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!