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Transcript of Surrey dl 1, 3
Paradigm Shift in Turbo Processingfrom P2P to Network –‐ from P2P to Network –
Slepian Wolf and CEO Problem Viewpoints
Tad Matsumoto* ** and Khoirul Anwar*
Slepian Wolf, and CEO Problem Viewpoints
Tad Matsumoto*, ** and Khoirul Anwar*Information Theory and Signal Processing Lab.
* Japan Advanced Institute of Japan Advanced Institute of Science and Technology (JAIST), Japan
** CWC, University of Oulu, Finland, y ,
April 19, 2013
* This Material to be published in IEEE Trans. on Signal Processing
Preliminaries (1)
Japan experienced huge disaster in March 2011, and still a lot of people are in refugee’s shelter/and still a lot of people are in refugee s shelter/temporary houses.
- Lost lives: 15,854, data effective as of March 8, 201218,183, Sept 30, 2012
- Unfound: 3,203 2,700- Injured: 26,992 6,114
Preliminaries (2)7000 5007000
6000
500
400Tohoku Electric Power Supply
April 7 the next earthquake (M6 0)
5000
300
NTT
ations
Dead of Ele
April 7, the next earthquake (M6.0)Dead Base Stations:NTT DoCoMo: 1200 BTSKDDI (au) : 500 BTSSoftbank : 2200 BTS
4000
3000200
SoftBank Mobile
KDDI (au)ead Ba
se Staectric Pow
er
EMOBILE: 200 BTS
2000
100
KDDI (au)
EMOBILE
De r Supply
1000
0
100
011 12 13 14 15 16
March 201111 12 13 14 15 16 … 1 2 3 4 5 6 7 8 9… 25 26 28 2 6
April 2011 May 2011
Our Networks are Fragile!Our Networks are Fragile! What can we do?
S
Q
S
A
B
P Q
RZ
X
CD
E
Z
T
Lossy Link
E
F
U
VY
Devastated Area Ordinary Areay
Lossless Link
- The key is “Accept Distortion less than Specified” CEO Problem- Very high energy and spectrum efficiencies required.Very high energy and spectrum efficiencies required.-Seek for beyond the P2P Shannon Limit. Achieve the limit of network
as a whole!
Starting Point: System Model+
H11
C1 Π1 D1Π1−1
Π1
Hb1
+‐
1 Π1 D1Π1
IMO
C-M
MSE
H21
H12
1
C2 Π2
MI
FD/S
C
D2Π2−1
H22b2 2 2 D2Π2
Π2 +‐
2
Block at m‐th transmit antenna:
Bl k f ll iBlock from all transmit antennas:
FD/SC MMSE: Frequency Domain Soft Cancellation Minimum Mean Square ErrorFD/SC‐MMSE: Frequency Domain Soft Cancellation Minimum Mean Square Error
6
Multiuser MIMO SC/MMSE/
H11U 1
+Π 10
0
H11
H21C1 Π
1
User 1:
d1 C1-1Π1
−1
MSE
1 ‐
1d̂
10‐1
H22
H12
C2 Π
User 2:
d
MIM
OFD
/SC‐MM
1 d̂10
‐2
ERC2 Π2
d2
C2-1Π2
−1
Π2
+‐
2d
10‐3Av
erage BE
MIMO SC/MMSE jointly decode information from each user
The decoding is performed separately for 10‐4 ?
If sources are correlated
each user.Encoder: NSNRCC 4(17,15) , FFT=512, 2x2
MIMO, Rayleigh 64‐path, Decoder: BCJR Log‐8 6 4 2 0 2 4 6 8
10‐5
7
MAP‐8 ‐6 ‐4 ‐2 0 2 4 6 8
Per‐antenna receive SNR (dB)
T. Matsumoto and K. Anwar ‐MIMO Spatial Turbo Coding with Iterative Equalization
Idea: Vertical Iteration (STC)+
H11Π1
b ˆ
+
‐ ‐
xC1 Π1 D1
Π1−1
SE
H21b b
+‐
x
Π0Π0
MIM
OFD
/SC
-MM
S
Π0−1
H12
C2 Π2
F
D2Π2−1
H22 +
‐
yd
Π2 +‐ ‐
Vertical iteration is expected improve the performance because of space diversity utilization from antenna 1 and 2 and coding gain [Mariela et al., ‘06].
This design is called as Spatial Turbo Code (STC) since the output of second decoder
8
This design is called as Spatial Turbo Code (STC) since the output of second decoder is not multiplexed but transmitted in parallel over the space.
