1. Broadcasting Delay-Constrained Traffic over Unreliable Wireless Links with Network Coding
I-Hong Hou and P.R. Kumar

2. Wireless Broadcasting: Video Streaming

3. Application Characteristics
Traditional Applications
Video Streaming
No per-packet delay bounds
Need to delivery every packet correctly
Strict per-packet delay bounds
Expired packets are not useful
Can tolerate a small amount of packet losses

4. Performance in the Future
High Throughput ≠

5. Performance in the Future
High Timely Throughput =
Timely Throughput: Throughput of packets that are delivered on time

6. Challenges from Wireless Transmissions
Wireless transmissions are subject to shadowing, fading, and interference
Therefore, wireless transmissions are unreliable

7. Challenges from Wireless Broadcast
ACKs are not implemented in broadcast
Costly to obtain feedbacks from all clients
No per-transmission feedback information

8. Challenges from Wireless Broadcast
ACKs are not implemented in broadcast
Costly to obtain feedbacks from all clients
No per-transmission feedback information

9. System Model for Wireless Broadcast with Delay Constraints

10. Client-Server Model
Flows
Clients
Timeline 1 A B C AP 2 3

11. Traffic Model 1 A B C
Packet Generation AP 2
Interval 3

12. Traffic Model 1 A A B B B C C C AP 2 A B C C B 3

13. Model for Delay Constraints1 A B C
Packet Generation AP 2
Deadline
Interval 3

14. Model for Delay Constraints
Delays of delivered packets are no larger than the length of an interval 1 A B C
A,C expire AP 2 A C
Interval 3

15. Model for Unreliable Broadcast
Client n receives each transmission successfully with prob. pn 1 A B C p1 p2 AP 2 A B p3 C C B 3

16. Scheduling Example 1 A B C p1 A A A A A p2 AP 2 A B X p3 C C B A 3 X

17. Duplicate Packets are ignored
Scheduling Example
Duplicate Packets are ignored 1 A B C p1 X A A A A A A p2 AP 2 A B X X p3 C C B A A 3 X A

18. Scheduling Example p1 p2 p3 X 1 A B C A A X X B C C C C C AP 2 A B X X

19. Timely Throughput p1 p2 p3 X Delivered Timely Throughput A B C 1 0.5 2
1.0 3 1 p1 X A A X X B C p2 AP 2 X X C C B X p3 3 X A C X X X

20. Timely Throughput p1 p2 p3 X Delivered Timely Throughput A B C 1 0.5 2
1.0 3 1 p1 X A A X X B C p2 AP
Required Timely Throughput A B C 1
qA,1
qB,1
qC,1 2
qA,2
qB,2
qC,2 3
qA,3
qB,3
qC,3 2 X X C C B X p3 3 X A C X X X

21. Timely Throughput RequirementsA B C 1
0.5 2
1.0 3 A C B C B 1 p1 A A X X X B C p2 A C B C B AP 2 X X C C B X p3
Required A B C 1
qA,1
qB,1
qC,1 2
qA,2
qB,2
qC,2 3
qA,3
qB,3
qC,3 A C B C B 3 X A C X X X

22. Summary of Model Flows have strict per-packet delay bound
Clients have timely throughput requirements on each flow
Wireless transmissions are unreliable
AP does not have feedback information
Goal:
Design policies to fulfill timely throughput requirements for all flows and all clients as long as they are feasible

23. Scheduling Policies

24. Delivery Debt
Slope = qA,1
Delivery Debt

25. Expected Delivery Debt
AP does not have feedback information
But, AP can estimate packet deliveries
Expected delivery debt for client n and flow i at the kth interval
di,n(k):= kqi,n-E{# of packets client n receives from flow i}
Client n receives A with probability 1-(1-pn)2,
and receives B with probability pn AP A A B

26. A Framework for Designing Policies
Policy: Maximize
∑di,n(k)+Prob(client n receives a packet from flow i)
in every interval
Theorem:
This policy fulfills a system as long as it is feasible
Feasibility Optimal Policy

27. A Policy without Coding
Marginal Delivery Probability (mi,n):
prob. that client n receives a new packet from flow i in a particular transmission
Greedy Algorithm:
schedule the flow i that maximizes ∑ndi,n(k)+mi,n in every time slot A
mA,n =pn
mA,n =pn(1-pn)
mA,n =pn(1-pn)2 AP

28. Optimality Result
Greedy Algorithm is feasibility optimal
Polynomial complexity per interval
However, it is only optimal among policies that do not employ network coding
Can we improve performance by employing network coding?

29. Network Coding: XOR Coding
Client cannot obtain packet A
Duplicate Packet X X X B B X 1 A A A B B B AP

30. Network Coding: XOR Coding
AP can broadcast packets contain A, B, or
Client obtains both packets X X X B X 1 A A B B AP

31. Pairwise XOR Policy Design of Pairwise XOR Policy: Theorem:
Only allow pairwise XOR
Satisfy some mild restrictions derived from Greedy Algorithm
Theorem:
Pairwise XOR Policy is feasibility optimal among all policies that satisfy the mild restrictions.
Pairwise XOR Policy fulfills every system that can be fulfilled without coding
Polynomial complexity per interval

32. Network Coding: Linear Coding
Client cannot obtain packet A
Duplicate Packet X X X B B X 1 A A A B B B AP

33. Network Coding: Linear Coding
AP broadcasts linear combinations of packets from flows
Client obtains both packets X X X
A+4B
A+5B X 1
A+B
A+2B
A+3B
A+4B
A+5B
A+6B AP

34. Optimal Grouping Policy
Design of Optimal Grouping Policy:
AP broadcasts linear combinations of packets
Satisfy some mild restrictions derived from Greedy Policy
Theorem:
Optimal Grouping Policy is feasibility optimal among all policies that satisfy the mild restrictions.
Optimal Grouping Policy fulfills every system that can be fulfilled without coding
Polynomial complexity per interval

35. Simulation Results

36. VoIP Traffic ITU-T G.711 IEEE 802.11b Packet size = 160 Bytes
Interval length = 40 ms
IEEE b
Transmission rate = 11 Mb/s
20 time slots in an interval

37. Network Topology 20 clients and one AP AP broadcasts 10 flows
qi,n= α, for 1 ≤ i ≤ 5; qi,n= β, for 6 ≤ i ≤ 10

38. Simulation Result
Plot all (α, β) that can be fulfilled by each policy

39. Conclusion
Studied the problem of broadcasting delay-constrained flows through wireless links
Proposed a model that jointly considers the following:
Per-packet delay bounds of flows
Timely throughput requirements of clients for each flow
Unreliable wireless transmissions
Lack of per-transmission feedbacks in broadcast
Proposed a policy that is feasibility optimal
Explored the usage of network coding to enhance performance