constellation shaping for bit-interleaved coded...
TRANSCRIPT
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Constellation Shaping for Bit-Interleaved Coded APSK
Dr. Matthew C. Valenti, Xingyu Xiang
Lane Department of Computer Science and Electrical EngineeringWest Virginia University
ICC - June 6, 2011
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 1 / 25
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Outline
1 Introduction
2 Constellation Shaping
3 Optimization Results
4 Implementation
5 Conclusion
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 2 / 25
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Introduction
Outline
1 Introduction
2 Constellation Shaping
3 Optimization Results
4 Implementation
5 Conclusion
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 3 / 25
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Introduction
Two Definitions
Constellation Shaping
Idea: transmit constellation signal points with lower energy morefrequently than those with higher energy
Goal: save transmit power, or achieve performance gain under thesame transmit power
How: we use non-linear short length shaping code in our paper
APSK (Amplitude phase-shift keying)
Included in DVB-S2 (second generation of the Digital VideoBroadcasting Satellite) and other communication standards
both spectral and energy efficient, well suited for nonlinear channels
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 4 / 25
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Introduction
Background
Information–theoretic Optimization Practical Implementation
“System implementation” ‐‐‐‐‐‐‐
Stephane Y. Le Goff, et al. in
“Modulation Optimization”‐‐‐‐‐‐‐‐
R D G d i K Li li i Stephane Y. Le Goff, et al. in reference [5, 6]R. D. Gaudenzi, K. Liolis in reference [2], [3], respectively
J i t ti i ti d t l t i l ti
Our work
Joint optimization and actual system simulation
‐‐‐‐‐‐‐‐ICC 2011
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 5 / 25
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Introduction
General flowchart
System with Optimum parametersconstellation shaping
(non‐uniform APSK modulation)
Capacity Analysis
Optimum parameters
modulation) Simulation Results
comparison
Performance Gain(Shaping gain)
Capacity A l i
System with uniform APSK
comparison ( p g g )
Analysismodulation
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 6 / 25
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Introduction
Mutual Information( MI ) and Channel Capacity
MI between two random variables, X and Y is given by,
I(X;Y ) = E
[log
(p(Y |X)p(Y )
)]Channel Capacity is the highest rate at which information can betransmitted over the channel with low error probability. Given thechannel and the receiver, capacity is defined as
C = maxp(x)
I(X;Y )
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 7 / 25
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Introduction
The mutual information between output Y and input X is
I(X;Y ) =
M−1∑j=0
p(xj)
∫p(y|xj) log2
p(y|xj)p(y)
dy.
M - number of input symbols.The integration can be solved using Gauss - Hermite Quadratures inAWGN channel.
-10 -5 0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
SNR(dB)
Info
rmat
ion
Rat
e
Information rate results of uniform 32-APSK modulationgenerated by two methodologies
By Monte-Carlo SimulationBy Gauss - Hermite Quadratures
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 8 / 25
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Constellation Shaping
Outline
1 Introduction
2 Constellation Shaping
3 Optimization Results
4 Implementation
5 Conclusion
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 9 / 25
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Constellation Shaping
Constellation Shaping for APSK
Our strategy is from S. LeGoff, IEEE T. Wireless, 2007.
Use shaping code to choose low-energy symbols more frequently
For a fixed average energy, shaping strategy spreads out the symbols
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
(a) 16apsk
-2 -1 0 1 2-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
(b) 32apsk
( Es = ΣM−1i=0 p(xi)Ei = 1)
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Constellation Shaping
Shaping Encoder
We design the shaping encoder to output more zeros than ones. Oneexample is,
Table: (5,3) shaping code.
3 input data bits 5 output codeword bits0 0 0 0 0 0 0 00 0 1 0 0 0 0 10 1 0 0 0 0 1 00 1 1 0 0 1 0 01 0 0 0 1 0 0 01 0 1 1 0 0 0 01 1 0 0 0 0 1 11 1 1 1 0 1 0 0
p0: the probability of 0 in the codeword table, (p0 =3140 above)
p1: the probability of 1 in the codeword table, (p1 =940 above)
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 11 / 25
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Constellation Shaping
16/32 APSK symbol-labeling map based on DVB-S2standard
B2
00111(1011)
00101(1010)
10000(0100) B1
B2
B1
00001(1000) B2
00110(0011)
10001(1100)
B3
01110
C2
11110B
301010
D11011
D11001
D11101
C2
11000 B
301000
D11111
C3
01101
C2
11100
10110(0111)
B3
01100
10111(1111)
A
10010(0101)
00010(0001)
B1
B1
10100(0110)
A
B2AA
00000(0000)
C3
01001
C1
C1
C1
C2
11010
00011(1001)
C1
10011(1101)
C3
01011
00100(0010)
C3
01111
10101(1110)
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Constellation Shaping
Shaping Operation
Channel101011101101 100101100110000100Channel Encoder
101011101101Bit Separation
1100
1100
1001
10000
110
ENC
00
0bitrd3
1
0101
bitnd20 0
00
0bitst1
0
0bit (MSB)th0
0
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 13 / 25
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Constellation Shaping
32-APSK results with continuous output optimized over p0
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0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Es/No (dB)
