The rate flexibility and probabilistic shaping gain of $4$-dimensional
signaling is experimentally tested for short-reach, unrepeated transmission. A
rate granularity of 0.5 bits/QAM symbol is achieved with a distribution matcher
based on a simple look-up table.Comment: Presented at OFC'18, San Diego, CA, US

Böcherer, Georg

Da Ros, Francesco

Forchhammer, Søren

Kramer, Gerhard

Schulte, Patrick

Steiner, Fabian

Yankov, Metodi Plamenov

English

arXiv

The rate flexibility and probabilistic shaping gain of 4-dimensional signaling is experimentally tested for short-reach, unrepeated transmission. A rate granularity of 0.5 bits/QAM symbol is achieved with a distribution matcher based on a simple look-up table

Bocherer, Georg

Online Research Database In Technology

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Downloaded from orbit.dtu.dk on: Jul 07, 2018Experimental Verification of Rate Flexibility and Probabilistic Shaping by 4D SignalingSteiner, Fabian; Da Ros, Francesco; Yankov, Metodi Plamenov; Bocherer, Georg; Schulte, Patrick;Forchhammer, Søren; Kramer, GerhardPublished in:2018 Optical Fiber Communications Conference and ExpositionLink to article, DOI:10.1364/OFC.2018.M4E.3Publication date:2018Document VersionPeer reviewed versionLink back to DTU OrbitCitation (APA):Steiner, F., Da Ros, F., Yankov, M. P., Bocherer, G., Schulte, P., Forchhammer, S., & Kramer, G. (2018).Experimental Verification of Rate Flexibility and Probabilistic Shaping by 4D Signaling. In 2018 Optical FiberCommunications Conference and Exposition  (pp. 1-3). Optical Society of America. DOI:10.1364/OFC.2018.M4E.3Experimental Verification of Rate Flexibility andProbabilistic Shaping by 4D SignalingFabian Steiner(1), Francesco Da Ros(2), Metodi Plamenov Yankov(2), Georg Böcherer(1),Patrick Schulte(1), Søren Forchhammer(2), Gerhard Kramer(1)(1) Technical University of Munich, 80333 Munich, Germany(2) DTU Fotonik, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmarkfabian.steiner@tum.deAbstract: The rate flexibility and probabilistic shaping gain of 4-dimensional signalingis experimentally tested for short-reach, unrepeated transmission. A rate granularity of0.5 bits/QAM symbol is achieved with a distribution matcher based on a simple look-up table.OCIS codes: 060.2330, 060.1660, 060.4080.1. IntroductionFlexibility is a key requirement for next-generation optical transponders to meet the demands of different deploymentscenarios. Recently, probabilistic amplitude shaping (PAS) [1] gained broad interest as a means to realize shapinggains and a fine granularity in spectral efficiencies (SEs) for an extended reach and higher net data rates. A key enablerfor PAS is the distribution matcher (DM), which maps uniform bits to symbols with desired properties (e.g., a goodempirical distribution, low average power) in a reversible manner. Most work so far considered constant compositiondistribution matching (CCDM) [2], which has excellent performance but introduces additional complexity becauseof the arithmetic coding. In [3], the authors extend PAS to higher dimensions and suggest a shell mapper as DM toselect low power sequences from a 4-dimensional (4D) hypercube consisting of the 4-fold Cartesian product of M-aryamplitude shift keying (ASK) constellations.In this paper, we show experimentally that rate-adaptation with steps of 0.5bits/QAM symbol (bpQs) can beachieved with the scheme of [3] and a simple look-up table. We compare this method to conventional PAS withCCDM and uniform constellations. The results are based on short-reach, unrepeated transmissions of 100 km, 140 kmand 180 km.2. Rate-Adaptation and Achievable Rates2.1. Signaling SchemesWe distinguish three signaling and receiver schemes. PAS-nD-1D is the conventional setting using a high, n-dimensional (nD) DM and 1D demapping. PAS-4D-4D uses a 4D DM and also demaps in 4D. A variant of thelatter is