Probabilistic Shaping of High-Order QAM for Optical Fiber Systems Tobias Fehenberger Institute for Communications Engineering Joint work with Domaniç Lavery, Robert Maher, Alex Alvarado, Polina Bayvel Optical 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 Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 2/14
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
Probabilistic Shaping Method 1 Communication system with uniform QAM FEC Encoder QAM Mapping Channel QAM Demapping FEC Decoder 1 Böcherer et al., IEEE Trans. Comm., 2015 Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 4/14
Probabilistic Shaping Method 1 Communication system with uniform QAM FEC Encoder QAM Mapping Channel QAM Demapping FEC Decoder Optical Tx SSMF EDFA Optical Rx 1 Böcherer et al., IEEE Trans. Comm., 2015 Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 4/14
Probabilistic Shaping Method 1 Communication system with shaped QAM Distribution Matcher 2 FEC Encoder QAM Mapping Channel QAM Demapping FEC Decoder Distribution Dematcher Optical Tx SSMF EDFA Optical Rx Low-complexity distribution matcher 2 added outside FEC Very minor modifications to FEC encoder/decoder required 1 Böcherer et al., IEEE Trans. Comm., 2015 2 Schulte and Böcherer, IEEE Trans. Inf. Theory, 2015 Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 4/14
Probabilistic Shaping Method (cont d) Probability mass function (PMF) of channel input X : where and ν are scalars. P X (x i ) e ν x i 2, 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
Probabilistic Shaping Method (cont d) Probability mass function (PMF) of channel input X : where and ν are scalars. P X (x i ) e ν x i 2, Optimization problem for each SNR: choose and ν so that mutual information is maximized One PMF per SNR 16QAM uniform 1/8 PX 1/16 0 1 0 1 0 1 1 Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
Probabilistic Shaping Method (cont d) Probability mass function (PMF) of channel input X : where and ν are scalars. P X (x i ) e ν x i 2, Optimization problem for each SNR: choose and ν so that mutual information is maximized One PMF per SNR 16QAM shaped for 10 db SNR 1/8 PX 1/16 0 1 0 1 0 1 1 Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
Probabilistic Shaping Method (cont d) Probability mass function (PMF) of channel input X : where and ν are scalars. P X (x i ) e ν x i 2, Optimization problem for each SNR: choose and ν so that mutual information is maximized One PMF per SNR 16QAM shaped for 5 db SNR 1/8 PX 1/16 0 1 0 1 0 1 1 Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
Probabilistic Shaping Method (cont d) Probability mass function (PMF) of channel input X : where and ν are scalars. P X (x i ) e ν x i 2, Optimization problem for each SNR: choose and ν so that mutual information is maximized One PMF per SNR 1/8 16QAM uniform 16QAM shaped for 5 db SNR PX 1/16 0 1 0 1 0 1 1 Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 5/14
B2B Experiments: Setup ECL 1.1 khz DSP FPGA DAC LPF LPF IQ Mod Linear Amplifiers EDFA Pol Mux 1.5 khz ECL ASE Receiver Digital Coherent Receiver LO Sig Pol. Diverse Coherent Receiver ADC De-Skew and Normalization Matched RRC Filtering CMA Pre-EQ Filter Taps Blind QAM RDE CPE and GSOP AIR Estimation Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 6/14
B2B Experiments: Results 12 Shannon capacity 16QAM uniform 64QAM uniform AIR [bit/4d-sym] 10 8 6 4 2 3 4 5 6 7 8 9 10 11 12 E b /N 0 [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
B2B Experiments: Results AIR [bit/4d-sym] 12 10 8 Shannon capacity 16QAM uniform 64QAM uniform 16QAM shaped 64QAM shaped 6 4 2 3 4 5 6 7 8 9 10 11 12 E b /N 0 [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
B2B Experiments: Results AIR [bit/4d-sym] 12 10 8 Shannon capacity 16QAM uniform 64QAM uniform 16QAM shaped 64QAM shaped 6 16QAM gain: 0.43 db 4 2 3 4 5 6 7 8 9 10 11 12 E b /N 0 [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
B2B Experiments: Results AIR [bit/4d-sym] 12 10 8 Shannon capacity 16QAM uniform 64QAM uniform 16QAM shaped 64QAM shaped 64QAM gain: 0.8 db 6 16QAM gain: 0.43 db 4 2 3 4 5 6 7 8 9 10 11 12 E b /N 0 [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
