Low Complexity Encoding for Network Codes Yuval Cassuto Michelle Effros Sidharth Jaggi.
Universal Linked Multiple Access Source Codes Sidharth Jaggi Prof. Michelle Effros.
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Transcript of Universal Linked Multiple Access Source Codes Sidharth Jaggi Prof. Michelle Effros.
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Universal Linked Multiple Access Source Codes
Sidharth JaggiProf. Michelle Effros
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Source Codes (SCs)
Multiple Access SCs
Models for Source Coding
)ˆ,ˆ( nn YX
Y
X
Z
RX(Q)
RY(Q)
nX
nY
![Page 3: Universal Linked Multiple Access Source Codes Sidharth Jaggi Prof. Michelle Effros.](https://reader033.fdocuments.in/reader033/viewer/2022050916/5a4d1b6e7f8b9ab0599b4362/html5/thumbnails/3.jpg)
Slepian-Wolf
Slepian-WolfRate Region
),( YXHQ
)(YHQ
)|( YXHQ
)|( XYHQ
)(XHQ
RX(Q)
RY(Q)
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Source Codes (SCs)
Multiple Access SCs
Universal MASCs?
Models for Source Coding
?))(),((?,
Rate Wolf-Slepian0
QRQRPQ
YX
e
} memoryless distributions on{
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Universal MASCs?Let
),(),()()(),()(:,
YXHYXHyQyQxQxQQQ
QQ 21 212121
),( YXHQ1
)(YHQ
)(XHQ
),( YXHQ2
1Q2Q
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Universal MASCs?
nY
?),(),( yxQyxQ 21 or
or or
22
11
?)(?)()()(
QRQRQRQR
YX
YXnX
1Q2Q
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Source Codes (SCs)
Universal SCs Multiple Access SCs Missing Link
Linked MASCs
Models for Source Coding
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Linked MASC (LMASC) Model
Y
X
Z
Xavier
Yvonne
Zorba
XR
YR
nX
nY
YXr XYr )ˆ,ˆ( nn YX
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(0,0)-LMASCs
Y
X
Z
Xavier
Yvonne
Zorba
nX
nY
),(, 00 XYYX rr
YXr XYr
XR
YR
)ˆ,ˆ( nn YX
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),( YXHQ
)(YHQ
)|( YXHQ
)|( XYHQ
)(XHQ
RX
RY
(0,0)-LMASC Rate Region
(0,0)-LMASC Rate Region =Slepian-WolfRate Region
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Source Codes (SCs)
Universal SCs Multiple Access SCs
Linked MASCs
Universal LMASCs?
Universal LMASCs?
?),(?,
Region RateSW on point Any 0
YX
e
RRPQ
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Universal (0,0)-LMASCsCode
nC
Y
X
Z
Xavier
Yvonne
Zorba
nX
nY
)(QRX
)(QRY
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Universal (0,0)-LMASCsCode
0))(( QCP ne
nC
Y
X
Z
Xavier
Yvonne
Zorba
nX
nY
YXr XYr
XR
YR
)ˆ,ˆ( nn YX
),())(( 00QCr n
),())(( 00 QCR n
))(),(()())(( , QRQRRREQCR YXYXQn
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Results for (0,0)-LMASCsIf ,)( r
nenCr
,)(
eP
nn
e CP 2
,)( Rn
enCR
Example:
,)( /31nCr n
.)(/ 31
2 ne nCP
,)( /61 nCR n
then
Tradeoffs
12 PRr eee
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Y
X
Z
Xavier
Yvonne
Zorba
nX
nY
),(),( 00 XYYX rr
XR
YR
LMASCs ),( XYYX rr
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YXrYHQ )(
YXrYXHQ )|(
),( YXHQ
YXr
YXr
XR
YR
Y
X
ZYXr 0
YXrYXHQ )|(
YXrYHQ )(
Achievable Region
Universal Coding possible
LMASCs ),( XYYX rr
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Y
X
Z
Yvonne
Zorba
nX
nY
XR
YR
)ˆ,ˆ,...,ˆ( nnn YXA
Xavier
AlgernonA
AR
nA -encoder LMASCs=
l -encoder MASCl
-encoder LMASCsl
Universal Coding possible
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Y
X
Z
Xavier
Yvonne
Zorba
XR
YR
nX
nY
XZr
YZr
(0,0)-FMASCs =(0,0)-LMASCs( , )-FMASCs =(0,0)-LMASCsUniversal Coding possible
XZr YZr
Feedback MASCs
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Y
X
Z
Xavier
Yvonne
Zorba)ˆ( nPRY
)(nmX )(nmY
nY
nX
)ˆ,ˆ( nn YX
)ˆ( nPRX
)ˆ( nPCn
Proof Sketch - Universal LMASCs
nP̂ ),,( )()( nmnm YXLet be the type of
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nP
Q
Proof Sketch - Universal LMASCs
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What could possibly go wrong?
||ˆ|| QPn)(n
nP̂
Q
•Estimate “far off”
Probability of Error Rate Redundancy
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),( nn YX 11
nP̂
Q
What could possibly go wrong?
),( nn YX 22
Probability of Error Redundancy• Atypicalit
y• Code failsnC
• Source
mismatch
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ConclusionsX
ZMASC
(0,0)-LMASC
Universality
Universality
Y
XZ
Y
-
LMASCUniversality
XZ
Y
),( XYYX rr
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ConclusionsX
Z(0,0)-FMASCY
l -encoder - LMASC Universality
Universality
XZ
Y
Universality -
FMASC
),( YZXZ rr
Complicated diagrams
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The bottom line is…
It WORKS!