A PAPR Reduction Technique Based On

296 J. OPT. COMMUN. NETW./VOL. 4, NO. 4/APRIL 2012 Silva et al.

A PAPR Reduction Technique Based on aConstant Envelope OFDM Approach forFiber Nonlinearity Mitigation in Optical

Direct-Detection SystemsJair A. L. Silva, Adolfo V. T. Cartaxo, and Marcelo E. V. Segatto

Abstract—In this paper, we propose a new peak-to-averagepower ratio reduction technique based on a constant enve-lope orthogonal frequency division multiplexing (CE-OFDM)approach to mitigate fiber induced nonlinearities in direct-detection optical OFDM (DDO-OFDM) systems. Simulationresults show that the proposed 10 Gbps DDO-CE-OFDMsystem using 16-quadrature amplitude modulation (16-QAM),2.66 GHz signal bandwidth, and different values of electricalphase modulation index outperforms DDO-OFDM systems as itincreases the fiber nonlinearity tolerance in fiber links withoutoptical dispersion compensation. The bit error rate of theproposed transmission scheme is decreased by a factor of 1000if compared to conventional DDO-OFDM systems, for 10 dBmof optical input power and considering a span of 960 km ofstandard single-mode fiber.

Index Terms—Constant envelope OFDM signals; Fiber non-linearity; Orthogonal frequency division multiplexing (OFDM);Peak-to-average power ratio (PAPR).

I. INTRODUCTION

O rthogonal frequency division multiplexing (OFDM) is apopular modulation technique that provides a relatively

straightforward way to accommodate high data rate links overharsh wireless channels characterized by severe multipathfading [1]. Recently, interest in using OFDM in opticalfiber communication applications has increased due to itspotential of electrical equalization to mitigate chromaticdispersion (CD) and polarization mode dispersion (PMD) [2–5].Experimental demonstrations have been reported for bothcoherent optical (CO) OFDM (CO-OFDM) and direct-detectionoptical (DDO) OFDM (DDO-OFDM) [6–9]. A 10 Gbps opticalDDO-OFDM system is cost effective because it requires asimple receiver architecture as it can use the same opticalcomponents as a 10 Gbps on–off keying system. However, thehigh peak-to-average power ratio (PAPR) produced by large

Manuscript received July 14, 2011; revised January 5, 2012; acceptedFebruary 16, 2012; published March 5, 2012 (Doc. ID 151008).

Jair A. L. Silva (e-mail: [email protected]) is with the Instituto Federal doEspírito Santo, Vitória, Brazil.

Adolfo V. T. Cartaxo is with the Instituto de Telecomunicações, InstitutoSuperior Técnico, Lisbon Technical University, 1049-001 Lisboa, Portugal.

Marcelo E. V. Segatto is with the Laboratório de Telecomunicações,Universidade Federal do Espírito Santo, Vitória, Brazil.

Digital Object Identifier 10.1364/JOCN.4.000296

amplitude fluctuations of the modulated waveform is one ofthe major drawbacks of this technique. The advocated multiplesubcarriers in any OFDM system makes it susceptible tothe nonlinear amplification effects commonly associated withthe transmitter’s power amplifier (PA) [1]. Therefore, spectralbroadening, intermodulation distortion, and, consequently,performance degradation are prominent problems to beaddressed in such multicarrier systems. In fiber optical OFDMsystems, PAPR reduction techniques are important challengesin order to increase their tolerance to optical modulatorintermodulation and fiber nonlinearity impairments [10,11].Clipping, peak windowing, coding, iterative decoding, tonereservation, and predistortion are distinctly PAPR reductionschemes with different effectiveness provided by tradeoffs thatmay include increased complexity, reduced spectral efficiency,and performance degradation [12,13]. A suitable solution forthis impairment that is based on phase modulation is describedin [14,15]. This so-called constant envelope (CE) OFDM(CE-OFDM) technique, which involves a signal transformationin the transmitter and an inverse transformation at thereceiver, reduces the PAPR to 0 dB.

