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Paradigm Shift in Turbo ProcessingParadigm Shift in Turbo Processing‐ from P2P to Network –

Sl i W lf d CEO P bl Vi i tSlepian Wolf and CEO Problem Viewpoints

Tad Matsumoto and Xin HeTad Matsumoto and Xin HeInformation Theory and Signal Processing 

LaboratoryLaboratorySchool of Information Science, JAIST

April 19,  2013

This research is funded by JAIST Challenge‐Encouraging Research Grant.

Outline 2

• ReviewReviewMotivationCEO ProblemCEO Problem

• WSN with P EstimationWSN with P EstimationProposed System ModelP Estimation AlgorithmP Estimation AlgorithmPerformance Evaluation

• Conclusions and Future Work

Slepian Wolf Relay 3p y

• So far, we have solved the Slepian-Wolf relaying model by including vertical iteration.

DestinationDestination

Utilizing intra link correlationUtilizing intra-link correlationby vertical iteration toimprove the performance.

SourceSource

Source does not containerrors before encoding.

Relayerrors before encoding.

Proposed Relay Scheme: ACC‐DTC＋+ ＋+

M1 M1

ExtractionExtraction

)1()0()1(0)P(x =+=−== xpPxPp oo

Probability Update (fc)

K

4

)0()1()1()1P(x)()()()(

=+=−== xpPxPppp

oo

oo

)1()0()0()1(

1

1ˆ ==+==

=

= ∑ kyoPkxoPkyoPkxK

koP

Kp

Location of RelayLocation of Relay

RDS

1d 3dd

DSR

B

4d 4d

ddd

R

A

(a) (b)

Symmetric  Asymmetric 

BER at Relay

100

Relay of the proposed ACC DTC Ps=1

y

10-1

10 Relay of the proposed ACC-DTC, Ps=1, only extract (no iterations)

10-2

10

R l f S TC

10-3

10

BER

Relay of DTC,

Relay of SuTC, decoding with 5 iterations

10-4

10

Probability of Errors p at RelayAWGN ChannelI t l l th 10 000

y(no iterations)

-5

10 Interleaver length: 10,000 DTC, SRCC G=([3,2]3)8SuTC, SRCC G=([17,15]17)8Proposed, NSNRCC G=([3,2])8

-8 -6 -4 -2 0 2 410SNRsr (dB)

BER Performance in AWGN: 

100

AWGN Channel

Estimated p is used: Not artificial bit‐flipping S R link.

10-1

Interleaver length: 10000 DTC, SRCC G=([3,2]3)8

SuTC, SRCC G=([17,15]17)8Proposed, NSNRCC G=([3,2])8

10-2 SuT

10-3

10

BER

TC(B

), T=3

Proposed (B

Pro

4

10 B), Ps=2,Pr=2

posed (A), Ps=

10-4

2, T=4

=1, Pr=16, T=1

7-8 -6 -4 -2 0 2 410

-5

SNRsd (dB)

1

CEO Problem 8

• Error happens before encoding.

SourceFinal

destinationSource destination

• The goal is to make a paradigm shift from the Slepian-Wolf lossless-basedi l t k d i t l li k b d d i b d th CEO bl

Forwarding nodes

wireless network design to lossy link-based design, based on the CEO problem frame work.

CEO problem 9p• A CEO is interested in estimating a random source process u.• M agents observe noisy versions of random source process and have noiseless g y pbit pipes with finite rate to the CEO.

• Wk is the error happening before encoding due to the accuracy of observation.

Wireless Sensor Networks  10

• A wireless sensor network (WSN) consists of spatially distributed autonomoussensors to monitor physical or environmental conditions, such as temperature, sound,p y , p , ,pressure, etc. and to cooperatively pass their data through the network to a main location.

…

Sensing Fusin

…

phase k

…

observe

S

gObject Center

…

http://wsncanada.ca/index.php?page=adopt‐a‐forest

Sensors

A parallel WSN coding strategy 11p g gy• P = [ p1, p2, …., pM]T is the vector of observation error probabilities. The major problem is to estimate P. p

S FC S i AWGN h l d/ bl k R l i h f di h lSensors‐FC: Static AWGN channels and/or block Rayleigh fading channels

Why estimating P ? 12y g• Significant gain by utilizing P knowledge can be achieved.

100

10-1

10

10-2

ER)

Not utilizingP knowledge

Utilizing Pknowledge

10-3

ror R

ate

(BE

10-4B

it Er

M = 4. Without GIM = 4. With GIM = 7 Without GI

10-5

M = 7. Without GIM = 7. With GIM = 12. Without GIM = 12. With GIM = 16. Without GI

-12 -10 -8 -6 -4 -2 010

-6

per-link SNR (dB)

M 16. Without GIM = 16. With GI

Decoding Strategy using fc Function   13g gy g fc• Global iteration (GI) is introduced to reduce the computational complexity.

l l i i ( )local iteration (LI)

GI

A prioriLLRLLR

CalculatorPEstimator

local iteration (LI)

GI

local iteration (LI)

fc: LLR updating function that exploits the correlation knowledge P.