mut
ual i
nfor
mat
ion
32APSK in AWGN
Uniformg=1g=2g=3
11.4 11.6 11.8 123.83
3.84
3.85
3.86
3.87
3.88
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 14 / 25
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Optimization Results
Outline
1 Introduction
2 Constellation Shaping
3 Optimization Results
4 Implementation
5 Conclusion
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 15 / 25
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Optimization Results
Algorithm used for jointly optimization
p0
γg
Capacity Results Comparison
Optimized parameters
1 Fix the SNR, radius ratios γ,number of shaping bits(g).
2 Vary p0 from 0.5 to 0.99 inincrements of 0.005.
3 For each value of p0, compute thecorresponding information rate.
4 Go over the information rate arrayand find the highest informationrate, record the values of p0 andγ, g that produce it.
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 16 / 25
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Optimization Results
Shaping Gain and its evaluation
0 1 2 3 4 5-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Information Rate
Shap
ing
Gai
n (d
B)
32-APSK shaping gain with different shaping bits
g=1g=2g=3
(3.99, 0.3077)
(4.1, 0.175)
(3.88, 0.2648)
-10 0 10 20 300
1
2
3
4
5
Es/No (dB)m
utua
l inf
orm
atio
n
11.211.411.611.8 12
3.8
3.9
4
uniformshaping g=1
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 17 / 25
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Optimization Results
optimum p0 and γ
-10 -5 0 5 10 15 20 25 30
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Es/No
optim
al p
0
Optimal p0 of 32APSK in AWGN channel
Uniformg=1g=2g=3
(a) optimal p0 of 32APSK
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1.5
2
2.5
3
3.5
4
4.5
5
Es/Noop
timal
in
dex
Optimal index of 32APSK in AWGN channel
Uniformg=1g=2g=3
(b) optimal γ index of 32APSK
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 18 / 25
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Implementation
Outline
1 Introduction
2 Constellation Shaping
3 Optimization Results
4 Implementation
5 Conclusion
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 19 / 25
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Implementation
Implementation
BICM-ID (bit-interleaved coded-modulation with iterative decoding)System
f iInformation sequence
Turbo BitShaping EncoderTurbo
EncoderBit
SeparatorEncoder Modulator
Channel
b
Estimated bit probabilities
Shaping
DemodulatorTurbo DecoderBit
SeparatorDecoder
feedback‐1
FeedbackInformation
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 20 / 25
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Implementation
Optimum Parameters
Maximum shaping gain achieved in AWGN for M-APSK with g shapingbits. The optimized p0 and γ are shown. The related information rate andSNR value(in dB) are also listed.
M g R Eb/N0 (capacity value) gain p0 γ
161 3.09 4.714 dB 0.091 dB 0.623 2.702 2.95 4.077 dB 0.322 dB 0.688 2.57
321 3.88 5.915 dB 0.265 dB 0.716 {2.64,4.64}2 4.06 6.517 dB 0.175 dB 0.623 {2.53,4.30}3 3.89 5.898 dB 0.310 dB 0.656 {2.53,4.30}
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 21 / 25
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Implementation
BER Curves
Parameters used for the 32-APSK simulation
γ R Rc Rs Eb/N0 (capacity value){2.64,4.64} 3.849 5000/6491 1 6.092 dB3.858 5000/6190 7/9 5.834 dB
BER curves of 32-APSK in AWGN at rate R=3.85 bits/symbol
5 5.5 6 6.5 7 7.5 8 8.5 910 5
10 4
10 3
10 2
10 1
100
Eb/N0 in dB
BER
Uniform BICMUniform BICM IDBICM ID w/ ShapingBICM w/ Shaping
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 22 / 25
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Conclusion
Outline
1 Introduction
2 Constellation Shaping
3 Optimization Results
4 Implementation
5 Conclusion
Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 23 / 25
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Conclusion
Conclusion
The simple constellation-shaping strategy considered in this paper canachieve shaping gains of about 0.6 dB.
This work can be further extended to include LDPC code, which willmake the system fully compatible with DVB-S2 standard
Extrinsic information transfer chart (EXIT chart) can be used tooptimize the parameter of the error correction code
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Conclusion Questions
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IntroductionConstellation ShapingOptimization ResultsImplementationConclusionQuestions