Frank Schreckenbach, Munich University of Technology NEWCOM 2005 Analysis and Design of Mappings for Iterative Decoding of Bit-Interleaved Coded Modulation* Frank Schreckenbach Institute for Communications Engineering Munich University of Technology, Germany Norbert Görtz School of Engineering and Electronics, University of Edinbrugh, UK * This work was supported by NEWCOM and DoCoMo Communications Laboratories Europe GmbH
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Analysis and Design of Mappings for Iterative Decoding of Bit-Interleaved Coded Modulation*
Analysis and Design of Mappings for Iterative Decoding of Bit-Interleaved Coded Modulation*. Frank Schreckenbach Institute for Communications Engineering Munich University of Technology, Germany. Norbert Görtz School of Engineering and Electronics, University of Edinbrugh, UK. - PowerPoint PPT Presentation
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Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Analysis and Design of Mappings for Iterative Decoding of
Bit-Interleaved Coded Modulation*
Frank SchreckenbachInstitute for Communications Engineering
Munich University of Technology, Germany
Norbert GörtzSchool of Engineering and Electronics,
University of Edinbrugh, UK
* This work was supported by NEWCOM and DoCoMo Communications Laboratories Europe GmbH
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
System model: BICM and BICM-ID
Encoder Interleaver
DecoderDe-
interleaver
data
data estimate
c Mapper
DemapperDetector/ Equalizer
Le(C)
InterleaverLa(C)
ChannelCode: Convolutional, Turbo, LDPC
e.g. QPSK, 16QAM
AWGN, OFDM, ISI, MIMO
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Outline
• Consider mapping as coding entity: characterization with Euclidean distance spectrum EXIT charts
• Optimization of mapping: Quadratic Assignment Problem (QAP) Binary Switching Algorithm
• Future work - Open problems
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Euclidean distance spectrum
Distance
Frequency λ1 λ2
Gray
Anti Gray
QPSK, no a priori information at the demapper.
1101
1000
1101
1000
1001
1100
1001
1100
Gray
Anti-Gray
1st bit 2nd bit
1 2d 2 2d
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Euclidean distance spectrum
Distance
Frequency λ1 λ2
Gray 4Anti Gray
QPSK, no a priori information at the demapper.
1101
1000
1101
1000
1001
1100
1001
1100
Gray
Anti-Gray
1st bit 2nd bit
1 2d 2 2d
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Euclidean distance spectrum
Distance
Frequency λ1 λ2
Gray 4 4Anti Gray
QPSK, no a priori information at the demapper.
1101
1000
1101
1000
1001
1100
1001
1100
Gray
Anti-Gray
1st bit 2nd bit
1 2d 2 2d
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Euclidean distance spectrum
Distance
Frequency λ1 λ2
Gray 4 4
Anti Gray 6
QPSK, no a priori information at the demapper.
1101
1000
1101
1000
1001
1100
1001
1100
Gray
Anti-Gray
1st bit 2nd bit
1 2d 2 2d
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Euclidean distance spectrum
Distance
Frequency λ1 λ2
Gray 4 4
Anti Gray 6 2
QPSK, no a priori information at the demapper.
1101
1000
1101
1000
1001
1100
1001
1100
Gray
Anti-Gray
1st bit 2nd bit
1 2d 2 2d
Note that without a priori information, the distances d2 might not be relevant. An expurgated distance spectrum would be more precise.
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Euclidean distance spectrum
Distance
Frequency λ1 λ2
Gray 4 4
Anti Gray 6 2
QPSK, no a priori information at the demapper.
1 2d 2 2d
Distance
Frequency λ1 λ2
Gray
Anti Gray
1 2d 2 2d
QPSK, ideal a priori information at the demapper : signal constellation is reduced to a symbol pair.
1101
1000
1101
1000
1001
1100
1001
1100
Gray
Anti-Gray
1st bit 2nd bit
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Euclidean distance spectrum
Distance
Frequency λ1 λ2
Gray 4 4
Anti Gray 6 2
QPSK, no a priori information at the demapper.
