Broadcasting Delay-Constrained Traffic over Unreliable Wireless Links with

Network Coding

I-Hong Hou and P.R. Kumar

1

Wireless Broadcasting: Video Streaming

2

Application Characteristics

3

No per-packet delay bounds

Need to delivery every packet correctly

Traditional

Applications

Video Streamin

g

Strict per-packet delay bounds Expired packets

are not useful Can tolerate a small

amount of packet losses

Performance in the Future

4

High Throughput ≠

Performance in the Future

5

High Timely Throughput =

Timely Throughput: Throughput of packets that are delivered on time

Wireless transmissions are subject to shadowing, fading, and interference

Therefore, wireless transmissions are unreliable

Challenges from Wireless Transmissions

6

Challenges from Wireless Broadcast

7

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

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

Challenges from Wireless Broadcast

8

System Model for Wireless Broadcast with Delay Constraints

9

Client-Server Model

10

AP

1

2

3

A B C

Flows Clients

Timeline

Traffic Model

11

AP

1

2

3

A B C

Interval

Packet Generation

CCC

Traffic Model

12

AP

1

2

3

A BA

A

C

B

C

B

B

B

C

Model for Delay Constraints

13

AP

1

2

3

A B

Packet Generati

onDeadlin

e

Interval

C

Model for Delay Constraints

14

AP

1

2

3

A B

A,C expire

Interval

A

C

Delays of delivered packets are no larger than the length of an

interval

C

Model for Unreliable Broadcast

15

AP

1

2

3

A B

A

C C

B

B

Client n receives each transmission

successfully with prob. pn

p1

p2

p3

C

Scheduling Example

16

AP

1

2

3

A B

A

C C

B

B

p1

p2

p3

A

AAAA

A

X

X

C

Scheduling Example

17

AP

1

2

3

A B

A

C C

B

B

p1

p2

p3

A

AAAA

A

X

XA

A

X

A

X

Duplicate Packets are ignored

C

Scheduling Example

18

AP

1

2

3

A B

A

C C

B

B

p1

p2

p3

A

A

X

XA

A

X

A

CCCC

C

X

C

C

X CBX

BC

X X

X

XC B C

Timely Throughput

19

AP

1

2

3

p1

p2

p3

A

X

X

A

X

A

X

C

C

X CBX

BC

X X

X

X

Delivered Timely Throughput

A B C

1 0.5

0.5

0.5

2 0 0.5

1.0

3 0.5

0 0.5

Timely Throughput

20

AP

1

2

3

p1

p2

p3

A

X

X

A

X

A

X

C

C

X CBX

BC

X X

X

X

Delivered Timely Throughput

A B C

1 0.5

0.5

0.5

2 0 0.5

1.0

3 0.5

0 0.5Required

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

Timely Throughput Requirements

21

AP

1

2

3

A C B C B

A C B C B

A C B C B

p1

p2

p3

A

X

X

A

X

A

X X

C

C

C

BC

BX

X X

X

X

Timely Throughput

A B C

1 0.5

0.5

0.5

2 0 0.5

1.0

3 0.5

0 0.5

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

Summary of Model

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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

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Delivery Debt

24

Slope = qA,1

Delivery Debt

Expected Delivery Debt

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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}

AP A A B

Client n receives A with probability 1-(1-pn)2, and receives B with probability pn

A Framework for Designing Policies

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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

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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 A A

mA,n =pn mA,n =pn(1-pn)

mA,n =pn(1-pn)2

AP

Optimality Result

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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

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A BAP

1

A B BA

Duplicate Packet

Client cannot obtain packet A

X BX B XX

Network Coding: XOR Coding

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A BAP

1

A B

Client obtains both packets

X BX XX

XOR Coding: AP can broadcast packets contain A, B, or A B

A B

A=B (A B)

A B A B

Pairwise XOR Policy

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Design of Pairwise XOR Policy: 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

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A BAP

1

A B BA

Duplicate Packet

Client cannot obtain packet A

X BX B XX

Network Coding: Linear Coding

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AP

1

Client obtains both packets

X X XX

A+B A+2B A+3B A+4B A+5B A+6B

A+4B A+5B

( 5 ) ( 4 )

( 4 ) 4*

B A B A B

A A B B

Linear Coding: AP broadcasts linear combinations of packets from flows

Optimal Grouping Policy

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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

35

VoIP Traffic

36

ITU-T G.711 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

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Simulation Result

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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

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