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Network Coding Schemes for Underwater Networks The Benefits of Implicit Acknowledgement Daniel E. Lucani, Muriel Médard, Milica Stojanovic Massachusetts Institute of Technology

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Introduction Acoustic underwater communications [1]: –Low propagation speed: High transmission delays Trade-off: probability of collision and transmission delay –Path loss dependent on transmission distance and signal frequency: Bandwidth determined by distance –Random fading channel with high packet erasures Application: fixed acoustic sensor networks –Battery-powered devices –Expected to operate for long time New network coding method: relies on implicit acknowledgements to achieve best performance in terms of power consumption and transmission delay for all loads [1] Stojanovic, M., ”On the Relationship Between Capacity and Distance in an Underwater Acoustic Communication Channel”, in Proc. WUWnet ’06, pp. 41-47, Los Angeles, Sept. 2006 –Minimize power consumption: Reduce transmissions per packet –Trade-off: Minimize transmission delay

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Node Network Coding Originally developed for wired networks [2] Nodes can perform mathematical operations on packets –Routing is particular case of network coding: forwarding and replication –Simple, powerful: Linear combination of packets [3, 4] Random linear combination of packets [5] –Distributed computation –Good performance in erasure channels [2] Ahlswede, et al, ”Network Information Flow”, IEEE Trans. Inf. Theory, pp. 1204-1216, Jul. 2000 [3] S.-Y. R. Li, et al, “Linear network coding”, IEEE Trans. Inf. Theory, pp. 371–381, Feb. 2003. [4] R. Koetter and M. Médard, “An algebraic approach to network coding,” IEEE/ACM Trans. Networking, vol. 11, no. 5, pp. 782–795, Oct. 2003. [5] T. Ho, et al,“A random linear network coding approach to multicast,” IEEE Trans. on Info. Theory, vol. 52, no. 10, pp. 4413- 4430, October 2006. Packet A λPacket Aλ Packet B μA+ρBμ, ρ Coded Code Data Coded Code Data

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Network Coding Degree of freedom (dof): Number of independent equations used to generate packet Good match for underwater acoustic communications: –Good performance in channels with high packet erasures –Outperforms routing in wireless scenario for number of transmissions per packet and delay [6, 7] Expect reduced power consumption Expect low transmission delay –Distributed computation of codes at each node: topology independent Previous work in [8] – End-to-end packet loss and total transmissions (No retransmission) –Simplified channel: link erasure probability [6] Lun, D. S., et al,”Minimum-Cost Multicast Over Coded Packet Networks”, IEEE Trans. on Info. Theory, vol. 52, no. 6, pp. 2608-2623, Jun. 2006 [7] Lun, D. S., et al, ”Network Coding for Efficient Wireless Unicast”, In Proc. IEEE International Zurich Seminar on Communications 2006, pp. 74-77, Zurich, Feb. 2006 [8] Z. Guo, P. Xie, J. H. Cui and B. Wang. "On Applying Network Coding to Underwater Sensor Networks", In Proc. of WUWNet '06, pp. 109-112, Los Angeles, Sept. 2006

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Channel Model Attenuation: With the spreading factor and Thorp’s formula Noise: is the power sprectral density (p.s.d) decays with frequency at approximately 18dB/dec SNR [1]: With optimum bandwidth for distance power to achieve SNR level for given. [1] Stojanovic, M., in Proc. WUWnet ’06, pp. 41-47, Los Angeles, Sept. 2006

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Channel Model SNR changing distance but keeping B(l): Equivalent bit SNR: where Erasure probability: computed using this with PSK bit error probability, assuming fast channel decorrelation and fixed packet size

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MAC Model Previous work includes various MAC protocols [9], e.g. CSMA, polling, CDMA, TDMA, FDMA –CSMA/TDMA/Polling: latency compromises usefulness –FDMA: reduction in bandwidth with –CDMA: high SNR limits performance. Also, difficult to do effective power control Most modems (designed for point to point communication) support one-way polling or fixed transmission assignment Simulations: using last assumption. Transmissions occur every time T [9] Kilfoyle, D. B. and Baggeroer, A. B. ” The State of the Art in Underwater Acoustic Telemetry”, IEEE Journal of Oceanic Engineering,vol. 25, no. 1, Jan. 2000 R2R2 R1R1 Low SNR R2R2 R1R1 High SNR

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Node 1 Node 2Node 3 MAC Model Node 1 Node 2Node 3 Data Routing Coded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.Code Network Coding Rateless Fashion Data Coded Pq.CodeCoded Pq.CodeCoded Pq.Code Network Coding with Implicit ACK Coded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.CodeCoded Pq.Code ACK

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Simulation Results Delay (measured in T units) and power consumption to transmit N packets from Tx node to Rx Packets generated with probability P source each T time Fixed number of packets Network Coding: –Better delay performance –Rateless fashion: poor power consumption performance in low P source Node 1Node 2Node 4 Node 3 D1D1 D2D2 D3D3

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Simulation Results Network coding with implicit acknowledgement: –Best power consumption performance over all P source –Best delay performance over all loads –Approximates opportunistic routing with link-by-link ACK as load decreases Cannot take advantage of linear combination Delay: High P source Power: Low P source

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Simulation Results Increasing network size network coding with implicit acknowledgement: –Improves power consumption per node –Gives lowest delay per added node Similar results to [7]. However, [7] does not consider implicit acknowledgement method [7] Lun, D. S., et al, In Proc. IEEE Inter. Zurich Seminar on Comms. 2006,Zurich, Feb. 2006

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Conclusions Conventional routing schemes have limitations: power consumption and delay Why network coding? Good match to underwater acoustic scenario: –Good performance in channels with high packet erasures –Outperforms routing in wireless scenario in terms of number of transmissions per packet and delay Network coding with implicit acknowledgements: –New proposed method: use transmitted data packets as implicit ACK for upstream nodes –Has best overall performance: transmission delay and power consumption

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