quantization and transmission in wireless multi-hop networks
TRANSCRIPT
QUANTIZATIONANDTRANSMISSIONINWIRELESSMULTI-HOPNETWORKS
Behzad M. Dogahe
Department of Electrical and Computer Engineering
Motivation
Applica6ons
Voice
StreamingMul6media
Gaming
WirelessAd-HocNetworksRemoteCompu6ng
Requirements(QoS)
DataRate
Reliability
End-to-EndDelay
Powerlevel
Reproduc6onFidelity
Classifica6on
Resources
Power
Bandwidth
• Co-existèShareresourcesèConges6onControl
• DigitalèQuan6za6on
Problem Statement
• Goal:Transmitdatainwirelessmul6-hopnetworkwithQoSdependonrate,end-to-enddelay.Atthedecoder,notonlyreconstruc6ngquan6zedsignalbutalsoclassifythem.
QoS
Rate
End-to-endDelayReproduc6onFidelityClassifica6on
Resources
Power
Linkcapacity
Problem Statement Breakdown
MainGoal(rate,delay,power,quan6za6on,classifica6on)
Problem1(rate,delay,power)
Problem2(Quan6za6on,Classifica6on)
CombinedSolu6on
QoSinsharedresourceconstrainednetwork
1.TransportandPhysical
2.Presenta6onLink
Problem 1
MainGoal(rate,delay,power,quan6za6on,classifica6on)
Problem1(rate,delay,power)
Problem2(Quan6za6on,Classifica6on)
CombinedSolu6on
QoSinsharedresourceconstrainednetwork
1.TransportandPhysical
2.Presenta6onLink
Problem 2
MainGoal(rate,delay,power,quan6za6on,classifica6on)
Problem1(rate,delay,power)
Problem2(Quan6za6on,Classifica6on)
CombinedSolu6on
QoSinsharedresourceconstrainednetwork
1.TransportandPhysical
2.Presenta6onLink
Combining2Problems
MainGoal(rate,delay,power,quan6za6on,classifica6on)
Problem1(rate,delay,power)
Problem2(Quan6za6on,Classifica6on)
CombinedSolu6on
QoSinsharedresourceconstrainednetwork
1.TransportandPhysical
2.Presenta6onLink
Problem 1
• Problem1:BalancingPowerandRatetoAchieveBoundedAverageDelayinWirelessNetworks
QoS
Rate
End-to-endDelayReproduc6onFidelity
Classifica6on
Resources
Power
LinkCapacity
Problem 1
q Application running on a wireless multi-hop network q Link capacities are interference dependent. q How can we balance power control and congestion control to improve the overall network performance (Data Rate and Delay Requirements of the Sessions)?
1x
2x 3x
4x
Background
q Congestion Control: A mechanism that regulates the allowed rates so that the total traffic load on a link does not exceed the capacity. (Example: Congestion-Avoidance in TCP) q Congestion avoidance in TCP approximates a distributed algorithm that implicitly solves network utility maximization (NUM) problems.
QoS
Ratev
End-to-endDelay
Reproduc6onFidelity
Classifica6on
Resources
Power
LinkCapacity
Developing Problem Statement
Network Utility Maximization q Each source has a Utility Function
§ A Quality Measure § Example: TCP-Vegas
q Most Basic NUM: )log()( sss xxU α=
lcx
xU
lsLlss
ss
ssxs
∀≤∑
∑
∈
∀
,)(:
}:{)(max
Subject to:
sx : Data Rate of Session s
lc : Capacity of Link l
Developing Problem Statement
q Capacities of the Wireless Links are dependent on the Transmission Power and Interference : Transmitter Power on Link l
: Noise on Link l Kisaconstantthatdependsonthemodula6onandtherequiredbiterror.Gpathgainandpathloss.
QoS
Rate
End-to-endDelay
Reproduc6onFidelity
Classifica6on
Resources
Powerv
LinkCapacityv
Parameters
QoS
Rate✔
End-to-endDelay
Reproduc6onFidelity
Classifica6on
Resources
Power✔
LinkCapacity✔
Background - Delay
End-to-EndDelay:
Propaga6onDelay TransmissionDelay QueuingDelay
Forapplica6onsproducingburstydata,queuingdelaycanbequitesignificant,
thereforeitisthedominantcomponentoftotaldelay.
