Multicast with Network Coding in Application-Layer Overlay Networks

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

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. S Network R1 R2 R3 R4 R5 Main Resultsof Network Coding • If the capacity of any sink Ri≥ C, then multicast rate of C is achievable, generally with network coding.

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. S R1 R2 R3 R4 Preliminaries • k-redundant multicast graph (DAG) • Intermediate nodes have indegree ≤ k • Receiver nodes have indegree = k • Nodes of indegree k have maxflow = k

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

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. S R1 R2 R3 R4 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 Δ = 4

10. S R1 R2 R3 R4 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 Δ = 4

11. Construct Multicast Graph • First path pf • 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. Construct Multicast Graph • Second path ps S

13. Construct Multicast Graph • Second path ps S

14. Construct Multicast Graph • Second path ps S

15. Construct Multicast Graph • Second path ps S

16. Construct Multicast Graph • Second path ps S

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][v1 v2]T • Send C out along all outputs • How to assign (v1, v2) to each node so as to guarantee reception?

18. Linear Coding Multicast (LCM) • Output of any node • C = [X Y][v1 v2]T = [a b][p q]T, because X, Y are linear combinations of a and b. • X = [a b][px qx]T and Y = [a b][py qy]T (same logic) X Y [v1, v2] [a b][p q]T C = [X Y][v1 v2]T

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

20. Performance Evaluation

21. Performance Evaluation

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