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Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping of High-Order QAMfor Optical Fiber Systems
Tobias Fehenberger
Institute for Communications EngineeringTechnical University of Munich
Joint work with Domanic Lavery, Robert Maher, Alex Alvarado, Polina BayvelOptical Networks Group, University College London (UCL)
Munich Workshop on Information Theory of Optical Fiber
December 8, 2015
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 1/14
Institute for Communications Engineering Technical University of Munich
Motivation• Higher spectral efficiencies for increased data rates
• Practical limitations:
• transmit power• transceiver SNR• modulation order
• Potential solution: probabilistic constellation shaping
• Shaping gives sensitivity gain of up to 1.53 dB
• Shaping has low complexity
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 2/14
Institute for Communications Engineering Technical University of Munich
Outline
1 Probabilistic Shaping Method
2 B2B Experiments
3 Fiber Simulations
4 Mismatched Probabilistic Shaping
5 Conclusion
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 3/14
Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping Method1
Communication system with uniform QAM
FECEncoder
QAMMapping
ChannelQAM
DemappingFEC
Decoder
SSMF
OpticalTx
OpticalRx
EDFA
1Bocherer et al., IEEE Trans. Comm., 2015
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 4/14
Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping Method1
Communication system with uniform QAM
FECEncoder
QAMMapping
ChannelQAM
DemappingFEC
Decoder
SSMF
OpticalTx
OpticalRx
EDFA
1Bocherer et al., IEEE Trans. Comm., 2015
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 4/14
Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping Method1
Communication system with shaped QAM
DistributionMatcher2
FECEncoder
QAMMapping
ChannelQAM
DemappingFEC
DecoderDistributionDematcher
SSMF
OpticalTx
OpticalRx
EDFA
• Low-complexity distribution matcher2 added “outside” FEC
• Very minor modifications to FEC encoder/decoder required
1Bocherer et al., IEEE Trans. Comm., 20152Schulte and Bocherer, IEEE Trans. Inf. Theory, 2015
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 4/14
Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping Method (cont’d)• Probability mass function (PMF) of channel input X :
P∆X (xi ) ∼ e−ν|xi |2,
where ∆ and ν are scalars.• Optimization problem for each SNR: choose ∆ and ν so that
mutual information is maximized⇒ One PMF per SNR
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping Method (cont’d)• Probability mass function (PMF) of channel input X :
P∆X (xi ) ∼ e−ν|xi |2,
where ∆ and ν are scalars.• Optimization problem for each SNR: choose ∆ and ν so that
mutual information is maximized⇒ One PMF per SNR
−10
1
−10
1
0
1/16
1/8
PX
16QAM uniform
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping Method (cont’d)• Probability mass function (PMF) of channel input X :
P∆X (xi ) ∼ e−ν|xi |2,
where ∆ and ν are scalars.• Optimization problem for each SNR: choose ∆ and ν so that
mutual information is maximized⇒ One PMF per SNR
−10
1
−10
1
0
1/16
1/8
PX
16QAM shaped for 10 dB SNR
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping Method (cont’d)• Probability mass function (PMF) of channel input X :
P∆X (xi ) ∼ e−ν|xi |2,
where ∆ and ν are scalars.• Optimization problem for each SNR: choose ∆ and ν so that
mutual information is maximized⇒ One PMF per SNR
−10
1
−10
1
0
1/16
1/8
PX
16QAM shaped for 5 dB SNR
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
Institute for Communications Engineering Technical University of Munich
Probabilistic Shaping Method (cont’d)• Probability mass function (PMF) of channel input X :
P∆X (xi ) ∼ e−ν|xi |2,
where ∆ and ν are scalars.• Optimization problem for each SNR: choose ∆ and ν so that
mutual information is maximized⇒ One PMF per SNR
−10
1
−10
1
0
1/16
1/8
PX
16QAM uniform