B2B Experiments: Results AIR [bit/4d-sym] 12 10 8 Shannon capacity 16QAM uniform 64QAM uniform 16QAM shaped 64QAM shaped 64QAM gain: 0.8 db 6 16QAM gain: 0.43 db 4 2 3 4 5 6 7 8 9 10 11 12 E b /N 0 [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 7/14
Experimental Results: B2B (cont d) Sensitivity gain [db] 0.8 0.6 0.4 0.2 16QAM 64QAM AWGN ref. Significant gain over uniform Gains present over wide SNR range Good match with AWGN reference 0 0 5 10 15 20 25 SNR [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 8/14
Fiber Simulations AIR [bit/4d-sym] 11 10.5 10 9.5 DP-64QAM @ 28 GBaud RRC pulse shaping 9 WDM channels WDM spacing: 30 GHz 1000 km SMF w/ EDFAs EDC only Uniform input Uniform Input + EDC 9 6 4 2 0 2 Launch power per channel [dbm] AIR (at opt. power) 10.5 bit/4d-sym Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 9/14
Fiber Simulations AIR [bit/4d-sym] 11 10.5 10 9.5 Shaped Input + EDC Uniform Input + EDC 9 6 4 2 0 2 Launch power per channel [dbm] 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
Fiber Simulations AIR [bit/4d-sym] 11 10.5 10 9.5 Uniform Input + DBP Shaped Input + EDC Uniform Input + EDC 9 6 4 2 0 2 Launch power per channel [dbm] 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
Fiber Simulations AIR [bit/4d-sym] 11 10.5 10 9.5 Shaped Input + DBP Uniform Input + DBP Shaped Input + EDC Uniform Input + EDC 9 6 4 2 0 2 Launch power per channel [dbm] 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
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 using mismatched shaping instead of perfectly matched shaping Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 10/14
Mismatched Shaping: 64QAM over AWGN Channel SNR [db] 25 20 15 10 Green: penalty 0.1 db Green+Blue: penalty 0.2 db Green+Blue+Red: penalty 0.3 db 5 5 10 15 20 25 Shaping SNR [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 11/14
Mismatched Shaping: 64QAM over AWGN Channel SNR [db] 25 20 15 10 Green: penalty 0.1 db Green+Blue: penalty 0.2 db Green+Blue+Red: penalty 0.3 db 5 5 10 15 20 25 Shaping SNR [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 11/14
Mismatched Shaping: 64QAM over AWGN Channel SNR [db] 25 20 15 10 5 5 10 15 20 25 Shaping SNR [db] Green: penalty 0.1 db Green+Blue: penalty 0.2 db Green+Blue+Red: penalty 0.3 db Takeaway Shaping is robust for AWGN channel Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 11/14
Mismatched Shaping: Fiber Simulations DP-64QAM @ 28 GBaud AIR Gain [bit/4d-sym] 0.2 0.1 RRC pulse shaping 9 WDM channels WDM spacing: 30 GHz 1000 km SMF w/ EDFAs Opt. launch power (-1 dbm) 0 3 2 1 0 1 2 3 SNR mismatch [db] Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 12/14
Mismatched Shaping: Fiber Simulations DP-64QAM @ 28 GBaud AIR Gain [bit/4d-sym] 0.2 0.1 0 3 2 1 0 1 2 3 SNR mismatch [db] RRC pulse shaping 9 WDM channels WDM spacing: 30 GHz 1000 km SMF w/ EDFAs Opt. launch power (-1 dbm) Takeaway Shaping is robust for nonlinear fiber channel Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 12/14
Conclusion Experimental demonstration of 0.8 db sensitivity gain by probabilistic 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
Thank you. References T. Fehenberger, G. Böcherer, 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. G. Böcherer, P. Schulte, and F. Steiner, Bandwidth efficient and rate-matched low-density parity-check coded modulation, IEEE Trans. Commun., Oct. 2015. P. Schulte and G. Böcherer, Constant composition distribution matching, IEEE Trans. Inf. Theory, Nov. 2015. T. Fehenberger, D. Lavery, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, Sensitivity gains by mismatched probabilistic shaping for optical communication systems, http://arxiv.org/abs/1510.03565v2, 2015. F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM, in Proc. European Conference and Exhibition on Optical Communication (ECOC), Paper PDP.3.4, Sep. 2015. Tobias Fehenberger Probabilistic Shaping of High-Order QAM for Optical Fiber Systems 14/14