Recently, we have proposed a new method to improve thetolerance to Mach–Zehnder modulator (MZM) nonlinearitiesin which a constant envelope electrical OFDM waveform thatyields 3 dB of PAPR, obtained by modulating the phase of anelectrical carrier centered on half electrical signal bandwidth,externally modulates an optical carrier of a continuous wave(CW) laser [16]. Subsequently, in [17], the same idea wasused to relax digital-to-analog and analog-to-digital converter(DAC/ADC) requirements in the same types of optical system.The simulation results showed a relative improvement oftransmission capacity in comparison with conventional DDO-OFDM systems in terms of quantization bits of the DAC/ADC.The same signal phase transform concepts were extended morerecently in [18] by adding optical carrier suppression in orderto reduce the bandwidth and receiver complexity for the higheroptical modulation index (OMI) in 20 and 40 km of standardsingle-mode fiber (SSMF). However, none of those reporteddiscussions have considered the possibility of fiber nonlinearityimprovement provided by constant envelope electrical OFDMwaveforms. Experimental demonstrations reported in [19,20]investigate the tolerance to fiber nonlinearities of opticalOFDM signals with low PAPR in DDO-OFDM systems.Recently, Johannes et al. [21] have introduced the constant

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Silva et al. VOL. 4, NO. 4/APRIL 2012/J. OPT. COMMUN. NETW. 297

envelope OFDM concept to improve the fiber nonlinearitytolerance and the phase noise tolerance in CO-OFDM systems.However, optical phase modulators (PMs) are used in all thosesolutions instead of an electrical phase modulator prior to anoptical intensity modulator (IM) as proposed in [16].

In this paper, we extend the basic concept of the proposeddirect-detection optical constant envelope (DDO-CE) OFDM(DDO-CE-OFDM) transmission system of SSMF withoutoptical dispersion compensation. We report simulation resultsof a 10 Gbps DDO-CE-OFDM system using 16-QAM subcarriermodulation and 2.66 GHz signal bandwidth. The results reveala substantial increase of fiber nonlinearity tolerance whencompared to the conventional DDO-OFDM system.

This paper is organized as follows. Section II brieflydescribes the CE-OFDM method proposed in [14,15]. The mostimportant design aspects of the proposed DDO-CE-OFDMtransmission system are explained in Section III, with adetailed description of its application to direct-detectionsystems. Simulation results are reported in Section IV, andconcluding remarks are made in Section V.

II. CONSTANT ENVELOPE OFDM

CE-OFDM is a modulation format described by Thompsonet al. in [15] for wireless transmission systems. In this format,an electrical carrier is phase modulated by conventional OFDMwaveforms, which results in constant complex envelope signalswith 0 dB PAPR. Therefore, it exploits the advantages ofOFDM signals and provides power efficiency, as efficientpower amplification can be achieved without causing nonlineardistortion or spectral broadening by a communication systemthat shares many of the same functional blocks of a standardDFT-based OFDM signaling format. Signal and systemdefinitions of the CE-OFDM format exploited in this paper aredescribed next.

A. Signal Description

In this constant envelope signaling format, the information-bearing message signal is a real-valued OFDM waveform x(t)=C

∑Ns−1k=1 ℜ[X (k)]cos

(2πkt

T

)−ℑ[X (k)]sin

(2πkt

T

). The signal x(t)

modulates the phase of a carrier resulting in a bandpass signalwritten as

s(t)=ℜ{Ae jφ(t)e j2π fc t}= A cos[2π fc t+φ(t)], (1)

with {X (k)}Ns−1k=1 the M-QAM data symbols, T = N

Fsthe

signaling interval duration, N = 2Ns + 2 the fast Fouriertransform length, Fs the sampling rate, and C a constant,where A is the signal amplitude, fc is the carrier frequency,and the phase signal during the nth signal interval nT ≤ t <(n+1)T is

φ(t)= θn +2πhCN x(t), (2)

where h is referred to as the modulation index, CN is aconstant used to normalize the variance of the message signal,and θn is a memory term designed to make the modulation

hπhπ

Fig. 1. (Color online) Power spectrum of conventional OFDM andCE-OFDM signals generated with Ns = 64 data subcarriers mappedon 16-QAM.

hπhπhπhπhπhπ

Fig. 2. (Color online) BER versus SNR performance of the simulatedCE-OFDM system over AWGN channels. (N = 2048 IFFT/FFT size,Ns = 1023 subcarriers, 16-QAM subcarrier modulation).

phase continuous [14]. When θn = 0, the modulation ismemoryless. The bandwidth of s(t) is usefully expressed asB = max(2πh,1)BW Hz, which is an RMS (root-mean-square)bandwidth lower bounded by the bandwidth of conventionalOFDM signals BW Hz, which depends on the electricalmodulation index h. Further details of CE-OFDM signaldescription can be found in [14,15].

