SOURCECODING AND PARALLELROUTING A. Ephremides - - PowerPoint PPT Presentation

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SOURCECODING AND PARALLELROUTING

• A. Ephremides

UniversityofMaryland DIMACS- 3/19/03

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CROSS-LAYERISSUES

Compression(Layer6)andTransmission(Layer1)

• energyefficiencyperspective.
• tradeoffbetweentransmission(RF)andprocessingenergy.
• incontextofsensornetworks,addedfeatureofdetectiongivesaspecial

slanttocompression

Compression(ITsourcecoding)andRouting(Layer3)

• couplingofinformationtheoryandnetworking.
• revealsnoveltrade-offs

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MAINIDEA

• MultipleDescriptioncoding
• different(coupled)representationsofsourcesignals.
• eachdescriptionrequiresfewerbitsthanasingledescription.
• ParallelRouting
• redundanttransmissionofpacketcopiesoverseparateroutes.
• protectsagainstlongdelaysand/orerrors
• JointCompression/Routing
• sendeachdescriptionoveraseparateroute
• “cancel”redundancywithcompression
• Trade-offstudy

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BACKGROUND

• Sourceemitsi.i.d.Gaussianvariables(0-mean,unitvariance).
• D=meansquarederrordistortion
• R=representationrate(bits/symbol)
• Symbolsaresenttoadestinationnode;somodifydistortionmeasure
• T:delay
• Thinkofeachsymbolasaseparate“packet”oflengthRbits
• 2R

D=2

• 2R

2 , T

• D=

1, T>

• ≤

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BACKGROUND(Continued)

• Multiple(i.e.Double)DescriptionCoding

(Ozarow,ElCamal/Cover,Wyner etal circa’80-’82)

• Eachdescriptionissenttodestinationoverseparateroute
• ithdescriptionhasrateRi,individualmsedistortiondi,anddelayTi
• d0 isjointdistortion

1 2

R R R + =

1 2 1 2 1 2 1 2

• 2(R +R )

1 2

• 2R
• 2R
• 2(R +R )
• 2R

1 1 2

• 2R

2 1 2 1 2

2 d = , T

• &T
• 2

+2

• 2

d =2 , T

• &T >
• D=

d =2 ,T >

• &T
• 1, T >
• &T >
• ≤

≤

• ≤
• ≤

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BACKGROUND(Continued)

• Previousformuladescribestheboundaryoftheachievablerate-distortion

region.

• “Inside”theregionwehave
• Note:δi →0,noredundancy,“lean” compression,“effective” rateRi,

minimumdistortion. δi →1,maximumredundancy,ineffectivecompression,“effective” rate 0,maximumdistortion

• Choiceofδ affectsdistortion-ratevaluesand representationcomplexity

i i 1 2 1 2

• 2R (1-
• )

i 2(R +R ) 2 2(R +R ) 1 2 1 2 i

d =2 1 d 2 . 1 ( ) where =(1-d )(1 d )& d d 2 where0

1representsthe"redundancy"ofthe representations

− −

= − Π − Λ Π − Λ = − ≤ ≤

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SIMPLENETWORKMODEL

s E1 E2 R1 R2 MUX λs λs q

MDC decoder

D λs λs λs λN λN λ λ C1 C2

S S N 1 2

=sourcesymbolrate("packets"/s)

• thertrafficrate

= R R R=bits/packet

Ν

λ λ = λ λ + λ + =

1 1 2 2

CodingParameters R = R R

1,

α + δ δ

1 2

q=networkparameter initiallyC C =

• noiselesstransmission

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AVERAGEDISTORTION

Objective:MinE[D] bychoiceofα,δ1,δ2,q (forfixedR,C1 =C2 =C,λ,∆)

• Needqueuinganalysistoexpressthedelayprobability

(useM/G/1formulas)

• PerformNumericalMinimization
• *=willdenotesoptimalvalues

[ ] [ ] [ ] [ ] [ ]

1 2 1 1 2 2 1 2 1 2

Pr , Pr , Pr , 1 Pr ,

• E D

d T T d T T d T T T T = ≤ ∆ ≤ ∆ + ≤ ∆ > ∆ + > ≤ ∆ + > ∆ > ∆

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FIRSTRESULTS

• PhaseTransitionBehavior

q* λc E(D*)

1/2

λc q* λ λ

• Beyondacriticalloadvaluedonotmixtraffic

(i.e.dedicateeachdescriptioncompletelytoitspath)

• Belowthatvaluemixthoroughly(50-50)

q=1/2

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FIRSTRESULTS(Continued)

λc λ

1/2 α*=R1/(R1+R2) Belowλcencodesymmetrically(noadvantage todifferentiatedescriptions) Graduallydroptheredundancy Factortozero(“lean”compression) Load (orrate)

ρ1 λc λ ρ2

• Keeptheloadononequeue

belowsaturationandsendall theremainingtraffictothe

• therqueue

i i i i

R R C C λ ρ = λ =

λc λ

.82

δ*

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INTELLIGENTSWITCH

• droppacketswhosesojournstimesexceed∆ (whilestillinqueue).
• onlychange:“impatientcustomer”queuingbehavior

Note:Atheavyloads intelligentswitchwith dumm mixingisworse thanintelligentmixing withdumm switch

Explanation:- ISdropspackets“uniformly”atbothqueues

• Optimalmixinggivesupononequeuetotally(garbagebag)

butkeepsonequeuemaximallyuseful

1 ( ) 2 MDC q =

1 ( ) 2 IS q =

( ) E D

λc λ

*( *) MDC q q = ( *) IS q q =

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PROBINGFURTHER

• SofarR wasfixed(totalrate)
• Asλ increases,wemaybeabletocontroltheloadby

manipulatingpacketlengthswithouttheconstraintthat

• IfthereisanoptimalR*,bysymmetryweshouldhave
• Also,sincebothqueueswouldbeequallyloaded,packetswould

belostwithlowprobabilityatbothaswedecreaseR;hencewe shouldchoosetominimized0

• Infact,then,
• Notoptimal

* * * 1 2

2 R R R = =

1 2

R R fixed + =

* *

*

1 2 2 log 2

R R

R

− ∗ ∗ 1 2

+ δ = δ =

∗ ∗ 1 2

δ , δ

*

* 2

2

R

d

−

=

&

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CONFIRMATION

( ) E D

λc λ

withR* MDC withR* SDC *& ( *) MDC IS q q =

EvenSDCwithoptimalR*outperformsMDC*withISat highloads

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CONFIRMATION(CONTINUED)

* MDC SDC

* R

λ

• Ifinsteadofminimizingd0weminimizeE[D]wefindthatbothR*and

E(D)areindistinguishablyclose(hence,intuitionwasgood)

• Atverylowloads(λ → 0),onemightexpectthattheoptimumR* might

increasewithoutbound.

• Thisisnotthecase(verylongpacketsincreasethedelaysufficiently

towipeoutdistortiongains)

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FURTHERTHOUGHTS

• Arethesetrade-offsextendabletonon-Gaussiansymbolsandnon-

trivialnetworkspaths?

• Canwetranslatetheresultstopracticalcompressionschemes?
• Whataretheenergyimplicationsofthetrade-off?Dowespend

moreorlessenergywhenweuseparallelpathswithmultiple descriptions?

• Whathappensifnoiseisaddedinthesystem?
• Whathappensinawirelessenvironmentwhereinadvertent

multicastingoccurs?