1. Multicast with Network Coding in Application-Layer Overlay Networks Y. Zhu, B. Li, and J. Guo University of Toronto Present by Cheng Huang 10.30.2003

2. 2 Network Coding S TU W YZ ab a a a b b b ab a a b b a or b? S TU W YZ X S TU W YZ X ab a a b b a+b How to send 2 pieces of data a and b to nodes Y and Z simultaneously?

3. 3 Basics of Network Coding Conventional network nodes –Route or duplicate traffic Network nodes with coding capability –Perform operations on incoming traffics Basic operations  encoding/decoding Linear operations  Linear Network Coding Network coding can increase multicast capacity –“ Network Information Flow, ” IEEE Trans. Information Theory, 46(4), 2000.

4. 4 Main Results of Network Coding If the capacity of any sink R i ≥ C, then multicast rate of C is achievable, generally with network coding. S R2R5R3R1R4 Network

5. 5 Linear Network Coding Network nodes only perform LINEAR operations on incoming traffics –Any node can retrieve information at a rate equal to its capacity Example: –Source multicasts 12 pieces of data –Node of capacity 4 retrieves all data in 3 seconds –Node of capacity 3 in 4 seconds and of capacity 1 in 12 seconds –Sufficient condition: network is acyclic. –“ Linear Network Coding, ” IEEE Trans. Information Theory, 49(2), 2003.

6. 6 Preliminaries k-redundant multicast graph (DAG) –Intermediate nodes have indegree ≤ k –Receiver nodes have indegree = k –Nodes of indegree k have maxflow = k S R1R3R2R4

7. 7 Algorithm Rudimentary graph –Relatively densely connected Rudimentary tree Multicast graph

8. 8 Build Rudimentary Graph/Tree Node maintains a list of neighbors and exchanges with other nodes Edge e has a weight w(e) = (β,λ) Path p consists of edges –Preferable path: large bandwidth or low delay Add/remove edges dynamically –Δ-constraint Rudimentary tree –Z. Wang and J. Crowcroft (1996) –Distributed algorithm to find shortest widest paths

9. 9 Construct Multicast Graph Basics –Leaf intermediate node All children are receiver nodes –Saturation Intermediate node degree(v) = Δ Leaf intermediate node degree(v) = Δ-1 S R1R3R2R4 Δ = 4

10. 10 Construct Multicast Graph Basics –Leaf intermediate node All children are receiver nodes –Saturation Intermediate node degree(v) = Δ Leaf intermediate node degree(v) = Δ-1 S R1R3R2R4 Δ = 4

11. 11 Construct Multicast Graph First path p f –Unsaturated neighbors exist Selects the best path among these neighbors –All neighbors saturated Find (breath-first) k unsaturated nodes from source node s Select the best path

12. 12 Construct Multicast Graph Second path p s S

13. 13 Construct Multicast Graph Second path p s S

14. 14 Construct Multicast Graph Second path p s S

15. 15 Construct Multicast Graph Second path p s S

16. 16 Construct Multicast Graph Second path p s S

17. 17 Linear Coding Multicast (LCM) Node with 1 input –Simple forwarding Node with 2 inputs –Receive X, Y from left, right inputs, respectively –Compute C = [X Y][v 1 v 2 ] T –Send C out along all outputs How to assign (v 1, v 2 ) to each node so as to guarantee reception?

18. 18 Linear Coding Multicast (LCM) Output of any node –C = [X Y][v 1 v 2 ] T = [a b][p q] T, because X, Y are linear combinations of a and b. –X = [a b][p x q x ] T and Y = [a b][p y q y ] T (same logic) XY C = [X Y][v 1 v 2 ] T [v 1, v 2 ] [a b][p q] T

19. 19 Performance Evaluation INET topology generator (University of Michigan) Comparison –DVMRP IP layer multicast protocol –Narada Application layer multicast protocol

20. 20 Performance Evaluation

21. 21 Performance Evaluation

22. 22 Conclusions Propose a practical network coding scheme to exploit existing theoretical bounds Demonstrate throughput advantage of network coding, compared to existing application layer multicast