The document discusses using network coding to optimize routing schemes for multicasting in mobile ad-hoc networks. It defines the problem and assumptions, such as independent information sources and specifying multicast requirements. Network coding is described as employing coding at nodes rather than just relaying data. Simulations show that calculating the optimal routing scheme is much less complex with network coding compared to conventional routing, and the network coding solution uses close to the minimum possible energy.

1. Network Coding for Multicasting in Mobile Ad-Hoc Networks http://www.ikbear.com http://twitter.com/ikbear

2. Outline Introduction to network coding Definition of the problem Approaches to optimal routing schemes in network coding Simulation results Conclusions

3. Network coding Convential networking views network switches as simple relays who only repeat and replicate data Network coding[1] has been proposed as an alternative to this – instead each node of the network employs coding With this clever method we can achieve admissible rate for the network in scenarios where the conventional method can’t.

4. Assumptions In general we consider all information sources to be mutually independent We will only study one information source multicasting to many sinks

5. Multicast requirements We specify multicast requirements on a directional graph G with: a :{1,...,m}  V (source) Ex: a(2)=1 => vertex 1 sends information source 2 b :{1,...,m}  2 V (set of sinks) Ex: b(2)={5,6,7} => vertices 5,6 and 7 receive information source 2 h =[ h 1 ...h m ] (information rate of sources)

6. Definition of the channel The capacity of each link (i,j) between vertices i and j in graph G is R ij We can characterize admissible rate of the network by: The fundamental literature of network coding aims at characterizing the coding rate region R i.e. The set of all admissible R for any type of G and any set of multicast requirements

7. Max-flow min-cut theroem Ultimate constraints on capacity between two points in a network (represented as the graph G) is the capacity of the minimal-cut (the bottleneck) 1 1 1 1 1 1 1 Capacity: 2 Capacity: 1 Source Sinks Intermediate nodes 1 1

8. Network coding in action Lets look at a route in an “old fashion” network relaying. In general, we can not achieve the network capacity We want to send bits A and B from a to b 1 and b 2 A B A A A A a b 2 B A b 1 B {A,B} {A} Min-cut max-flow states that We should be able to send 2 bits to b 1 and b 2 but how?

9. Network coding in action By employing network coding at intermediate nodes we can in fact achieve R . This is a simple example using XOR to encode. It is evident that b 1 and b 2 can in fact retrieve A and B. In general (with longer messages) coding forms multiple linear equations which can be solved by Gaussian reduction. A B A  B A a b 2 B A b 1 B {A,B} {A,B} A  B A  B

10. Network coding in action Even though the previous example indicates a nice result, we do not know the network topology in general We have two options: Except that we don’t know the topology and deal with it. [2] proposes a solution to this, via random network codes. That paper shows that we can in fact achieve capacity with probability exponentially approaching 1 when nodes randomly and independently select linear mappings from input onto output links. Another solution is to try to find the topology and calculate the optimal routing scheme with an LP[3]. We will focus on this solution in respect to MANETs for the rest of the talk.

11. Minimum energy multicast in Mobile Ad-Hoc networks [3] Energy is a prime concern in Mobile Ad-Hoc networks RF communications consume great amount of energy relative to computational effort Therefore, we are willing to do more processing to reduce communications This is an ideal scenario for network coding: less communications at the cost of coding In addition, network coding provides built-in error correction codes, which greatly benefit MANETs. Finally, the broadcast nature of the wireless MAC is beneficial to network coding

12. Proposed Network Coding solution in wireless mobile scenario: The number of transmissions to send 2 bits from a source to sink: a+b: 9 b:4 a:8 b:1 a:5 a:4 a:5 b:2 b:3 a:6 a:7 a:2 a:1 network coding 9 transmissions energy per bit = 4.5 a:3 a a,b a a,b b,a a:1 conventional routing 5 transmissions (x2) energy-per-bit: 5 a

13. Simulations: the setup We’ll imagine houses in a neighborhood (static MANET) We want to: Find the optimal routing scheme Calculate the energy spent by that scheme Multicast requirements: a(x) = 28 b(x) = {6,52,1,53} h : adjustable (LP paramenter) Maximum broadcast range of a particular node (for p max ) is 300m

14. Simulation result The performance of the network can be calculated with a linear program We won’t go into the gory details of the LP setup in this presentation. The objective of the LP is to minimize total energy E spent in system We will run an LP to optimize E with two constraint scenarios: Conventional multicast routing Network coding multicast routing The optimization results are best expressed with figures.

15. Simulation results

16. Simulations result Optimizing the routing scheme with network coding yielded a different route than that of the convential routing optimiziation. We can see resemblence with the previously covered example and the optimal network coding routing scheme. Note that finding the optimal routing scheme with convential routing is NP hard (actually very similar to travelling salesman problem) whereas optimizing with coding is solved in linear time. This is a significant result – calculating the the optimal solution with coding took 1/30 the time that it took to calculate the conventional optimal solution Finally, the network coding solution used 98.08% of the conventional routing solution.

17. Conclusions and future work Network coding introduces benefits to MANETs, especially considering the broadcast nature of the MAC layer Simulations and analysis show that calculating an optimal scheme is much less complex in the coding scenario than in the conventional scenario

18. Future work Interesting topics to consider is the scenario with multiple sources Also, the simulations only considered power spent by RF communications (not by extra CPU introduced by coding). They assumed the transmission power could be adjusted exactly and that reducing transmission range reduced power consumption relative to d(i,j) -3 (d(i,j): distance between i and j) Experiments with Crossbow MicaZ and Mica2Dot nodes[4] have shown that this assumption does not apply to these devices. This could be an implementation issue, but does introduce a considerable point concerning practical implementations. Comparing the work of [3] to a solution employing random coding would be interesting.

19. References [1] R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeung, "Network information Flow", IEEE Trans. Information Theory, IT-46(4):1204-1216, Jul. 2000. [2] T. Ho, R. Koetter, M. Medard, D. Karger and M. Effros, "The Benefits of Coding over Routing in a Randomized Setting", ISIT 2003. [3] P. A. Chou, Y. Wu and S. Y. Kung. "Minimum-Energy Multicast in Mobile Ad hoc Networks using Network Coding". 2004 IEEE Information Theory Workshop, San Antonio, Oct 25-29, 2004. [4] M. Haenggi and D. Puccinelli. "Routing in Ad Hoc Networks: A Case for Long Hops", IEEE Communications Magazine, October 2005.

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