16QAM shaped for 5 dB SNR
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
Institute for Communications Engineering Technical University of Munich
B2B Experiments: Setup
ECL
1.1 kHz
IQ Mod
EDFA
PolMux
LPF LPF
Linear
Amplifiers
DACFPGADSP
Digital
CoherentReceiver
ECL
1.5 kHz
ASE
Receiver
Po
l.D
iver
seC
oh
eren
tR
ecei
ver
AD
C
De-
Ske
wan
dN
orm
aliz
atio
n
Mat
ched
RR
CF
ilter
ing
CM
AP
re-E
Q
Blin
dQ
AM
RD
E
CP
Ean
dG
SO
P
AIR
Est
imat
ion
LO
Sig
Filt
erT
aps
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 6/14
Institute for Communications Engineering Technical University of Munich
B2B Experiments: Results
2 3 4 5 6 7 8 9 10 11 124
6
8
10
12
Eb/N0 [dB]
AIR
[bit/4D-sym
]
Shannon capacity
16QAM uniform
64QAM uniform
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
Institute for Communications Engineering Technical University of Munich
B2B Experiments: Results
2 3 4 5 6 7 8 9 10 11 124
6
8
10
12
Eb/N0 [dB]
AIR
[bit/4D-sym
]
Shannon capacity
16QAM uniform
64QAM uniform
16QAM shaped
64QAM shaped
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
Institute for Communications Engineering Technical University of Munich
B2B Experiments: Results
2 3 4 5 6 7 8 9 10 11 124
6
8
10
12
16QAM gain:0.43 dB
Eb/N0 [dB]
AIR
[bit/4D-sym
]
Shannon capacity
16QAM uniform
64QAM uniform
16QAM shaped
64QAM shaped
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
Institute for Communications Engineering Technical University of Munich
B2B Experiments: Results
2 3 4 5 6 7 8 9 10 11 124
6
8
10
12
16QAM gain:0.43 dB
64QAM gain: 0.8 dB
Eb/N0 [dB]
AIR
[bit/4D-sym
]
Shannon capacity
16QAM uniform
64QAM uniform
16QAM shaped
64QAM shaped
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
Institute for Communications Engineering Technical University of Munich
B2B Experiments: Results
2 3 4 5 6 7 8 9 10 11 124
6
8
10
12
16QAM gain:0.43 dB
64QAM gain: 0.8 dB
Eb/N0 [dB]
AIR
[bit/4D-sym
]
Shannon capacity
16QAM uniform
64QAM uniform
16QAM shaped
64QAM shaped
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
Institute for Communications Engineering Technical University of Munich
Experimental Results: B2B (cont’d)
0 5 10 15 20 250
0.2
0.4
0.6
0.8
SNR [dB]
Sensitivity
gain[dB]
16QAM
64QAM
AWGN ref.
• Significant gain over uniform
• Gains present over wideSNR range
• Good match with AWGNreference
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 8/14
Institute for Communications Engineering Technical University of Munich
Fiber Simulations
−6 −4 −2 0 29
9.5
10
10.5
11
Launch power per channel [dBm]
AIR
[bit/4D-sym
]
Uniform Input + EDC
• DP-64QAM @ 28 GBaud
• RRC pulse shaping
• 9 WDM channels
• WDM spacing: 30 GHz
• 1000 km SMF w/ EDFAs
• EDC only
• Uniform input
AIR (at opt. power)
10.5 bit/4D-sym
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 9/14
Institute for Communications Engineering Technical University of Munich
Fiber Simulations
−6 −4 −2 0 29
9.5
10
10.5
11
Launch power per channel [dBm]
AIR
[bit/4D-sym
]
Shaped Input + EDC
Uniform Input + EDC
• DP-64QAM @ 28 GBaud
• RRC pulse shaping
• 9 WDM channels
• WDM spacing: 30 GHz
• 1000 km SMF w/ EDFAs
• EDC only
• Shaped Input
Shaping Gain
0.23 bit/4D-sym
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 9/14
Institute for Communications Engineering Technical University of Munich
Fiber Simulations
−6 −4 −2 0 29
9.5
10
10.5
11
Launch power per channel [dBm]
AIR
[bit/4D-sym
]
Uniform Input + DBP
Shaped Input + EDC
Uniform Input + EDC
• DP-64QAM @ 28 GBaud
• RRC pulse shaping
• 9 WDM channels
• WDM spacing: 30 GHz
• 1000 km SMF w/ EDFAs
• Ideal single-channel DBP
• Uniform input
DBP Gain
0.21 bit/4D-sym
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 9/14
Institute for Communications Engineering Technical University of Munich
Fiber Simulations
−6 −4 −2 0 29
9.5
10
10.5
11
Launch power per channel [dBm]
AIR
[bit/4D-sym
]
Shaped Input + DBP
Uniform Input + DBP
Shaped Input + EDC
Uniform Input + EDC
• DP-64QAM @ 28 GBaud
• RRC pulse shaping
