  collecte sufficient number of different sensor data packets and performing rateless encoding is the task of sensor nodes In this paper, we describe a novel packet-centric technique for data gathering in WSN based on distributed rateless codes.  although processed by network nodes, encoded packets (rateless packets) carry the key information in their headers to control the encoding process, while moving around the network

4 Introduction Packet-centric  Each rateless packet is initially assigned a randomly selected degree from a given rateless code degree distribution  And randomly traverses the network collecting sensor data until a target degree is reached, after which the rateless packet is stored in a random sensor node.  By shifting the encoding paradigm from nodes to packets, the distributed rateless encoding is significantly simplified, any degree distribution can be exactly obtained, and the encoding process is robust to node failures.  To achieve the efficiency of the centralized rateless codes, the rateless packet approach relies on efficient uniform combining of sensor data packets into rateless packets and their uniform dispersion throughout the network.

5 Rateless codes A measure of the rateless code efficiency is the average amount of encoded symbols N’ avg needed for successful decoding at the receiver.  It can be also expressed using the average reception overhead ε > 0, defined as N’ avg = (1+ε)N. LT codes are encoded by selecting uniformly at random d different information symbols and their bitwise XOR-ing into the encoded symbol. We focus on the distributed rateless code design based on LT codes.

6 Fig. 1. LT code design: each encoded symbol is obtained by XOR-ing d information symbols selected uniformly at random where the degree d is randomly drawn from the degree distribution Ω(d).

7 Distributed rateless coding using rateless packet Random geometric graph G(N, r) model  N sensor nodes are uniformly placed on a unit square area  Any sensor node can reliably communicate with any neighbor within the transmission range r.  Sensor measurements are performed periodically by all N sensors in the network The measured data are placed in an equal-length sensor data packets, one per sensor node.  The goal of the distributed rateless coding scheme is to create and disperse a sufficient number of rateless packets in a distributed fashion uniformly across the WSN.

8 Distributed rateless coding using rateless packet The goal of the design of distributed rateless coding scheme is to make the data gathering as efficient as possible by minimizing the average number of rateless packets sufficient for the decoding of all the sensor data.  Rateless Packet Gathering Using Mobile Collector  Rateless Packet Gathering From Local Neighborhood

9 Rateless packet Rateless packets are generated from sensor measurements stored as equal-length sensor data packets in each of N sensor nodes.  Generation ID : the period when the data were measured,  Sensor ID’s : the sensors whose data packets are encoded in the data field,  Degree Counter and Mixing-Time Counter fields control the encoding process.

10 Rateless packet The process of creating rateless packets consists of 3 phases: initialization, encoding and dispersion of the rateless packets. 1) the initialization phase  bN rateless packets are initialized across N sensor nodes of the WSN.  Every sensor node generates b rateless packets, copies its current sensor data packet in the rateless packet data field and puts its ID in the sensor ID’s header field.  To each of b rateless packets, sensor independently associates a degree d drawn randomly from a selected degree distribution Ω(d).  As the rateless packet content is initialized with the local sensor data packet, the degree counter is set to value d − 1, which is the remaining degree to be collected.  Finally, the mixing-time counter is set to the chosen (global) mixing-time value τ.

11 Rateless packet 2) the encoding phase  the task of each rateless packet is to add to its content the remaining d−1 sensor datapackets selected uniformly at random by performing random walk across the WSN.  The probabilities p ij of selecting sensor node j from the set N(i) are obtained locally by each sensor node i.  While performing a random walk, every rateless packet is processed by every sensor node on the path using the following simple rule. If the mixing-time counter ＞ 0  the sensor node only updates the rateless packet header  the mixing-time counter - 1  forward the rateless packet to the next random hop If the mixing-time counter = 0  the sensor node adds its sensor data packet to the rateless packet content,  degree counter - 1  puts its Sensor ID in the list of Sensor ID’s,  resets the mixing-time counter to its initial value τ  forwards the rateless packet to the next random hop. Finally, upon collecting d sensor data packets the rateless packet completes its encoding phase.

12 Rateless packet 3) the dispersion phase  The goal of the dispersion phase is to place the rateless packet in its final random position in the network.  To prevent any correlation between the content of the rateless packet and the node where it is finally stored, each rateless packet continues its random walk for another τ hops.

13 Fig. 3. Example of rateless packet initialization, encoding and dispersion phase.

14 Distributed uniform sampling of sensor nodes We describe random walks in the context of disseminating a source block.  sensor: node in the graph  The next hop is randomly chosen from the neighbors of the source node. A random walk corresponds to a time-reversible Markov chain. 2 popular algorithms that output the matrix P having uniform stationary distribution that can be easily implemented in the distributed WSN scenario.  Maximum-Degree (MD) Algorithm [16]: Sensor node i associates the transition probabilities pij for forwarding rateless packets to any of its neighbors j from N(i).