B. Electrical Phase Modulation Index h Induced Tradeoff

The modulation index h plays an important role in constantenvelope OFDM modulations as it induces a tradeoff betweensignal bandwidth and system performance. It can be seenfrom Figs. 1 and 2 that the system performance improves forCE-OFDM signals with larger bandwidths.


The power spectral density depicted in Fig. 1 shows thatthe CE-OFDM signal bandwidth increases with h. Figure 1also shows the bandwidth of the conventional OFDM waveformx(t) for comparison purposes. Notice from Fig. 1 that, for highmodulation index (2πh > 1), the CE-OFDM signal spectrumhas more out-of-band power than conventional OFDM. Asexpected, for 2πh ≤ 1, the bandwidths are almost the same.Figure 2 gives a bit error rate (BER) comparison for differentvalues of the index h of CE-OFDM schemes on additive whiteGaussian noise (AWGN) channels in order to illustrate thetradeoff induced by the electrical phase index. The simulationresults shown prove that constant envelope OFDM systems arehighly sensitive to the modulation index h. As expected, thesmaller the value of h, the worse the BER. This is explained bythe fact that the phase waveforms of CE-OFDM signals withsmaller h are more vulnerable to noise due to its narrowerdynamic range [22].

The theoretical BER approximation shown in Fig. 2 isexpressed as [15]

BER≈ 2(

M−1Mlog2M

)Q

(2πh

√6log2M

M2 −1SNR

), (3)

where Q(x) = ∫ ∞x e−y2/2d y/

p2π is the Gaussian Q-function

and SNR = Eb/N0 is the bit energy-to-noise density ratio.Its accuracy for high carrier-to-noise ratio (CNR) has beenproved in [15] through simulation results of a CE-OFDMdesigned for wireless channel systems. However, the constantenvelope technique we propose in this paper is suitablefor optical intensity-modulated direct-detection system. Theslight performance difference between the simulation resultsand the approximation (3) shown in Fig. 2 for each phasemodulation index 2πh considered can be explained by the highCNR standard approximation normally employed in phasedemodulator receiver analysis [15].

III. SUITABLE CONSTANT ENVELOPE OFDM FOR

OPTICAL DIRECT-DETECTION SYSTEMS

The transformation technique outlined in [15] was proposedfor wireless communications in fading channels. However, thegenerated complex CE-OFDM signals with PAPR = 0 dB arenot suitable for high data rate IMDD optical communicationsystems that use single-drive or dual-drive Mach–Zehndermodulators (MZMs) as the optical modulator. Indeed, lowPAPR and real coefficient signals are desirable in the MZMbranches.

A. The Proposed DDO-CE-OFDM System

The DDO-CE-OFDM system for IMDD optical commu-nications proposed in this paper is a modified version ofThompson’s technique [14] according to the system modelrepresented in Fig. 3. It provides a 3 dB PAPR electrical OFDMsignal with real coefficients to a single-drive MZM. At firstglance, this low fluctuation modulating signal diminishes thenonlinear distortions induced by MZM operation.

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h – Phase modulation indexOFDM Tx

Photodetector

FFT – Fast Fourier transform

CP–1 – Remove cyclic prefix

arg – arctangent of an argument

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Fig. 3. (Color online) DDO-CE-OFDM system model.

As depicted in Fig. 3, during each block interval of T seconds,an inverse fast Fourier transform (IFFT) calculates a block oftime samples {x[n]} at Fs = N/T sampling rate. To generatea real-valued sequence, its input is the conjugate symmetricvector{

0, X [1], X [2], . . . , X [Ns],0, X∗[Ns], . . . , X∗[2], X∗[1]}, (4)

where ∗ is a complex conjugate operator and {X [k]}Nsk=1 are

M-QAM parallel data subcarriers. After IFFT processing, thetime domain electrical OFDM signal x[n]=∑N

k=1X [k]e j2πkn/N

of N = 2Ns +2 real-valued coefficients is windowed by a raisedcosine filter. The generated OFDM signal phase modulatesa phase modulator with carrier frequency fc and phasemodulation index of 2πh. After cyclical extension, a continuoustime signal of PAPR = 3 dB produced at the output of theCE-OFDM transmitter block modulates an optical carrier bya single-drive MZM biased at its intensity null point.

