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Optimal Description BandwidthOptimal Description BandwidthAssignment for MultipleAssignment for Multiple--DescriptionDescription--Coded VideoCoded Video
XIA Pengye Henry
Supervisor: Prof. Gary S.-H. Chan
August 17, 2010
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OutlineOutline
y Introduction and Related Work
y Formulation and Complexity
y Exact Solution and the Threshold Value
y Efficient Heuristic SAMBA
y Illustrative Simulation Results
y Conclusion
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Can you imagine your life withoutCan you imagine your life without
video streaming service?video streaming service?
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LargeLarge--Scale Multimedia StreamingScale Multimedia Streaming
y The server has a video to be streamed toa large group of users
It may use multiple unicasts, IP multicast, peer-to-peer overlay multicast
y Need to effectively satisfy user bandwidthheterogeneity
Mobile streaming: 100 Kb/s
Internet streaming: 500 Kb/s
MPEG video: 1 Mb/s
HDTV: 10 Mb/s or more
2 orders of magnitude difference!
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Illustration: Video Streaming toIllustration: Video Streaming to
Users of Heterogeneous BandwidthUsers of Heterogeneous Bandwidth
5
Bandwidth
Mismatch
1 2 5 7 10
AccessNetwork
5
1 2 0 2 5
Video streaming rate: 5 units
Assume that all bandwidths and streaming rates are normalized tosome integer units (E.g., 50 Kb/s)
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Addressing BandwidthAddressing Bandwidth
HeterogeneityHeterogeneityy Provides multi-rate video for
heterogeneous network
y Several Solutions:
#1: Multiple streams
#2: Layered coding (aka SVC)
#3: Multiple description coding
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Multiple streamsMultiple streams
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Bandwidth
Mismatch
1 2 5 7 10
AccessNetwork
5
1 0 0 2 5
Multiple streams: bandwidth 2 units and 5 units
2
# of streaming rates = # of streams
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Layered CodingLayered Coding
8
Bandwidth
Mismatch
1 2 5 7 10
AccessNetwork
5
1 2 0 0 3
Layer Bandwidths: Base layer with bandwidth 5units, enhancement layer with 2 units
2
# of streaming rates = # of layers
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Multiple Description CodingMultiple Description Coding
9
Bandwidth
Mismatch
1 2 5 7 10
AccessNetwork
5
1 0 0 0 3
Description bandwidths: 2 units and 5 units
2
# of streaming rates = 2^(# of descriptions)-1
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MDC: Strength and IssuesMDC: Strength and Issues
y Strength:
Provides more choices of streaming rate tomatch user receiving bandwidths.
Descriptions are independent. More robust tonetwork dynamic.
y Issues:
Optimal description bandwidth assignment Coding efficiency Optimal description #.
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Model for MD Coded Video ServiceModel for MD Coded Video Service
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Access Network
MDC video server anddescription bandwidthassignment
d1 d2 dmdescriptions««
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Research SettingResearch Setting
y Consider a video stream to be accessed by a large pool
of users with heterogeneous bandwidths.
y Users employ a ́ greedyµ approach to maximize theirvideo quality.
Each user joins the descriptions so that the total bandwidth bestmatches the receiving bandwidth without overflowing
y The server encodes the video into multipledescriptions and advertise them to the users.
It has a good picture on the user bandwidth profile it is serving.
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Research ProblemResearch Problem
y Given: description number, user receiving
bandwidths and their importance (interms of weight)
y How to assign bandwidth to each of the
descriptions so that the overall userbandwidth experience (in terms of user
satisfaction) is maximized?
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Contribution HighlightContribution Highlight
y Problem formulation and complexity analysis Optimization problem with coding efficiency
consideration
NP-hard proof
y Exact solution and threshold value Polynomial time algorithm to match all the
receiving bandwidths, when description # is noless than threshold.
y An efficient heuristic: SAMBA Virtually matches the optimum
Optimal choice for description #.
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Related Work Related Work
y MDC was first proposed to enhance
performance of telephone system, in Bell·sLab.
y A comprehensive survey of MDC can be
found in [1].
y Much of previous work on MDC only
focus on the error resilient techniques[2][3].
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Related Work (Cont.)Related Work (Cont.)
y To the best of our knowledge, [4] and [5]
have addressed the description bandwidthassignment in MDC.
y Our work advances in
General formulation with coding efficiencyconsideration
Exact solution and threshold value
Study of optimal description number
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OutlineOutline
y Introduction and Related Work
y Formulation and Complexity
y Exact Solution and the Threshold Value
y Efficient Heuristic SAMBA
y
Illustrative Simulation Results
y Conclusion
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Problem FormulationProblem Formulation
y We formulate an optimization problem toset description bandwidth.
y Input: m : description number c j : receiving bandwidth of user j
: weight (importance) of user j
y Output: : optimal description bandwidth
assignment vectory Bandwidths are normalized to some units
(say 50 kb/s).