STC vs. Turbo Code
C ΠMUX
Spatial Turbo Code +
C -1Π1−1
Π1‐
Π0
C1 Π1MUX
Π0
C11Π1
MIM
OSC
-MM
SE
Π0−1
+
‐
C2 Π2MUX
FD/
C2-1
Π2−1
+
‐
T b C d
+Π2
‐
C1
C1-1
+DEMUX
‐
Turbo Code
Π0
C1
MUX Π0Π0
−1‐
Π0
9
C2C2
-1+
‐
STC vs. Turbo Code
C ΠMUX
Spatial Turbo Code +
C -1Π1−1
Π1‐
Π0
C1 Π1MUX
Π0
C11Π1
MIM
OSC
-MM
SE
Π0−1
+
‐H=UDVH
C2 Π2MUX
FD/
C2-1
Π2−1
+
‐
T b C d
+Π2
‐
C1
C1-1
+DEMUX
‐
Turbo Code
Π0
C1
MUX Π0Π0
−1‐
Π0
10
C2C2
-1+
‐
Contibution of Vertical Iterations
0.9
1
Vertical Iteration converts CC Turbo0 7
0.8
converts CC TurboStuck point is shifted to the right side.
Convolutional code0.6
0.7
+
C1-1Π1
−1
Π1‐
0.4
0.5
Π0
1
MIM
OD
/SC
-MM
SE
Π0−1
+
‐Turbo code
0.2
0.3
200 channel Realizations
FD
C2-1
Π2−1
+
‐
0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 10
0.1 FFT: 512, SNR=‐3.5dB, Channel: Rayleigh 64‐path, Encoder: SRCC 4(17,15)17
11
+Π2
‐0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Is BER 0 Always Guaranteed?Fact: Conditioning Reduces Entropy
)|()( YXHXH ≥Turbo Feedback works as Conditioning
L),,|(),|()|()( 211 LLYXHLYXHYXHXH ≥≥≥Mutual Information between Transmitted Coded Bit and LLR:
)|()();( LXHXHLXI −=N i i i d t LNow, giving index to L:
)|()();( 11 LXHXHLXI −=
),;(),|()()|()();( 212122 LLXILLXHXHLXHXHLXI =−≤−= ),;(),|()()|()();( 212122 LLXILLXHXHLXHXHLXI ≤
),,;(),,|()()|()();( NNNN LLXILLXHXHLXHXHLXI LL 11 =−≤−=M
This means that:1),;(),;();( 21211 →≤≤≤ NLLLXILLXILXI LL
if0),,|( 1 →NLLXH L
BER Performance of STC
Parameters:100
500 channel realizations
Transmitter:Encoder: SRCC 4(17 15) 17
10-1
4(17,15),17Interleaver=1024 (random)10-2
BER
Channel:MIMO 2x2Equal Power 64-10-3Av
erag
e B
w/o verticaliteration
w/ verticaliteration
2x2 Equal Power 64path
Receiver:10-4
iteration2 MIM
O AW
GN 5 Gain: 6dB
Decoder: BCJR Log-MAPFFT=512
10-5
N Capacity/dim
(H1V5)
13
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 710
Average Per-Antenna SNR [dB]
m
How to Model Correlated Sources?
peP == )1(Bit flipping e
Π1+
peP −== 1)0(
C1 Π1 C1‐1Π1−1
Π1
XX
‐
R1 τ
Π0
1
MO
‐MMSE
Π0−1
‐
d
fc
MI
FD/SC ‐
C 1
e
‐
mod
fc
C2 C2‐1Π2−1
Π2
Π2Π0
‐+
R2eXY ⊕=
Probability Update (fc)
Joint Decoding+
)0()1()1()1P(x)1()0()1(0)P(x
=+=−===+=−==
xpPxPpxpPxPp
oo
oo
How to estimate p at the receiver?
Probability Update (fc)
K1
14
{ }∑=
==+===K
kkokokoko yPxPyPxP
Kp
110011 )()()()(ˆ
L
L
update peppeplnLLR
+−+−
=)()(
11
Slepian‐Wolf TheorempD
R
C1X RX
SC2Y
Correlated Joint Dec.
