1. Multicast + Network Coding in Ad Hoc Networks CS 218 Fall 2008

2. 2 Routing vs Network Coding y1y1 y2y2 y3y3 f 1 (y 1,y 2,y 3 ) f 2 (y 1,y 2,y 3 ) y1y1 y3y3 y1y1 y3y3

3. 3 Benefit of Network Coding x y x  y AC B AC B AC B x y AC B AC B y x AC B AC B 4 transmissions without NC 3 transmissions with NC y = x  (x  y) x AC B y (Katabi’05, Chou’04)

4. 4 NC achieves multicast capacity  Alswede, Cai, Li, Yeung (2000): min t Є T MinCut( s, t ) is always achievable by network coding h = min t Є T MinCut( s, t ) is “multicast capacity” sender receiver optimal routing throughput = 1 network coding throughput = 2 coding node a,b a a a a b b b b a+b,a,b

5. 5 How to code? Sender s Directed graph ( V,E ) Given: Receiver set T (subset of V )

6. 6 Random Linear Coding xyz Random combination buffer Sender Destination A α x + β y + γ z Every packet p carries e = [e 1 e 2 e 3 ] encoding vector prefix indicating how it is constructed (e.g., coded packet p = ∑e i x i where x i is original packet) Intermediate nodes randomly mix incoming packets to generate outgoing packets

7. 7 Random Linear Coding a*p 1 + b*p 2 + c*p 3 = n 1 p1p1 p2p2 p3p3 n1n1 n2n2 n3n3 d*p 1 + e*p 2 + f*p 3 = n 2 g*p 1 + h*p 2 + e*p 3 = n 3 Original Packets

8. 8 Random Linear Coding (cont.) 5*p 1 [1] + 8*p 2 [1] + 1*p 3 [1] = n 1 [1] p1p1 p2p2 p3p3 n1n1 n2n2 n3n3 2*p 1 [1] + 3*p 2 [1] + 7*p 3 [1] = n 2 [1] 9*p 1 [1] + 6*p 2 [1] + 5*p 3 [1] = n 3 [1] [5 8 1][2 3 7] [9 6 5] Original Packets Recover original by matrix inversion

9. 9 Random Linear Coding (cont.) An application generates a stream of frames … Block/Generation 1Block 2 time … Network layer generates stream of coded packets A random linear combination of Block 1 frames A random linear combination of Block 2 frames Generation 1 Generation 2 (delay)

10. 10 Forwarding – RLC SourceReceiver

11. 11 Random Network Coding Receivers recover original by matrix inversion random combination buffer Intermediate nodes randomly mix incoming packets to generate outgoing packets Every packet p carries e = [e 1 e 2 e 3 ] encoding vector prefix indicating how it is constructed (e.g., coded packet p = ∑e i x i where x i is original packet)

12. 12 Robust Multicast using NC  In tactical nets one must consider: Random errors; External interference/jamming Motion; path breakage  Target application: Multicast (buffered) video streaming  Some loss tolerance  Some delay tolerance (store & playback at destination) - non interactive

13. 13 Problem Statement  Multicast streaming in mobile wireless networks is non-trivial Streaming requires: high reliability (but not 100%), low delay (but not 0) But network is: unreliable, bandwidth- limited  Major concern: packet drops Lossy wireless channel (uncorrelated, random like errors) Route breakage due to mobility, congestion, etc (correlated errors)

14. 14 Conventional vs NC Multicast  Conventional Approaches Time diversity => O/H, delay?  Recovery scheme a la ARQ (Reliable Multicast)  (End-to-end) Coding (FEC, MDC, …) Multipath diversity (ODMRP, …) => O/H?  NC Approach Main ingredient: Random network coding (by M édard et al., Chou et al.) Exploit time and multipath diversity Controlled-loss (near 100%), bounded-delay (hundreds of ms) Suitable for buffered streaming Real time version (tens of ms delay bound) possible

15. 15 Simulation experiments  Settings QualNet 100 nodes on 1500 x 1500 m 2 5 Kbytes/sec traffic (512B packet) - light load Single source; multiple destinations Random Waypoint Mobility 20 receivers  Metrics Good Packet ratio: num. of data packets received within deadline (1sec) vs. total num. of data packets generated Normalized packet O/H: total no. of packets generated vs no. of data packet received Delay: packet delivery time