Developing Problem Statement
The New Requirement: q Bounded Average Queuing Delay
§ Each Link Modeled as an M/G/1 Queue § General Packet Length Distribution
• Mean 1/µ , and Variance 𝜎↑2
∑∈
−+
−=
)(:
//)1()(
sLlssll
l xccTE µβµβ
2/)1( 22σµβ +=
ll dTE ≤)(ld : Maximum Allowed Delay on Link l
(.)E : Expected Value
Problem Statement
ll dTE ≤)(
DelayRequirementofSessionsMinimumRateRequirement
Non-convexè high-SIR&changeofvariable
Problem Statement (Lagrangian Dual)
Lagrangian lλ : Lagrange Multipliers
Lagrange Dual Function:
Dual Problem:
Problem Statement (link: delay & power)
• Delay Distribution Problem
• Power Allocation Problem
§ Update Equation
Solution Steps
Main Problem
Source Problem Link Problem
Dual Decomposition Lagrange Multipliers lλ
Solved at Each Source
Power Allocation
Delay Distribution
sx
lP
De-Centralized Delay Distribution
Dual Decomposition sν
ld
Derived Algorithm
1. Initialize
2. At Each Source:
3. Each Transmitter Calculates ‘m’ locally and Transmits it to All other Transmitters by a Flooding Protocol
4. Each Transmitter Updates its Power
Derived Algorithm
4.1. Initialize
4.2. Link Updates its Delay Share
4.3. Delay Price Update
5. Each Link Updates its Link Price:
Simulations
q 5 Nodes, 4 Sessions q Delay Requirement: 10 ms q Maximum Power: 0.12 W q Utility Function:
Observations
q Sessions reduced data rates to achieve lower queuing delays based on the constraints.
q Some transmitters consume more power to handle the delay requirements of the sessions.
q Some transmitters reduce power to reduce the interference on other links.
Remarks
q Presented problem of allocating resources of bandwidth and power in a multi-hop wireless network. q Incorporated average queuing delay requirement of sessions in the NUM Problem.
q Transferred the non-convex problem to a convex optimization by high-SIR and change of variable. Presented a distributed iterative algorithm.
q This augmented NUM formulation allowed application to tradeoff rate, power and queuing delay according to its needs.
Problem 2
MainGoal(rate,delay,power,quan6za6on,classifica6on)
Problem1(rate,delay,power)
Problem2(Quan6za6on,Classifica6on)
CombinedSolu6on
QoSinsharedresourceconstrainednetwork
1.TransportandPhysical
2.Presenta6onLink
Problem 2
q Problem2:Quan6za6onForClassifica6onAccuracyInHigh-RateQuan6zers
QoS
Rate
End-to-endDelayReproduc6onFidelity
Classifica6on
Resources
Power
LinkCapacity
Problem 2 (more motivation)
q Quan6za6onofsignalsrequiredformanyapplica6onsq Originalsignalquan6zedatencoder.Atdecoderareplicathat
shouldresembleoriginalsignalinsomesenseisrecoveredq Presentquan6zersmakeefforttoreducethedistor6onof
signalinthesenseofreproduc6onfidelityq Considerscenariosinwhichsignalsaregeneratedfrom
mul6pleclasses.Theencoderfocusesonthetaskofquan6za6onwithoutanyregardstotheclassofthesignal
q Thequan6zedsignalreachesthedecoderwherenotonlytherecoveryofthesignalshouldtakeplacebutalsoadecisionistobemadeontheclassofthesignalbasedonthequan6zedversionofthesignalonly
Goal
q Goal:Designofaquan6zerthatisop6mizedforthetaskofreproduc6onfidelityandclassifica6onatthedecoder
q Applica6onScenarios:§ Wanttohavegoodsoundfidelity(goodvoice/audio
quality)butalsowanttobeabletoperformspeakerrecogni6on
§ Sensornetworkwherethesensorshavelowcomplexity,simplequan6zers,butthedecoder/sensorsinknodedoesmoresophis6catedprocessing(sotherawsignalvalueisneeded,butwealsowanttobeabletoclassifythesensedsignal)
Design of a Quantizerq GoalofQuan6za6onistominimize:
q whereisDistor6onMeasure
q ExamplesofDistor6onMeasure:§ MSE§ LogSpectralDistor6on
2ˆ)ˆ,( xxxxd −=
Quan6zerx )(ˆ xQx =
Design of a Quantizer – High-Rate theory
x
x̂
x
)(xp
x
)(xλ
x
x̂
x
)(xp
x
)(xλ
Inhigh-ratetheorypointdensityfunc6onrepresentsthedensityofcodebookpointsinanyregionforaquan6zer.Thedesignofaquan6zerisequivalenttodesignoftheop6malpointdensityfunc6on. )(xp :ProbabilityDensityFunc6on
Background
q Followingthestepsin[GardnerandRao]pointdensityfunc6onwillbederivedas
(nisthedimensionofx)W.R.GardnerandB.D.Rao,“Theore6calanalysisofthehigh-ratevectorquan6za6onoflpcparameters,”SpeechandAudioProcessing,IEEETransac7onson,vol.3,no.5,pp.367–381,sep1995.