X~
R
Relay
RY
C2Y RY
Slepian‐Wolf Theorem:
H(Y)RX > H(X|Y)
( | )H(Y) RY > H(Y|X)RX+RY > H(X,Y)
RX
H(Y|X) RX+RY=H(X,Y)
15
XH(X|Y) H(X)
Effect of Weak Correlation
Π +0 9
1SNR= -3.5dB
C1‐1Π1
−1
Π1
X
‐
0.8
0.9 Interleaver=1024SRCC-4 (17,15)Iterations=5x
Π0
MIM
OSC
‐MMSE
Π0−1
‐fc
0.6
0.7
MFD
/S
C2‐1Π2−1
‐fc
0.4
0.5
2
Π2Joint Decoding
‐+
0.2
0.3
0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 10
0.1
L
L
update peppeplnLLR
+−+−
=)()(
11
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
16
pep +)(1
STC‐SW: BER PerformanceParameters:10
0
200 channels realizations
Transmitter:Encoder: CC 4(17,15),17Interleaver 1024
10‐1
Interleaver=1024 (random)Correlation Model: Bit-flipping
10‐2
BER
pp g
Channel:MIMO 2x2Equal Power 64
10‐3Av
erage B
M Equal Power 64-path
Receiver:10‐4
MIM
O 2x2 C
Decoder: BCJR Log-MAPFFT=512
10‐5
p=0
Capacity
17
‐6 ‐4 ‐2 0 2 4 6 810
SNR (dB)
SW with Doped Accumulatorp
H Π1+L 0
a1;EQL a1;EQH11
C1 Π1 D1Π1
−1
‐
ΜP DA-1
0bê1
x x0 x00
τs1 1
Q +
M-1H12 +
‐Correlation
D-ACC
ú(p)0
L 0e1;EQ
s1 L e1;EQ
Π0
ultiu
ser
EH21e
Π0
Mu
D2Π2−1
H22 +‐
C2 Π2 P
D ACC
DA-1
L 0e2;EQy00y y0
Μs2
L e2;EQ
Π2 +‐
D-ACC
L 0a2;EQ
L a2;EQ
1818T. Matsumoto and K. Anwar ‐MIMO Spatial Turbo Coding with Iterative Equalization
Partial/Doped Accumulatorp
U
CU
UUUCUUUC UUU_UUU_
U: UncodedC: Coded _ _ _ C _ _ _ CPA PA-1
(a) (c)
UUUUUUUU UUU0UUU0U U U U U U U U
(a)
_ _ _ 0 _ _ _ 0PA0U U U C U U U C
(b) (d)
19
19
Problem of p and its Solution (SRCC)
0 9
1SNR= -3.5dBI t l 1024
Parameters:
0 7
0.8
0.9 Interleaver=1024SRCC-4 (17,15)Iterations=5x with PAcc, P=16
Transmitter:Encoder: CC 4(17,15),17
0.6
0.7( )
Interleaver=5000 (random)Correlation Model: Bit flipping
0.4
0.5 Bit-flipping
Channel:MIMO 2x2
0.2
0.3 Equal Power 64-path
Receiver:
0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 10
0.1Receiver:
Decoder: BCJR Log-MAPFFT=5120 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
20
STC‐SW: with PAcc
100
200 channels realizationsParameters:
10‐1
200 channels realizations
Transmitter:Encoder: CC 4(17,15),17
10‐2
ER
Interleaver=1024 (random)Correlation Model: Bit flipping
10‐3
Average BE Bit‐flipping
Channel:MIMO 2x2
10‐4
10A p=0.01
Equal Power 64‐path
Receiver:Decoder: BCJR Log‐
10‐5
10 Decoder: BCJR Log‐MAPFFT=512
21
‐6 ‐4 ‐2 0 2 4 6 810
SNR (dB)T. Matsumoto and K. Anwar ‐MIMO Spatial Turbo Coding with Iterative Equalization
SpCC‐SW: Freq. Selective Fading MIMO 2x2p q g010
Parameters:
10-1
p = 0.49T = 3
Transmitter:Encoder: CC 4(17,15)Interleaver=10000
10-2
BER
T 3
p = 0.30T = 3
p = 0.10T = 3
(random)Correlation Model: Bit‐flipping
10-3
Aver
age
B 3p = 0.01T = 6 Channel:
MIMO 2x2Equal Power 64‐path
10-4
Interleaver: 5120
known punknown p
p = 0.00T = 6
64-path FadingReceiver:
Decoder: BCJR Log‐MAP
10-5
Interleaver: 5120NSNRCC-4 (17,15)Iteration: 50(H1V5)
MAPFFT=512
-5 -4 -3 -2 -1 010
Average SNR (dB)22