Pair‐wise Correlation Equations 14q

(1)( )

(2)

Point Equation 15q

(3)

(4)

Iterative P Estimation Algorithm 16g

Plug intoPlug into 

Learning Curves 17g• SNR is enough, we can get the exact P knowledge.

2

2.5M = 12. SNR = -10dB. T = 2M = 12. SNR = -10dB. T = 1.5M = 12. SNR = -8dB. T = 1.5M = 12 SNR = 8dB T = 2

1 5

2

(MS

E)

M = 12. SNR = -8dB. T = 2

1

1.5

Squa

re E

rror

(

0 5

1

Mea

n S

0

0.5

5 10 15 20 250

Iteration times

BER Performances: Identical P 18

100

• The loss using estimate P is around 0.3~0.5dB in the case pk are equal to 0.01.

10-1

10M = 4. Estimated PM = 4. Known PM = 7. Estimated PM = 7. Known P

10-2

(BER

)

M = 12. Estimated PM = 12. Known PM = 16. Estimated PM = 16. Known P

10-3

Erro

r Rat

e (

10-4B

it E

Exact P

6

10-5

Exact PEstimate P

-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -310

-6

per-link SNR (dB)

BER Performances: Impact of P variation 19p• The estimation algorithm can still achieve good performance in the case P varies.

-1

100

1 good, 7 bad, Estimated1 good, 7 bad, Known1 bad, 7 good, Estimated1 bad 7 good Known

100

M = 10, EstimatedM = 10, Known

10-2

101

e (B

ER

)

1 bad, 7 good, Known

1 ll 0 001

10-2

e (B

ER

)

P ~ uniform distribution

10-3

t Err

or R

ate 1 small p 0.0017 large p 0.1

7 small p 0 00110

-4

t Err

or R

ate P ~ uniform distribution 

over (0, 0.1]

10-4

Bit 7 small p 0.001

1 large p 0.1 Bit

-14 -12 -10 -8 -6 -4 -2 0per-link SNR (dB)

-12 -10 -8 -6 -4 -2 010

-6

per-link SNR (dB)

BER and FER Performances 20

• In Rayleigh fading channel, instantaneous SNR of each link is different.

E ti ti l ith hi ll t f i f di• Estimation algorithm can achieve excellent performance in fading case.

100 10

0

10-2

10-1

R)

10-1FE

R)

MRC P = 0

10-3

10

or R

ate

(BE 10

Err

or R

ate

(F

M = 8. Without GIM = 8 Known

diversity order gain

MRC P   0

10-5

10-4

Bit

Erro

M = 8. Without GIMRC (M = 8, P = 0)

10-2

Fram

e E M = 8. Known

M = 8. Estimated Capacity Outage

P = 0Outage

-12 -10 -8 -6 -4 -210

-6

10

per-link average SNR (dB)

( , )M = 8. Estimated PM = 8. Known P

-10 -8 -6 -4 -2 0 2 410

-3

per-link average SNR (dB)

Outage

per link average SNR (dB) per-link average SNR (dB)

Predict Error Floor (Identical P)  21( )• In the case all the elements of P have identical value p, the error floor can be calculated by (6):y ( )

• If p is small enough, e.g., p = 0.01, (6) is determined by the last term.

Predict Error Floor (Identical P) Result 22( )

100

10-1

10

M2

3

10-2

r Rat

e

M: 2

2

3

4

10-4

10-3

Bit

Err

or M: 2M: 3M: 4M: 5

4

5

6Wellmatched

10-5

M: 6M: 7M: 8M: 16

7

8

-12 -10 -8 -6 -4 -210

-6

per-link SNR (dB)

M: 16

23Questions Remain Un‐answered:

1. Multiplexing transmission: MAC and/or Orthogonal;

2. Does Source-Channel Separation hold?

3. Based on network information theory, derive the rate-distortion bound (R (D D ) R (D D )) f l(R1(D1, D2), R2(D1, D2)) for general cases;

4. Establish techniques that can evaluate the convergence property of the decoding scheme while keeping the distortion lower than specoified;scheme while keeping the distortion lower than specoified;

5. Short Block Length case.

My long‐lasting friend, Prof. Lajos Hanzo ,said in EW 2012 in Poznan, 

“L j ill t ik b k”“Lajos will strike back”but 

“Tad has never been on strike!”Tad has never been on strike!