PAS-4D-2D, where a sub-optimal and less complex demapping in 2D is used. The PAS-4D schemes employ4D signaling with an M-ASK constellation in each dimension. For the binary labeling of the constellation points, weuse an m = log2(M4) bit binary reflected Gray code (BRGC). Following the principle of quadrant shaping (QS) [3],mQ =m−4 bits determine a point in a quadrant and mS = 4 bits represent the 4 sign bits. A rate-adaptation can be re-alized by a DM based on a look-up table with at most 2mQ entries, which selects a subset of 2k low-energy points fromthe 2mQ points in a quadrant. The corresponding DM rate is Rdm = k bits/4D-symbol. We refer to the resulting constel-lation asX . The SE is Rtx = Rdm +4 · γ bits/4D-symbol, where γ is the fraction of sign bits per dimension that carryadditional information bits. For the forward error correction (FEC) code rate Rc we have γ = 1− (1−Rc) · log2(M).Its blocklength is usually an integer multiple of m ·n. By choosing k, a rate adaptation with a granularity of 1 bit/4D-symbol, i.e., 0.5 bpQs is possible so that any SE within the set {0.5,1.0,1.5, . . . ,2log2(M)− 2}+ 2 · γ bpQs canbe realized with the same FEC overhead (OH). If the scheme is extended to N-dimensions (ND), a granularity of1/(N/2) bpQs is possible. The exemplary transmission modes of this work target SEs of 3 bpQs, 4 bpQs and 5 bpQsand are summarized in Table 1a. We assume a single FEC code with OH = 23% (Rc = 13/16).arXiv:1803.06746v1  [cs.IT]  18 Mar 2018Signaling mode Rtx[bpQs]|X | Rdm[bpQs]OHPAS-4D-4D-4.5 5.0 8182 4.5 23%PAS-4D-4D-3.5 4.0 2048 3.5 23%PAS-4D-4D-2.5 3.0 512 2.5 23%PAS-nD-1D-4.5 5.0 256 4.5 23%PAS-nD-1D-3.5 4.0 256 3.5 23%PAS-nD-1D-2.5 3.0 256 2.5 23%16-QAM uniform 3.0 16 – 33%64-QAM uniform 4.0 64 – 50%256-QAM uniform 5.0 256 – 60%(a) Signaling modes.256-QAM64-QAM16-QAMPAS-nD-1DPAS-4D-4DPAS-4D-2Dlog2(1+SNR)8 9 102.82.933.13.2SNR [dB]BMDRa[bpQs](b) Rtx = 3bpQs12 133.83.944.14.2SNR [dB](c) Rtx = 4bpQs15 164.84.955.15.2SNR [dB](d) Rtx = 5bpQsFig. 1: Simulated achievable rates of several signaling strategies for the linear AWGN channel.2.2. Achievable RatesWe denote the 4D transmit and receive vectors as x = (x1,x2,x3,x4) ∈X and y = (y1,y2,y3,y4) ∈ R4. During thetransmission experiment, we acquire sample sequences xK = (x1,x2, . . . ,xK) and yK = (y1,y2, . . . ,yK). An estimate ofthe achievable rate is [4]Ra =[H(X )− 1KK∑i=1− log2(q(xi,yi)∑a∈X q(a,yi))]+[bits/4D symbol] (1)where q(x,y) is the decoding metric for symbol-metric decoding (SMD) or bit-metric decoding (BMD) and [·]+ isshort for max(0, ·). For PAS-4D-2D, the decoding metric may also implement a sub-optimal and less complex rulebased on the respective 2D marginals.The calculated achievable rates for BMD and the linear additive white Gaussian noise (AWGN) channel are shownin Fig. 1. We observe that the PAS-4D modes are superior to their uniform {16,64,256}-QAM counterparts for allthree target SEs. The loss in power efficiency due to 2D demapping is at most 0.2 dB for BMD. The PAS-nD-1Dmodes virtually achieve Gaussian capacity.3. Transmission Experiment3.1. SetupWe experimentally investigate the 4D signaling scheme for a short-reach scenario and unrepeated transmission for100 km, 140 km and 180 km, where the four dimensions are transmitted as two complex dimensions in two subsequenttime slots. The CCDM for PAS-nD-1D operates in n= 6000 dimensions and the input distributions are taken from theMaxwell-Boltzmann family. The setup is shown in Fig. 2. The data symbols are interleaved with quadrature phase-shiftkeying (QPSK) pilots at a pilot rate of 10%. A frame alignment sequence is added at the beginning of the sequence andsquare root raised cosine (RRC) pulse shaping with a roll-off factor of 0.1 is applied [6]. We employ a wave-divisionmultiplexing (WDM) setup with 5 external cavity lasers (ECLs, 10 kHz linewidth) on a 25 GHz grid. An arbitrarywaveform generator (AWG, 20 GHz) drives the two IQ modulators. The four interferers (IQ mod 1) are combinedFig. 