One sideband of the double-sideband signal provided bythe optical modulator is suppressed by an optical filter. Thesingle-sideband (SSB) optical waveform is then transmittedover amplified1 dispersion-uncompensated spans of standardsingle-mode fiber. After bandpass filtering, the optical signalintensity is directly detected by a single photodiode.

The cyclic prefix samples are discarded in the electricalreceiver side before the phase demodulator. The inverseoperations to those performed at the transmitter are then im-plemented. The discrete phase demodulator is implemented byan arctangent processor that simply calculates its argument,followed by a phase unwrapper in order to minimize the effect

1 We assume that the erbium-doped fiber amplifiers (EDFAs) have high gain sothat amplified spontaneous emission (ASE) is the dominant noise source in thesystem.


TABLE IELECTRICAL PARAMETERS OF THE DDO-CE-OFDM

SYSTEM

Electrical parameters

Parameter Value

Bit rate Rb 10 GbpsFFT size N 2048Number of data subcarrier Ns = N−2

2 1023Subcarrier modulation 16-QAMCyclic prefix fraction CP 1

16OFDM signal bandwidth Bw = Rb ·Ns ·(1+CP)

N·log2(M) ≈2.66 GHz

Subcarrier spacing ∆= BwN ≈2.6 MHz

Cyclic prefix duration Tcp ≈24 nsOFDM symbol duration Ts ≈409 nsCentral frequency fc = Bw

2 ≈664 MHz

of phase ambiguities. Channel distortion compensation on eachsubcarrier is performed before symbol M-QAM demapping bya single-tap equalizer.

B. Optimum CSPR for DDO-CE-OFDM Systems

The carrier-to-signal power ratio (CSPR) parameter hasa large influence on direct-detection optical OFDM systemperformance. Low CSPR increases both the signal-to-noiseratio (SNR) and intermodulation distortions (IMDs) upondetection, while high CSPR essentially wastes power in theoptical carrier. The CSPR is defined as

CSPR[dB]= 10 log10

(Pc

Pin

), (5)

where Pc represents the power of the optical carrier and Pinis the data signal power at the output of the MZM biased atits intensity null point. The optical carrier is inserted in theoptical domain (optical biasing), as suggested in [23].

We have performed back-to-back (b2b) simulations ofthe proposed technique to assess the optimum CSPR thatimproves the receiver sensitivity. The relevant OFDM systemparameters used in all conducted simulations are summarizedin Table I.

The results in Fig. 4 show the required optical signal-to-noise ratio (OSNR) for BER = 10−3 of the proposedDDO-CE-OFDM for several values of the electrical phase mod-ulation index. Figure 4 also depicts simulation results of thefirst conventional DDO-OFDM described and experimentallydemonstrated in [24].

From Fig. 4, we can see that the optimum CSPR is found tobe 0 dB for 2πh = 0.8, 1.2, and 2.0, as it is for the conventionalsystem, which means that the best sensitivity is achieved whenthe optical carrier power equals the optical signal power. Asexpected, the DDO-CE-OFDM system performance stronglydepends on the phase modulation index, since the requiredOSNR for BER = 10−3 is ∼1, 5, and 8 dB larger than thatrequired for the conventional system for 2πh = 2.0, 1.2, and0.8, respectively. This result confirms the intrinsic performanceand bandwidth tradeoff of phase modulation schemes.

hπhπhπ

Fig. 4. (Color online) Required OSNR for BER = 10−3 as function ofthe CSPR.

hπhπhπ

Fig. 5. (Color online) Mean PAPR along link distance for commonDDO-OFDM and different electrical phase modulation index 2πh ofthe proposed DDO-CE-OFDM.

