probabilistic shaping of high-order qam for optical fiber ... · probabilistic shaping of...

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


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



Outline

1 Probabilistic Shaping Method

2 B2B Experiments

3 Fiber Simulations

4 Mismatched Probabilistic Shaping

5 Conclusion



Probabilistic Shaping Method1

Communication system with uniform QAM

FECEncoder

QAMMapping

ChannelQAM

DemappingFEC

Decoder

SSMF

OpticalTx

OpticalRx

EDFA

1Bocherer et al., IEEE Trans. Comm., 2015



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



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




P∆X (xi ) ∼ e−ν|xi |2,



−10

1

−10

1

0

1/16

1/8

PX

16QAM uniform




P∆X (xi ) ∼ e−ν|xi |2,



−10

1

−10

1

0

1/16

1/8

PX

16QAM shaped for 10 dB SNR




P∆X (xi ) ∼ e−ν|xi |2,



−10

1

−10

1

0

1/16

1/8

PX





P∆X (xi ) ∼ e−ν|xi |2,



−10

1

−10

1

0

1/16

1/8

PX

16QAM uniform




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



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




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




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




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



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



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



Fiber Simulations

−6 −4 −2 0 29

9.5

10

10.5

11


AIR

[bit/4D-sym

]

Shaped Input + EDC

Uniform Input + EDC



• 9 WDM channels



• EDC only

• Shaped Input

Shaping Gain

0.23 bit/4D-sym



Fiber Simulations

−6 −4 −2 0 29

9.5

10

10.5

11


AIR

[bit/4D-sym

]

Uniform Input + DBP

Shaped Input + EDC

Uniform Input + EDC



• 9 WDM channels



• Ideal single-channel DBP

• Uniform input

DBP Gain

0.21 bit/4D-sym



Fiber Simulations

−6 −4 −2 0 29

9.5

10

10.5

11


AIR

[bit/4D-sym

]

Shaped Input + DBP

Uniform Input + DBP

Shaped Input + EDC

Uniform Input + EDC



• 9 WDM channels



• Ideal single-channel DBP

• Shaped Input

DBP + Shaping Gain

0.41 bit/4D-sym



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



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



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



Mismatched Shaping: Fiber Simulations

−3 −2 −1 0 1 2 30

0.1

0.2

SNR mismatch [dB]

AIR

Gain[bit/4D-sym

]



• 9 WDM channels



• Opt. launch power (-1 dBm)



Mismatched Shaping: Fiber Simulations

−3 −2 −1 0 1 2 30

0.1

0.2

SNR mismatch [dB]

AIR

Gain[bit/4D-sym

]



• 9 WDM channels



• Opt. launch power (-1 dBm)

Takeaway

Shaping is robust fornonlinear fiber channel



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



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.


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