Problem Statement
q Wehavetoselectadistor6onmeasurethatiswelldefinedforclassifica6onpurposes
q WechosethesymmetricKullback-Leiblerdivergencemeasure
betweenprobabilityofclassgiventhesignalbeforeandajerquan6za6on
Problem Statement & Solution
Weassumeagenera6vemodelforclassifier.Henceandareknownapriori.
Trade-offDistor6onMeasure:
Optimal Mismatched Distortion Measure
q Studyperformanceofaquan6zertrainedbyminimizingthedistor6ond1butmeasuredbydistor6ond2.
q Thera6onaleforsuchanalysisistodesignaquan6zerwithdistor6onmeasureofrelevanced2butforprac6calandimplementa6onreasonswechoosetoquan6zewithdistor6onmeasured1.
q Showedthattheop6maldiagonalmatrixD1wouldhavethediagonalelementsofD2.
Simulations
q Signalisfromtwoclasseswithknowncondi6onalPDFs
q Dashedlinesrepresentthedecisionboundaries
q Pointdensityfunc6ondedicatescodebookpointstotheboundaries
Simulations
q Signalisfromtwoclasseswithknowncondi6onalPDFs
q Dashedlinesrepresentthedecisionboundaries
q Pointdensityfunc6ondedicatescodebookpointstotheboundaries
Simulations
q onlydedicatescodebookpointswherethesignalisconcentrated
q ByintroducingtradeoffbetweenMSEandclassifica6on,codebookpointsmovetotheclassifica6onboundaries
Simulations
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
KL Tradeoff(a=0.2)Tradeoff(a=0.8) MSE
10Bits
8Bits
6Bits
Classifica@onError(%)
q Thehigherthebitrateofquan6zerthebemerclassifica6onaccuracy
q AswemovefromMSEtoKL,theclassifica6onaccuracyimproves
Simulations
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0KL Tradeoff(a=0.2)Tradeoff(a=0.8) MSE
10Bits
8Bits
6Bits
Distor@on(dB)
q PureKLperformspoorlyasfarasthedistor6onofthesignal
q However,introducingtheslightesttradeoffwithMSEimprovesdistor6onsignificantly
Simulations
q onlydedicatescodebookpointswherethesignalisconcentrated
q ByintroducingtradeoffbetweenMSEandclassifica6on,codebookpointsmovetotheclassifica6onboundaries
Simulations
q Thehigherthebitrateofquan6zerthebemerclassifica6onaccuracy
q AswemovefromMSEtoKL,theclassifica6onaccuracyimproves
Classifica@onError(%)
0
0.1
0.2
0.3
0.4
0.5
0.6
KL Tradeoff(a=0.2) Tradeoff(a=0.8) MSE
12Bits
10Bits
8Bits
Simulations
q PureKLperformspoorlyasfarasthedistor6onofthesignal
q However,introducingtheslightesttradeoffwithMSEimprovesdistor6onsignificantly
-70
-60
-50
-40
-30
-20
-10
0KL Tradeoff(a=0.2) Tradeoff(a=0.8) MSE12Bits
10Bits
8Bits
Distor@on(dB)
Simulations (2-D Signal)
q Thehigherthebitrateofquan6zerthebemerclassifica6onaccuracy
q KLperformsbemerthanKL-DiagonalwhichperformsbemerthanMSE.
Classifica@onError(%)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
KL KL-Diag MSE
15Bits
14Bits
12Bits
Simulations
q KLperformspoorlyasfarasthedistor6onofthesignalfollowedbyKL-DiagandthenMSE.
-35
-30
-25
-20
-15
-10
-5
0KL KL-Diag MSE15Bits
14Bits
12Bits
Distor@on(dB)
Real Data Set
q DataSet§ IrisdatasetfromUCImachinelearningdepository.§ 4amributes:SepalandPetallengthandwidth§ 3classesofIrisplant,50instancesofeachclass
q Simula6onScheme§ 50Instancesofeachclassesdividedinto30fortrainingand
20fortes6ng§ Wedothispar66oningrandomlyandrepeattheexperiment
106mes.
