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
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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
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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
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AP
1
2
3
A BA
A
C
B
C
B
B
B
C
Model for Delay Constraints
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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
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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
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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
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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
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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
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VoIP Traffic
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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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