16. 16 ODMRP vs C-Cast: Reliability Good Packet Ratio

17. 17 ODMRP vs C-Cast: Efficiency

18. 18 ODMRP vs C-Cast: Delay

19. 19 Throughput Bounds  Max NC throughput in wireless networks? Previous simulation results based on light load. As load is increased, congestion leads to performance collapse  Evaluate max throughput analytically for a simple grid structure, the “corridor”: receivers sender

20. maximize f Wireless medium contention and scheduling constraints Wireless flow conservation constraints Linear Programming Formulation

21. 21 Maximum Multicast Throughput CodeCast vs Conventional Receivers Sender CORRIDOR MODEL

22. 22 A A A B B B C (1)(2) (3) (4) Link schedule achieving 2/3 throughput receiver sender (Assuming time-slotted system)

23. 23 F A+BA+B E EF DC AB GH FE CD H C+DC+D G AB A B B CD A C D (1)(2) (3) (4)(5)(6) (7)(8) (9) (10)(11)(12) Link schedule for NC achieving throughput of 2/3

24. 24 A A A B B A B B C (1)(2) (3) (4)(5) (6) Multicast with multiple embedded trees (no NC): Link schedule achieves 2/5 throughput C C D D C D (7)(7)(8)(8) (9)(9) (10)

25. 25 (1)(2) (3) (4)(5)(6) An “optimal” Single Tree multicast schedule that achieves 1/3 A A A B B B

26. Modeling Wireless Medium  We model the broadcast nature of the wireless medium using hyperarcs An hyperarc (i,J) represents a specific usage of the broadcast link from the sender i to a set of destination nodes, where is the number of neighbors of node i Total number of hyperarcs = iii (a) Examples of Hyperarcs in red Interference

27. 27 Modeling Wireless Medium (cont)  Wireless medium is shared, which is a main factor that limits the capacity of wireless multi–hop networks.  To model this shared nature of the medium, we map it into a graph theory problem, the Maximal Independent Set Enumeration Problem. A Independent Set represents a set of non interfering hyperarcs. (By finding only maximal sets, the number of sets is reduced.) i (a) I.S.(b) NO I.S.(c) Maximal I.S. Conflict!

28. 28 Modeling Wireless Medium (cont)  All hyperarcs in a Maximal I.S. can be activated at the same time. Scheduling is always feasible when only one Maximal I.S. is exclusively activated in a time slot.  Let be the fraction of time in which the k-th Maximal I.S. is activated. Clearly we have:  Let be the time share allocated to a hyperarc (i, J). Then, sufficient and necessary condition for a link schedule to be feasible is: where. (L: link capacity)

29. 29 Network Coding in P2P Swarming  P2P Swarming File is divided into many small pieces for distribution Clients request different pieces from the server/other peers When all pieces are downloaded, clients can re-construct the whole file Rare piece problem  P2P using Network Coding Avalanche, Infocom’05 1 2 6 5 Server 3 4 1 5 6 2 4 1 2 3 4 5 6 3 [Rodriguez, Biersack, Infocom’00]

30. 30 Multicast in VANETs - CodeTorrent  Content distribution in VANET such as ad movie clips etc  VANET challenges Error-prone channel Dense, but intermittent connectivity High, but restricted mobility patterns No guaranteed cooperativeness (only, users of the same interests will cooperate)  CodeTorrent approach Single-hop data pulling BitTorrent-style file swarming with random network coding to cope with dynamic environments

31. 31 Design Rationale  Why single-hop pulling? Multi-hop data pulling does not perform well in VANET (routing O/H is high) Users in multi-hop may not forward packets not useful to them (lack of incentive)!  Network coding Mitigate a rare piece problem Maximize the benefits of overhearing  Exploits mobility such that coded blocks are carried from AP and forwarded to other nodes Mobility helps data dissemination

32. 32 CodeTorrent: Basic Idea Internet Downloading a Coded Block from Gateway Outside Range of Gateway Download a “coded” piece Buffer Random Linear Combination of Blocks Exchange Re-Encoded Blocks Meeting Other Vehicles with Coded Blocks

33. 33 Simulations - Setup  Qualnet  IEEE 802.11b / 2Mbps  Real-track mobility model (Westwood map) 2.4x2.4 km 2  Distributing 1MB file 4KB block / 250 pieces 1KB per packet  # of APs: 3 Randomly located at the road sides  Comparing CarTorrent (w/ AODV) and CodeTorrent Vicinity of UCLA

34. 34 Simulation Results  Overall downloading progress 200 nodes 40% popularity

35. 35 Simulation Results  Speed helps disseminate from AP’s and C2C  Speed hurts multihop routing (CarT)  Car density+mhop promotes congestion (CarT) 40% popularity