Real Data Setsq Random
Codebooks§ MSE:Blue
Plus§ KL:RedCircle§ KL-Diag:
BlackCrossq Repeat
genera6ngrandomcodebooks1006mes
Simulations (Iris Data Set)
q Thehigherthebitrateofquan6zerthebemerclassifica6onaccuracy
q KLperformsbemerthanKL-DiagonalandMSEinthemiddle
Classifica@onError(%)
0
0.5
1
1.5
2
2.5
3
3.5
KL KL-Diag MSE
9Bits
8Bits
7Bits
Simulations (Iris Data Set)
q Thehigherthebitrateofquan6zerthebemerdistor6on
q MSEperformsbemer
-30
-25
-20
-15
-10
-5
0KL KL-Diag MSE9Bits
8Bits
7Bits
Distor@on(dB)
Simulations (Iris Data Set – 4 attributes)
q KLperformsbemer
thanKL-DiagonalandMSE
Classifica@onError(%)
0
2
4
6
8
10
12
14
KL KL-Diag MSE
9Bits
8Bits
7Bits
Simulations (Iris Data Set – 4 attributes)
• MSEperformsbemer
Distor@on(dB)
-12
-10
-8
-6
-4
-2
0
2
KL KL-Diag MSE
9Bits
8Bits
7Bits
Remarksq Proposedaquan6zerforthepurposeofobtainingamore
accurateclassifica6onandreconstruc6onatthedecoderq Employedhigh-ratetheoryforquan6zerdesign.q Op6malpointdensityfunc6onwasderivedq Theperformanceofthismethodwasexaminedandobserved
tobesuperiorinthetaskofclassifica6onofsignalsatthedecoder
q Thetradeoffbetweenthereproduc6onfidelityandclassifica6onaccuracywasstudiedaswell
Interrela6onshipsofthe2solu6ons
MainGoal(rate,delay,power,quan6za6on,classifica6on)
Problem1(rate,delay,power)
Problem2(Quan6za6on,Classifica6on)
CombinedSolu6on
QoSinsharedresourceconstrainednetwork
1.TransportandPhysical
2.Presenta6onLink
Interrela6onshipsofthe2solu6ons
MainGoal(rate,delay,power,quan6za6on,classifica6on)
Problem1(rate,delay,power)
Problem2(Quan6za6on,Classifica6on)
DateRate
Quan6zer
Bits/vector
Simulation
q Averageresultofclassifica6onerror.
q Rate&Classifica6on:S1>S4>S3>S2
q Classifica6on:KL>KL-Diag>MSE
q WithDelay:Slightlyworseclassifica6on.
0
2
4
6
8
10
12
14
16
18
KL KL-Diag MSE
Classifica@
onError(%
)
Quan@za@onMethod
Session1
Session1(delay)
Session2
Session3
Session4
Session4(delay)
Simulation
q Averageresultofdistor6onmeasure.
q Rate&Distor6on:S1>S4>S3>S2
q Distor6on:MSE>KL-Diag>KL
q Withdelay:Slightlyworsedistor6on
-25
-20
-15
-10
-5
0
5
KL KL-Diag MSE
Distor@o
n(dB)
Quan@za@onMethod
Session1
Session1(delay)
Session2
Session3
Session4
Session4(delay)
Simulationq Short-term
behavior:Movingaverageofclassifica6onerrorfor4sessions.
q Classifica6on:KL>KL-Diag>MSE
Contributionsq Westudiedtheproblemofresourcealloca6onandquan6za6ontoachieveQoS
inasharedresourceconstrainednetwork.
q Brokedownproblemintotwoproblemstobesolvedatdifferentnetworklayers.§ Firsttoachievedatarateanddelayrequirementswithpowercontrolofthe
transmimers.• AugmentedNUMproblem• Changeofvariableandhigh-SIRapproxima6ontotransformtoaconvex
problem.• Presentedadistributedsolu6on.
§ Secondtodesignaquan6zertoachievesignalreconstruc6onandbemerclassifica6onatthedecoder.• Introducedanewdistor6onmeasure,KLdivergence.• Designedaquan6zerbasedonthenewdistor6onmeasurewithhigh-
ratetheory.
Contributions§ Secondtodesignaquan6zertoachievesignalreconstruc6onandbemer
classifica6onatthedecoder.• Introducedanewdistor6onmeasure,KLdivergence.• Designedaquan6zerbasedonthenewdistor6onmeasurewithhigh-
ratetheory.• Derivedop6malmismatcheddistor6onmeasure
q Demonstratedthelinkageandinterrela6onshipsofthetwosolu6ons.
Proposed Future Workq Designofquan6zersthatperformwellwhenpairedwithmorenovelclassifiers
likeSupportVectorMachine.
q DesignofajointNUMandquan6za6onmethodthroughalargeraugmenta6onofthebasicNUMproblem.• AddQoSobtainedthroughclassifica6onandre-construc6ontotheobjec6ve
func6onorconstraints.• Includethedistor6onmeasureofthequan6zerintheNUM.• Highlynon-convexandwouldrequirechangeofvariablesandother
methodsbeyondwhatwepresentedinthisdisserta6ontoconverttheproblemintoaconvexop6miza6onproblem.
q StudyoftheconvergenceofNUMframeworkwhenmessagesarequan6zed.