2: Experimental setup of the transmission experiment.256-QAM uniform 64-QAM uniform 16-QAM uniform PAS-nD-1D PAS-4D-4D PAS-4D-2D5 104.84.955.15.25.35.45.5Pin [dBm]BMDRa[bpQs](a) 100 km8 10 12 143.63.73.83.944.14.24.34.44.54.6Pin [dBm](b) 140 km12 14 16 182.42.52.62.72.82.933.13.2Pin [dBm](c) 180 kmFig. 3: Achievable rates of the considered signaling strategies for the transmission experiment.with the central channel (IQ mod 2), a delay-and-add polarization emulator generates a dual-polarization signal andthe channels are individually decorrelated. The transmission link consists of an erbium doped fiber amplifier (EDFA)followed by a variable optical attenuator (VOA) that sets the total power launched into the standard single-modefiber (SSMF) of lengths 100 km, 140 km and 180 km. After transmission, the central channel is demodulated using astandard preamplified coherent receiver followed by a digital storage oscilloscope (DSO, 80 GSa/s and 33 GHz analogbandwidth). The receiver DSP is performed offline [6].3.2. ResultsIn back-to-back experiments, we validated that all modulation formats exhibit the same implementation penalty inthe operating regime of interest to ensure a fair comparison. The achievable rates for the transmission experimentsfor link lengths of 100 km, 140 km and 180 km are shown in Fig. 3. To operate efficiently for all three distances(corresponding to optimal launch powers of 9 dBm, 12 dBm and 15 dBm) at the desired SEs (dashed gray line), thethree different uniform constellations (16-, 64- and 256-QAM) would need to be operated with three different FECcodes (see Table 1a). The PAS modes allow a flexible operation with a single FEC. For increased transmission lengths,and therefore launch powers Pin, we observe that the PAS-nD-1D modes are penalized due to their increased higherorder moments and their severe impact on the non-linear interference noise (NLIN) [5, 6]. At the respective optimallaunch powers, the shaping gain of PAS-nD-1D is 0.2 bpQs, 0.15 bpQs, and 0.04 bpQs as compared to PAS-4D-4D.However, the PAS-4D DM is a simple look-up table with at most 2k = 29 = 512 entries. Moreover, 2D demapping(PAS-4D-2D) loses at most 0.1 bpQs for a target SE of 4 bpQs.4. Conclusions4D signal shaping and rate adaptation with a simple look-up table based DM allows a good trade-off between shapinggain and DM complexity. The suggested schemes are promising for transmission links where full fledged PAS istoo complex or penalized because of NLIN. Future work should investigate the tradeoff between higher dimensionalconstellations with N > 4, rate flexibility, and demapping complexity.References1. G. Böcherer, et al., “Bandwidth Efficient and Rate-Matched Low-Density Parity-Check Coded Modulation,”IEEE Trans. Commun., vol. 63, no. 12, pp. 4651–4665, Dec. 2015.2. P. Schulte and G. Böcherer, “Constant Composition Distribution Matching,” IEEE Trans. Inf. Theory, vol. 62,no. 1, pp. 430–434, Jan. 2016.3. P. Schulte, et al., “Four Dimensional Probabilistic Shaping for Fiber-Optic Communication,” in Proc. SPPCOM2017, Jul. 2017, paper SpM2F.5.4. G. Böcherer, “Achievable Rates for Probabilistic Shaping,” arXiv:1707.01134 [cs, math], Jul. 2017.5. T. Fehenberger, et al., “On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear FiberChannel,” J. Lightw. Technol., vol. 34, no. 21, pp. 5063–5073, Nov. 2016.6. J. Renner, et al., “Experimental Comparison of Probabilistic Shaping Methods for Unrepeated Fiber Transmis-sion,” preprint in J. Lightw. Technol., DOI: 10.1109/JLT.2017.2752243

Experimental Verification of Rate Flexibility and Probabilistic Shaping by 4D Signaling

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Experimental Verification of Rate Flexibility and Probabilistic Shaping by 4D Signaling

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