1 2d 2 2d
Distance
Frequency λ1 λ2
Gray 4 0Anti Gray
1 2d 2 2d
QPSK, ideal a priori information at the demapper : signal constellation is reduced to a symbol pair.
1101
1000
1101
1000
1001
1100
1001
1100
Gray
Anti-Gray
1st bit 2nd bit
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Euclidean distance spectrum
Distance
Frequency λ1 λ2
Gray 4 4
Anti Gray 6 2
QPSK, no a priori information at the demapper.
1 2d 2 2d
Distance
Frequency λ1 λ2
Gray 4 0
Anti Gray 2 2
1 2d 2 2d
QPSK, ideal a priori information at the demapper : signal constellation is reduced to a symbol pair.
1101
1000
1101
1000
1001
1100
1001
1100
Gray
Anti-Gray
1st bit 2nd bit
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
EXIT chart QPSK
Average mutual information between coded bits C at the transmitter and LLRs L at the receiver:
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
mutual information at input of demapper
mut
ual i
nfor
mat
ion
at o
utpu
t of d
emap
per
4-state conv. code
Gray
QPSK, AWGN channel
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
EXIT chart QPSK
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
mutual information at input of demapper
mut
ual i
nfor
mat
ion
at o
utpu
t of d
emap
per
4-state conv. code
GrayAnti-Gray
QPSK, AWGN channel
Average mutual information between coded bits C at the transmitter and LLRs L at the receiver:
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Bit-wise EXIT chart QPSK
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
mutual information at input of demapper
mut
ual i
nfor
mat
ion
at o
utpu
t of d
emap
per
4-state conv. code
Anti-Gray
Anti-Gray,bit 1 Anti-Gray,
bit 2
Compare to multilevel codes!
QPSK, AWGN channel
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Analytic EXIT chart QPSK
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
mutual information at input of demapper
mut
ual i
nfor
mat
ion
at o
utpu
t of d
emap
per
simulationanalytic+numeric
4-state conv. code
Gray
Anti-Gray
Anti-Gray,bit 1 Anti-Gray,
bit 2
Analytic and numeric computation with BEC a priori information.
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Bit Interleaved Coded Irregular Modulation (BICIM)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
mutual information at input of demapper
mut
ual i
nfor
mat
ion
at o
utpu
t of d
emap
per
QPSK16QAM50% QPSK, 50% 16QAM
4-state, rate 1/2 convolutional code
• Within one code block, use different signal constellations: fine adaptation of data rate to channel
characteristics with the modulation mappings: optimization of iterative decoding procedure
• Basic idea similar to irregular channel codes
• Low complexity, good performance with low and medium code rates
• EXIT chart: linear combination of EXIT functions.
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Optimization of mapping
• Goal: find optimal assignment of binary indexes to signal points.• Optimization for:
• No a priori information at the demapper (Gray mapping)• Ideal a priori information at the demapper• Trade off no/ideal a priori• Optimization for bit positions
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Optimization of mapping
• Goal: find optimal assignment of binary indexes to signal points.• Optimization for:
• No a priori information at the demapper (Gray mapping)• Ideal a priori information at the demapper• Trade off no/ideal a priori• Optimization for bit positions
• Exhaustive search intractable for high order signal constellations: 2m! possible mappings. 16QAM: 2·1013 possible mappings
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
Optimization of mapping
• Goal: find optimal assignment of binary indexes to signal points.• Optimization for:
• No a priori information at the demapper (Gray mapping)• Ideal a priori information at the demapper• Trade off no/ideal a priori• Optimization for bit positions
• Exhaustive search intractable for high order signal constellations: 2m! possible mappings. 16QAM: 2·1013 possible mappings
• Problem can be cast to a Quadratic Assignment Problem (QAP, Koopmans and Beckmann, 1957)• QAP is NP-hard, i.e. not solvable in polynomial time.• Famous applications are e.g. wirering in electronics or
assignment of facilities to locations.
Frank Schreckenbach, Munich University of TechnologyNEWCOM 2005
QAP Algorithms
• Binary Switching Algorithm (Zeger, 1990): try to switch the symbol with highest costs, i.e. the strongest contribution to a bad performance, with an other symbol such that the total cost is minimized.