15 Distributed uniform sampling of sensor nodes  Metropolis-Hastings (MH) Algorithm [15]: Sensor node i exchanges a single message containing its degree with each of its neighbors. After this simple information exchange, each sensor node i associates the transition probabilities pij

16 Simulation results WSN model  We assume a random geometric graph G(N, r) on a unit square.  The number of nodes is set to N = 500 or N =  The sensor range is set to r = 0.1 or r = Rateless packet degrees are selected from Robust Soliton degree distribution Ω RS (d) with parameters c = 0.03 and δ = 0.5. After the dispersion phase, rateless packets gathering and sensor data decoding is performed. The process of data gathering is investigated in 2 scenarios  Rateless Packet Gathering Using Mobile Collector  Rateless Packet Gathering From Local Neighborhood

17 Rateless Packet Gathering Using Mobile Collector We assume the existence of the mobile collector which starts the data gathering at a randomly selected sensor node and performs a random walk across G(N, r). At each sensor node, the collector moves all the rateless packets from the sensor node buffer memory into its own buffer memory. Once the collector collects N rateless packets, the procedure of “greedy” iterative BP decoding[14] is activated. Each new collected rateless packet, the decoder continues with the decoding process. When a sufficient number N of rateless packets is collected for successful decoding, the simulation is finished. The mixing-time constant C and the number of rateless packets b created at each sensor node.

18 Fig. 5. The average number of rateless packets N’ avg needed for successful decoding at the collector for sensor range r = 0.1. The efficiency N’ avg demonstrates slow convergence with the increase of C. The efficiency convergence is faster for smaller b.

19 Fig. 6. The average number of rateless packets N’ avg needed for successful decoding at the collector for sensor range r = The system efficiency N’ avg close to optimal is already achieved for the values as low as C = 3. The efficiency convergence is faster for smaller b. Use of small value for b and as small as possible value of C for which N’avg is close to optimal. By keeping both b and C small, the total energy consumption in the network, measured through the average number of hops of all rateless packets, is kept low.

20 Fig. 7. Performance comparison for different sensor ranges r and different probability transition matrix P design algorithms. NRW algorithm performs better than MD algorithm, and similarly as MH algorithm. NRW does not associate self-transition probabilities in the probability matrix P, which makes the flow of rateless packets more dynamic.

21 d avg : the average network node degree C avg : the average percentage of connected network graphs For low mixing time values, the required system performance can be achieved by properly adjusting the node range r.

22 Fig. 7. Performance comparison for different sensor ranges r and different probability transition matrix P design algorithms. Create smaller number of rateless packets was desirable as the system efficiency is shown to be better with small b for small values of C. The value of b dominantly affects energy-expenses of the rateless packet scheme

23 Fig. 8. System efficiency N’ avg and average path length P avg of mobile collector as a function of the number of rateless packets b produced at each sensor node. By increasing b, the average path length P avg of the mobile collector decreases (lower curves). The price of increased energy consumption and slight decrease in system efficiency N’ avg for lower values of C (upper curves).

24 Rateless Packet Gathering From Local Neighborhood Rateless packets are collected from any node in the network and only from its local neighborhood.  The neighboring nodes which are away up to the distance R. We assume that a network node attempts to decode the data of all sensors by collecting rateless packets from its local neighborhood within the range R. We observe 2 scenarios  1) the selected sensor is closest to the diagonal crossing of the WSN unit square area  2) a sensor is randomly selected

25 Fig. 9. Fraction of decoded sensor data packets recovered from all rateless packets in local sensor neighborhood of range R. If the sink is selected from the interior of the unit square area, the results in Fig. 9(a) are encouraging as they show that all the sensor data can be made very close (R ≈ 0.2 − 0.3) to any selected sink. Fig. 9(b), due to the edge effects, results for the random node case slightly deteriorate.

26 Conclusion In this paper, we introduced a novel distributed rateless coding scheme for data gathering in WSN based on creating and distributing rateless packets across the WSN. The proposed scheme is suitable for large scale WSNs deployed at inaccessible regions (e.g., mountainous areas).

27 References [6] A. Dimakis, V. Prabhakaran, K. Ramchandran, “Distributed Fountain Codes for Networked Storage,” Proc. IEEE ICASSP 2006, [7] A. Kamra, J. Feldman, V. Misra and D. Rubenstein, “Growth Codes: Maximizing Sensor Network Data Persistence,” Proc. ACM SIGCOMM 2006, Pisa, Italy, [8] Y. Lin, B. Liang and B. Li, “Data Persistance in Large-Scale Sensor Networks with Decentralized Fountain Codes,” Proc. IEEE INFOCOM 2007, Anchorage, AL, USA, [9] S. Aly, Z. Kong, and E. Soljanin, “Fountain codes based distributed storage algorithms for large-scale wireless sensor networks,” Proc. IEEE/ACM IPSN, S. Louis, MO, USA, [10] D. Munaretto, J. Widmer, M. Rossi and M. Zorzi, “Resilient Coding Algorithms for Sensor Network Data Persistance,” Proc. EWSN 2008, Bologna, Italy, [14] M. Luby, “LT Codes,” Proc. of the 43rd Annual IEEE Symp. Foundations of Computer Science (FOCS), Vancouver, Canada, November [15] N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys., vol. 21, pp. 1087–1092, [16] S. Boyd, P. Diaconis, and L. Xiao, “Fastest Mixing Markov Chain on a Graph,” SIAM Review, problems and techniques section, vol. 46(4), pp. 667– 689, December 2004.