Defence Final

8/3/2019 Defence Final

http://slidepdf.com/reader/full/defence-final 1/54

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

1



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

2



Can you imagine your life withoutCan you imagine your life without

video streaming service?video streaming service?

3



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!

4



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)



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

6



Multiple streamsMultiple streams

7

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



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



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



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 #.

10



Model for MD Coded Video ServiceModel for MD Coded Video Service

11

Access Network

MDC video server anddescription bandwidthassignment

d1 d2 dmdescriptions««



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.

12



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?

13



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 #.

14



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].

15



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

16



OutlineOutline





y

Illustrative Simulation Results

y Conclusion

17



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!



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



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



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.

21

§ i x



OutlineOutline





y


y Conclusion

22



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.

23



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



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



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



Exact Assignment AlgorithmExact Assignment Algorithm

y If and

y If and

y Clearly, the assignment algorithm takessimply computations to decidebandwidths for the descriptions.

27

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



OutlineOutline





y


y Conclusion

28



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

29



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.

30



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.

31



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].

32



Illustration: High TemperatureIllustration: High Temperature

33

Temperature: High

Current state

State of lower energyState of higher energy

Neighborhood

Transition?

High probability

Transition?Yes



Illustration: Low TemperatureIllustration: Low Temperature

34

Temperature: Low

Current state

State of lower energyState of higher energy

Neighborhood Transition?Yes

Transition?

Low probability



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

35

d T

21d d

TT

S



Details of AlgorithmDetails of Algorithm

36



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!



OutlineOutline



y Threshold Value and Exact Solution

y Efficient Heuristic: SAMBA

y


y Conclusion

38



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.

39

m.,1 !m

E



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

40



SAMBA performs much better andSAMBA performs much better and

virtually matches the optimumvirtually matches the optimum

41





The Existence of Optimal DescriptionThe Existence of Optimal DescriptionNumberNumber

43



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.

44

.0k ,k

"! jm jmr r f EE

jmind r f S E!



Satisfaction Model Affects theSatisfaction Model Affects the

Optimal Description NumberOptimal Description Number

45



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



Individual satisfaction:Individual satisfaction:

receiving bandwidth withreceiving bandwidth with

47

)10,0(~T

N c





48

)10,50(~T

N c





49

)10,100(~T

N c



OutlineOutline



y Threshold Value and Exact Solution


y

Illustrative Simulation Resultsy Conclusion

50



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

51



52

[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



References (Cont.)References (Cont.)

53

[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.



Q&AQ&A

y Thanks!

54

Documents

Defence Final