C. PAPR Evolution Along Fiber Links

PAPR evolution along the link due to fiber nonlinearitiesis an important issue in optical OFDM systems. Therefore,it is important to analyze the effect of subcarrier phasedecorrelation due to CD in the proposed technique. Figure 5depicts the mean PAPR2 as a function of the link distance forboth DDO-OFDM and DDO-CE-OFDM. In these simulations,we have considered 12 spans of 80 km SSMF with loss ofα = 0.2 dB/km, dispersion of D = 17 ps/(nm.km), effectivearea Aeff = 8 ·10−11m2, and nonlinear coefficient of γ = 1.3651/(W.km) at signal wavelength λ= 1550 nm.

It can be seen in Fig. 5 that the PAPR of the DDO-CE-OFDMsystem remains below that of conventional optical OFDMfor all spans and all phase modulation indices considered.As expected, among the phases modulation indices analyzed,

2 Calculated among 1000 transmitted symbols.


the lowest PAPR value is achieved for 2πh = 0.8 dueto its concentrated spectrum when compared with highermodulation indices. It is worth noting that the subcarrierdecorrelation scales with spectral distance (subcarrier spacing)due to CD as the signal propagates along the fiber.

IV. RESULTS AND DISCUSSION OF DDO-CE-OFDMSYSTEM PERFORMANCE

Monte Carlo simulations are used to estimate the BER inorder to investigate the performance of the DDO-CE-OFDMsystem under the influence of fiber nonlinearity impairments.The BER is evaluated by counting the number of different bitsbetween the ∼2.7 transmitted and received millions of bits.The ASE is assumed to be dominant over thermal and shotnoises, and it is modeled as an AWGN. Simulation resultsobtained by varying the optical input power (for CSPR =0 dB), transmission distance, and OSNR show the nonlineartolerance (NLT) of the proposed scheme depicted in Fig. 3.The electrical parameters used in all conducted simulationsfor both DDO-OFDM and DDO-CE-OFDM are summarized inTable I, and the optical parameters are those described inSubsection III.C. The signal propagation along SSMFs ismodeled by the generalized nonlinear Schrödinger equation,which includes the CD and Kerr effect nonlinearity of thefiber. The simulation of SSMF propagation uses the split-stepFourier method.

In Fig. 6, we compare the NLT of both the conventionalsystem and the proposed system along 80 km of dispersion-uncompensated SSMF transmission, by varying the fiberoptical input power from 0 to 16 dBm, for OSNR =15 dB(see Fig. 6(a)) and OSNR =20 dB (see Fig. 6(b)). Simulationresults are depicted in Figs. 7 and 8 for 160 km (two spansof 80 km) and 240 km (three spans of 80 km) fiber lengths. Wechose those fiber lengths because the nonlinear impairmentsare more significant than their effects in higher SSMF lengths.

The results shows that, in some specific cases, the proposedDDO-CE-OFDM system outperforms conventional OFDMsystems under the influence of fiber nonlinearities since ittolerates higher optical powers. It is less sensitive to nonlinearKerr effects for OSNR = 20 dB and electrical phase modulationindex 2πh = 2.0 for all optical signal power Pin values consid-ered for 80, 160, and 240 km. The results reported in Figs. 6, 7,and 8 also show that the increased NLT of the proposed systemdepends on the modulation index 2πh. It can be seen that theconventional OFDM system outperforms the DDO-CE-OFDMsystem for Pin < 7 and 10 dBm for 2πh = 1.2 and 0.8, respec-tively, along 160 km of SSMF, and with OSNR = 20 dB. ForOSNR = 15 dB, this is true for Pin < 6, 11, and 12 dBm, with2πh = 2.0, 1.2, and 0.8, respectively. This behavior is main-tained in 80 and 240 km SSMF fiber lengths. It is worth notingthat the DDO-CE-OFDM system performance is better whenthe modulation index 2πh is 2.0, despite its higher PAPR valuewhen compared to the other indices considered. Here, also, thisis explained by the fact that the phase waveforms of CE-OFDMsignals are more vulnerable to noise with smaller 2πh [22].

In Fig. 9, we compare the NLT for both the conventional andthe proposed systems after 960 km of uncompensated SSMF

(a)

(b)

hπhπhπ

hπhπhπ

Fig. 6. (Color online) System performance after 80 km of SSMF. (a)OSNR = 15 dB, and (b) OSNR = 20 dB.

transmission by varying the fiber optical input power from 0 to12 dBm and setting OSNR = 25 dB.