• 9 WDM channels
• WDM spacing: 30 GHz
• 1000 km SMF w/ EDFAs
• Ideal single-channel DBP
• Shaped Input
DBP + Shaping Gain
0.41 bit/4D-sym
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 9/14
Institute for Communications Engineering Technical University of Munich
Mismatched Probabilistic Shaping
• Ideally: One shaped input PMF for every SNR
• In reality: fluctuations of channel SNR after DSP
⇒ Mismatch between shaping SNR at TX and channel SNR
• We observed a robustness against such a mismatch
• Figure of merit: penalty in sensitivity gain from usingmismatched shaping instead of perfectly matched shaping
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 10/14
Institute for Communications Engineering Technical University of Munich
Mismatched Shaping: 64QAM over AWGN
5 10 15 20 255
10
15
20
25
Shaping SNR [dB]
Chan
nel
SNR
[dB]
• Green:penalty ≤ 0.1 dB
• Green+Blue:penalty ≤ 0.2 dB
• Green+Blue+Red:penalty ≤ 0.3 dB
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 11/14
Institute for Communications Engineering Technical University of Munich
Mismatched Shaping: 64QAM over AWGN
5 10 15 20 255
10
15
20
25
Shaping SNR [dB]
Chan
nel
SNR
[dB]
• Green:penalty ≤ 0.1 dB
• Green+Blue:penalty ≤ 0.2 dB
• Green+Blue+Red:penalty ≤ 0.3 dB
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 11/14
Institute for Communications Engineering Technical University of Munich
Mismatched Shaping: 64QAM over AWGN
5 10 15 20 255
10
15
20
25
Shaping SNR [dB]
Chan
nel
SNR
[dB]
• Green:penalty ≤ 0.1 dB
• Green+Blue:penalty ≤ 0.2 dB
• Green+Blue+Red:penalty ≤ 0.3 dB
Takeaway
Shaping is robust forAWGN channel
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 11/14
Institute for Communications Engineering Technical University of Munich
Mismatched Shaping: Fiber Simulations
−3 −2 −1 0 1 2 30
0.1
0.2
SNR mismatch [dB]
AIR
Gain[bit/4D-sym
]
• DP-64QAM @ 28 GBaud
• RRC pulse shaping
• 9 WDM channels
• WDM spacing: 30 GHz
• 1000 km SMF w/ EDFAs
• Opt. launch power (-1 dBm)
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 12/14
Institute for Communications Engineering Technical University of Munich
Mismatched Shaping: Fiber Simulations
−3 −2 −1 0 1 2 30
0.1
0.2
SNR mismatch [dB]
AIR
Gain[bit/4D-sym
]
• DP-64QAM @ 28 GBaud
• RRC pulse shaping
• 9 WDM channels
• WDM spacing: 30 GHz
• 1000 km SMF w/ EDFAs
• Opt. launch power (-1 dBm)
Takeaway
Shaping is robust fornonlinear fiber channel
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 12/14
Institute for Communications Engineering Technical University of Munich
Conclusion
• Experimental demonstration of 0.8 dB sensitivity gain byprobabilistic shaping
• Fiber simulations show gains of 0.23 bit/4D-sym by shaping(comparable to ideal single-channel DBP)
• Combine DBP and shaping
• Mismatched shaping: one or two input PMFs are sufficient
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 13/14
Institute for Communications Engineering Technical University of Munich
Thank you.
ReferencesI T. Fehenberger, G. Bocherer, A. Alvarado, and N. Hanik, “LDPC coded modulation with probabilistic shaping
for optical fiber systems,” in Proc. Optical Fiber Communication Conference (OFC), Paper Th.2.A.23, Mar.2015.
I G. Bocherer, P. Schulte, and F. Steiner, “Bandwidth efficient and rate-matched low-density parity-check codedmodulation,” IEEE Trans. Commun., Oct. 2015.
I P. Schulte and G. Bocherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory, Nov.2015.
I T. Fehenberger, D. Lavery, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik,“Sensitivity gains by mismatchedprobabilistic shaping for optical communication systems,” http://arxiv.org/abs/1510.03565v2, 2015.
I F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration ofcapacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proc. European Conference andExhibition on Optical Communication (ECOC), Paper PDP.3.4, Sep. 2015.
Tobias Fehenberger — Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 14/14