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

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

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

Minimize power consumption:

Reduce transmissions per packet

Trade-off:

Minimize transmission delay

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 Node [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. M é dard, “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 Packet A λ Packet A λ Packet B Packet B μ A+ ρ B μ , ρ Coded Code Data Coded Code Data

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

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

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

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

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 .

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

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

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 R 2 R 1 Low SNR R 2 R 1 High SNR

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

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

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 1 Node 2 Node 4 Node 3 D 1 D 2 D 3

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

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

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

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

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

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

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