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

Wireless Broadcasting: Video Streaming

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

Performance in the Future High Throughput ≠

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

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

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

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

System Model for Wireless Broadcast with Delay Constraints

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

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

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

Model for Delay Constraints 1 A B C Packet Generation AP 2 Deadline Interval 3

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

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

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

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

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

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

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

Timely Throughput Requirements A 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

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

Scheduling Policies

Delivery Debt Slope = qA,1 Delivery Debt

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

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

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

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?

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

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

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

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

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

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

Simulation Results

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

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

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

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