The results shown in Fig. 9 reveal that, for optical launchpower Pin ≤ 4 dBm, the conventional system performanceis better than that of the DDO-CE-OFDM systems with2πh = 0.8 and 1.2, but it is almost the same for 2πh = 2.0.However, for Pin ≥ 6 dBm, the proposed technique confirmsits robustness against nonlinearities. This is explained by thePAPR reduction conceived by the proposed constant envelopesystem. While the performance of the DDO-OFDM systemrapidly drops with optical launch power, the DDO-CE-OFDMsystem performance is almost maintained for all 2πh valuesconsidered.

We can conclude from Fig. 9 that the tradeoff betweensignal bandwidth and system performance associated withthe modulation index h greatly reduces with increasing fiberlength. The performance difference for the three indicesconsidered is not significant for 960 km of SSMF. This, andthe fact that for Pin < 6 dBm the performance of both systemsis almost the same, can be explained by the noise sensitivity ofthe proposed system, which limits the transmission distance.


(a)

(b)

hπhπhπ

hπhπhπ


We believe that for optical powers greater than 16 dBma negative impact due to nonlinearity will appear in theDDO-CE-OFDM system performance. To our knowledge, theproposed system also suffers from nonlinear distortion becauseof the varying amplitude of the constant envelope signals,which increases the PAPR at the end of the fiber link, asdepicted in Fig. 5. We conjecture that this conclusion extendsto the performance results obtained for 80, 160, and 240 km ofSSMF for OSNR = 15 and 20 dB.

Computational simulations have been performed to assessthe BER as a function of OSNR in order to illustrate theperformance difference of the two systems considered underthe influence of fiber nonlinearities. Here, also, the BER isevaluated by counting the number of different bits between the∼2.7 transmitted and received millions of bits. The amplifiedspontaneous emission is assumed to be dominant, and it ismodeled as an AWGN. The results shown in Fig. 10 wereobtained for a transmission distance of 960 km, optical inputlaunch power Pin = 8 dBm, and CSPR =0 dB.

The BER floor shown in Fig. 10 demonstrates the poor per-formance of the conventional optical OFDM system without aPAPR reduction scheme. However, for the DDO-CE-OFDM sys-

(a)

(b)

hπhπhπ

hπhπhπ


hπhπhπ

Fig. 9. (Color online) System performance after 960 km of SSMF withOSNR = 25 dB.

tem, a BER of less than 1×10−5 is observed at OSNR =18 dBfor electrical phase modulation parameter 2πh = 2.0. For 2πh =0.8 and 1.2, the proposed system outperforms the conventional


hπhπhπ

Fig. 10. (Color online) BER as a function of the OSNR after nonlinearpropagation along 960 km of SSMF.

one for OSNR values above 16 and 20 dB, respectively. Theseresults also reveal a best NLT of the constant envelopeOFDM system proposed in this paper for large values ofphase modulation index h even though they enlarge the signalbandwidth. The OSNR gains depicted in Fig. 10 for BER =1×10−3 are ∼3.5 and 7.5 dB for 2πh = 1.2 and 2.0, respectively,when compared to values for 2πh = 0.8.

V. CONCLUSION

A PAPR reduction technique based on electrical CE-OFDMmodulation to increase fiber nonlinearity tolerance in direct-detection optical OFDM systems has been proposed anddiscussed in this paper. We have simulated transmission ofa 10 Gbps DDO-CE-OFDM system with 16-QAM subcarriermodulation in a bandwidth of 2.66 GHz through 960 km ofuncompensated SSMF. Simulation results have shown that,especially for phase modulation index parameter 2πh = 2.0,the proposed technique outperforms a conventional 10 GbpsDDO-OFDM system. For 10 dBm of optical power at fiber inputand OSNR = 25 dB, the achieved BER values in the proposedDDO-CE-OFDM and conventional DDO-OFDM systems are≈10−5 and ≈10−2, respectively. Simulation results also showthat the proposed system outperforms the implementedconventional DDO-OFDM system for optical power greaterthan 0 dBm, OSNR =20 dB, and 2πh = 2.0 for a transmissiondistance up to 240 km of dispersion-uncompensated SSMF.Such a large NLT is attractive despite the spectral efficiencyreduction and increased complexity of the introduced system.

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