18
j[
m21 , ,, d d d d -T!
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ConstraintsConstraints
y Bandwidth non-overflow
y Individual satisfaction model
y Overall satisfaction model
19
)1( ., and 1
jcvd K v j j
m
i
ii j je!§
!
)2( jmind r f S E!
(3)
,
n
1 j
n
1 j
§
§
!
!!
j
jind jcd S
S
[
[T
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Optimization ProblemOptimization Problem
Given description number m, user receivingbandwidth and its importance , we findthe optimal bandwidth assignment to
maximize overall satisfaction , subject toEquations (1), (2) and (3).
20
j[ jc
d T
S
Optimizationat the server
Input OutputOptimal
descriptionbandwidth
assignment
(d1, d2, «, dm)
description
number m
receiving
bandwidth
and weight
information
(c j , w j ) foreach user j
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ComplexityComplexity
y We can prove that the problem is NP-hard, byfinding a polynomial reduction from the integersubset sum problem
Integer Subset Sum Problem:Given a set of integer number and an integer value t ,does there exist a subset whose sum equals t ?
Known as NP-Complete problem
(x1, x2, « , xm , t)Given description number m, user receivingbandwidths (x1, x2, « , xm , , t) and same weightfor each user, solve MDC assignment problem.
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§ i x
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OutlineOutline
y Introduction and Related Work
y Formulation and Complexity
y Exact Solution and the Threshold Value
y Efficient Heuristic SAMBA
y
Illustrative Simulation Results
y Conclusion
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Exact SolutionExact Solution
y There is a threshold value for description
number m.
y When m>=threshol d , we show there is
an exact assignment algorithm whichmatches all the receiving bandwidths in
polynomial time.
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A Simple ExampleA Simple Example
y Receiving bandwidth are integers in [1, 25].y Choose c j=20 for example
Binary form 20 = (10100)2 = 16 + 4 If descriptions are 1, 2, 4, «, the binary form
represents joining decision.y The maximum receiving bandwidth
25 = (11001)2 , length Binary form of any c j has length
y 5 descriptions can match all c j in[1, 25].
24
- ½ 5125log2 !
5e
168,4,2,,1
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A More Complex ExampleA More Complex Example
25
y Receiving bandwidth are integers in
[20, 25].
y ( c j-19 ) in [1, 6]
y Choose c j=24 for example Binary form of (24-19) = (101)2 = 4 + 1
By previous example, any (c j -19) can bematched by descriptions
y 4 descriptions can match all c j in[20, 25].
- ½ 316log2!
42,,1,19
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Threshold ValueThreshold Value
y Consider user bandwidth c j be an integer within
[a, b].
y The heterogeneity factor h=b-a+1.
y For a heterogeneity factor of 100, the threshold
value is 7 (if a=1)or 8 (if a>1).
26
- ½- ½°
¯®
!!
otherwise. ,2log
;1if ,1log
2
2
h
ahThreshol d
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Exact Assignment AlgorithmExact Assignment Algorithm
y If and
y If and
y Clearly, the assignment algorithm takessimply computations to decidebandwidths for the descriptions.
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1!a - ½ 1log2 u hm
- ½ hd 2log2 2,,2,2,1 -T!
1"a - ½ 2log2 u hm
- ½ had 2log2 2,,2,2,1,1 -
T!
)(mO
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OutlineOutline
y Introduction and Related Work
y Formulation and Complexity
y Exact Solution and the Threshold Value
y Efficient Heuristic SAMBA
y
Illustrative Simulation Results
y Conclusion
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Heuristic SAMBAHeuristic SAMBA
y In the general case, we present a heuristic
SAMBA (Simulated Annealing MDCBandwidth Assignment).
y The key is to address MDC bandwidthassignment problem when m is less than
the threshold
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Simulated AnnealingSimulated Annealing
y First proposed in 1983 to find approximatesolution for difficult combinatorial optimizationproblem [6].
y
Inspired by the annealing process in thestatistical mechanics.
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PropertiesProperties
y One of the local optimization technique
The search space is discrete and finite, eachpoint in the space is called a state.
Each state has an internal energy. The system may move from a state to its
neighbor state, which is called a transition.
y
Iteratively makes transition betweenstates to find the lowest energy state.
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Properties (Cont.)Properties (Cont.)
y Global optimum by randomization
Occasionally allows the system move to astate with higher energy.
Degree of randomization is controlled by atemperature value.
Temperature is initially high and slowlydecreases.
y Global optimum is guaranteed if the
temperature decreases slowly enough [7].
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Illustration: High TemperatureIllustration: High Temperature
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Temperature: High
Current state
State of lower energyState of higher energy
Neighborhood
Transition?
High probability
Transition?Yes
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Illustration: Low TemperatureIllustration: Low Temperature
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Temperature: Low
Current state
State of lower energyState of higher energy
Neighborhood Transition?Yes
Transition?
