1. 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 He
Information Theory and Signal Processing
LaboratoryLaboratory
School of Information Science, JAIST
April 19, 2013
This research is funded by JAIST Challenge‐Encouraging Research Grant.

2. Outline 2
• ReviewReview
Motivation
CEO ProblemCEO Problem
• WSN with P EstimationWSN with P Estimation
Proposed System Model
P Estimation AlgorithmP Estimation Algorithm
Performance Evaluation
• Conclusions and Future Work

3. 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 correlation
by vertical iteration to
improve the performance.
SourceSource
Source does not contain
errors before encoding.
Relay
errors before encoding.

4. 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
)()()()(
=+=−== xpPxPp
pp
oo
oo
)1()0()0()1(
1
1
ˆ ==+==
=
=
∑ kyoPkxoPkyoPkx
K
k
oP
K
p

5. Location of RelayLocation of Relay
R
DS
1
d 3
d
d
DS
R
B
4d 4d
ddd
R
A
(a) (b)
Symmetric Asymmetric

6. BER at Relay
10
0
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 Relay
AWGN Channel
I t l l th 10 000
y
(no iterations)
-5
10 Interleaver length: 10,000
DTC, SRCC G=([3,2]3)8
SuTC, SRCC G=([17,15]17)8
Proposed, NSNRCC G=([3,2])8
-8 -6 -4 -2 0 2 410
SNRsr (dB)

7. BER Performance in AWGN:
10
0
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)8
Proposed, 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 4
10
-5
SNRsd (dB)
1

8. CEO Problem 8
• Error happens before encoding.
Source
Final
destinationSource destination
• The goal is to make a paradigm shift from the Slepian-Wolf lossless-based
i 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.

9. 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 noiselessg y p
bit pipes with finite rate to the CEO.
• Wk is the error happening before encoding due to the accuracy of observation.

10. Wireless Sensor Networks 10
• A wireless sensor network (WSN) consists of spatially distributed autonomous
sensors 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
g
Object Center
…
http://wsncanada.ca/index.php?page=adopt‐a‐forest
Sensors

11. 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

12. Why estimating P ? 12y g
• Significant gain by utilizing P knowledge can be achieved.
10
0
10
-1
10
10
-2
ER)
Not utilizing
P knowledge
Utilizing P
knowledge
10
-3
rorRate(BE
10
-4
BitEr
M = 4. Without GI
M = 4. With GI
M = 7 Without GI
10
-5
M = 7. Without GI
M = 7. With GI
M = 12. Without GI
M = 12. With GI
M = 16. Without GI
-12 -10 -8 -6 -4 -2 0
10
-6
per-link SNR (dB)
M 16. Without GI
M = 16. With GI

13. 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 priori
LLRLLR
CalculatorP
Estimator
local iteration (LI)
GI
local iteration (LI)
fc: LLR updating function that exploits the correlation knowledge P.

14. Pair‐wise Correlation Equations 14q
(1)( )
(2)

15. Point Equation 15q
(3)
(4)

16. Iterative P Estimation Algorithm 16g
Plug intoPlug into

17. Learning Curves 17g
• SNR is enough, we can get the exact P knowledge.
2
2.5
M = 12. SNR = -10dB. T = 2
M = 12. SNR = -10dB. T = 1.5
M = 12. SNR = -8dB. T = 1.5
M = 12 SNR = 8dB T = 2
1 5
2
(MSE)
M = 12. SNR = -8dB. T = 2
1
1.5
SquareError(
0 5
1
MeanS
0
0.5
5 10 15 20 25
0
Iteration times

18. BER Performances: Identical P 18
10
0
• The loss using estimate P is around 0.3~0.5dB in the case pk are equal to 0.01.
10
-1
10
M = 4. Estimated P
M = 4. Known P
M = 7. Estimated P
M = 7. Known P
10
-2
(BER)
M = 12. Estimated P
M = 12. Known P
M = 16. Estimated P
M = 16. Known P
10
-3
ErrorRate(
10
-4
BitE
Exact P
6
10
-5
Exact P
Estimate P
-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3
10
-6
per-link SNR (dB)

19. BER Performances: Impact of P variation 19p
• The estimation algorithm can still achieve good performance in the case P varies.
-1
10
0
1 good, 7 bad, Estimated
1 good, 7 bad, Known
1 bad, 7 good, Estimated
1 bad 7 good Known
10
0
M = 10, Estimated
M = 10, Known
10
-2
10
1
e(BER)
1 bad, 7 good, Known
1 ll 0 001
10
-2
e(BER)
P ~ uniform distribution
10
-3
tErrorRate
1 small p 0.001
7 large p 0.1
7 small p 0 001
10
-4
tErrorRate
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 0
per-link SNR (dB)
-12 -10 -8 -6 -4 -2 0
10
-6
per-link SNR (dB)

20. 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.
10
0
10
0
10
-2
10
-1
R)
10
-1
FER)
MRC P = 0
10
-3
10
orRate(BE
10
ErrorRate(F
M = 8. Without GI
M = 8 Known
diversity order gain
MRC P 0
10
-5
10
-4
BitErro
M = 8. Without GI
MRC (M = 8, P = 0)
10
-2
FrameE
M = 8. Known
M = 8. Estimated
Capacity Outage
P = 0
Outage
-12 -10 -8 -6 -4 -2
10
-6
10
per-link average SNR (dB)
( , )
M = 8. Estimated P
M = 8. Known P
-10 -8 -6 -4 -2 0 2 4
10
-3
per-link average SNR (dB)
Outage
per link average SNR (dB) per-link average SNR (dB)

21. 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.

22. Predict Error Floor (Identical P) Result 22( )
10
0
10
-1
10
M
2
3
10
-2
rRate
M: 2
2
3
4
10
-4
10
-3
BitError
M: 2
M: 3
M: 4
M: 5
4
5
6
Well
matched
10
-5
M: 6
M: 7
M: 8
M: 16
7
8
-12 -10 -8 -6 -4 -2
10
-6
per-link SNR (dB)
M: 16

23. 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.

24. 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!