Low probability
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SAMBASAMBA
y State: the description vector
y Internal Energy:
y Distance between two states:
y Temperature T : Exponentially decay with # of
iterations
y Neighborhood radius: a decreasing function of T
y Transition probability to higher energy state:
a decreasing function of T
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d T
21d d
TT
S
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Details of AlgorithmDetails of Algorithm
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Complexity AnalysisComplexity Analysis
y SAMBA:
y Exhaustive Search:
y SAMBA is much more efficient than
exhaustive search because the constant KC is usually much smaller than .
37
m KC nO 2
ihnOm
i
m /2 1!
ihm
i/1!
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OutlineOutline
y Introduction and Related Work
y Formulation and Complexity
y Threshold Value and Exact Solution
y Efficient Heuristic: SAMBA
y
Illustrative Simulation Results
y Conclusion
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Environment and Baseline SettingEnvironment and Baseline Setting
y Numerical experiments are conducted on
PC using MATLAB
y Unless otherwise stated,
Video is encoded into 3 descriptions.
User receiving bandwidth is generated fromuniform distribution in [1, 100].
Each user has the same weight. Coding efficiency factor
Individual satisfaction is a quadratic function.
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m.,1 !m
E
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Comparison Schemes andComparison Schemes and
Performance MetricsPerformance Metricsy SAMBA has been compared with
Exhaustive search
Uniform assignment
Linear assignment
Random assignment
y The metrics include Overall satisfaction
Individual satisfaction
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SAMBA performs much better andSAMBA performs much better and
virtually matches the optimumvirtually matches the optimum
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The Existence of Optimal DescriptionThe Existence of Optimal DescriptionNumberNumber
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Influence of Individual SatisfactionInfluence of Individual Satisfaction
ModelModely Recall that individual satisfaction is
modeled as
y We consider a simple function f , where
y In simulation, we vary k to observe the
influence on the optimal description
number.
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.0k ,k
"! jm jmr r f EE
jmind r f S E!
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Satisfaction Model Affects theSatisfaction Model Affects the
Optimal Description NumberOptimal Description Number
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Influence of User ReceivingInfluence of User Receiving
Bandwidth DistributionBandwidth Distributiony In simulation, we consider that the
number of users of receiving bandwidth c
is proportional to a truncated normal
distribution, i.e.,
46
),(~ 2WQT N c
Example receiving
bandwidth distribution)5,10(~
T N c
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Individual satisfaction:Individual satisfaction:
receiving bandwidth withreceiving bandwidth with
47
)10,0(~T
N c
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Individual satisfaction:Individual satisfaction:
receiving bandwidth withreceiving bandwidth with
48
)10,50(~T
N c
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Individual satisfaction:Individual satisfaction:
receiving bandwidth withreceiving bandwidth with
49
)10,100(~T
N c
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OutlineOutline
y Introduction and Related Work
y Formulation and Complexity
y Threshold Value and Exact Solution
y Efficient Heuristic SAMBA
y
Illustrative Simulation Resultsy Conclusion
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ConclusionConclusion
y We study how to optimally assign
description bandwidth for MDC for videostreaming to large group.
y Contributions: Formulation and Complexity
Exact Solution and Threshold
Efficient Heuristic SAMBA
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[1] V. Goyal, ́ Multiple description coding: compression meets the network,µIEEE Signal P roc essing Magazine, vol. 18, no. 5, pp. 74-93, Sept. 2001
[2] M.H. Firooz, K. Ronasi, M.R. Pakravan, A.N. Avanaki, ́ Wavelet-basedUnbalanced Un-equivalent Multiple Description Coding for P2P Networks,µ
IEEE ICT- MICC 2007, pp. 242-247, May 2007.
[3] Mengyao Ma, O.C. Au, LiWei Guo, S.-H. Gary Chan, P.H.W. Wong,´Error Concealment for Frame Losses in MDC,µ IEEE T rans. Multimedia ,
vol. 10, no. 8, pp. 1638-1647, Dec. 2008.
[4] Bin. Li, J. Liu, J. Xu, Bo. Li, X. Cao, ́ Bandwidth provisioning formultiple description coding based video distribution,µ W ireless P ersonal
Multimedia C ommunic ations , 2002., v ol . 2, pp. 802-806, Oc t. 2002.
[5] P. Xia, X. Jin, and S.-H. Chan, ´Optimal Bandwidth Assignment forMultiple Description Coding in Media Streaming,µ IEEE CCNC· 09, Jan.
2009.
ReferencesReferences
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References (Cont.)References (Cont.)
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[6] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulatedannealing," Science, vol. 220, no. 4598, pp. 671{680, May 1983.
[7] S.Geman and D. Geman, "Stochastic relaxation, gibbs distributions and thebayesian restoration of images," IEEE Transactions on Pattern Analysis and
Machine Intelligence, vol. 6, no. 6, pp. 721{741,Nov. 1984.
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Q&AQ&A
y Thanks!
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