135 research outputs found
Discrete multitone modulation for short-range optical communications
As the need for higher information throughput increases, standard solutions such as copper lines and radio links seem to approach their limits. Therefore, optical solutions, after having conquered the long and medium-range networks, are nowadays also migrating into short-range data communication scenarios, offering the possibility of high capacity information transfer for both professional as well as consumer applications. The challenge is to offer cost-effective and robust optical solutions at relatively short (¿ 1 km) transmission distances, where traditional single-mode fiber for long-haul transmission systems are unsuitable. Solutions such as multimode glass fibers (MMF), plastic optical fibers (POF), using light-emitting diodes (LED) or low-cost vertical cavity surface emitting laser diodes (VCSEL), and optical wireless links (based on LEDs) are therefore being proposed and seem to be promising candidates. These solutions feature low costs, easy handling and installation, flexibility, and robustness, which are all very suitable characteristics for consumer needs. However, this comes at the expense of less bandwidth when compared to single-mode fiber systems. This thesis investigates the use of digital signal processing in order to overcome the bandwidth limitations in short-range optical communication systems, ensuring that such solutions are future-proof. In particular, discrete multitone (DMT) modulation is proposed and investigated in order to increase the capacity of such systems. Derived from the more general orthogonal frequency division multiplexing (OFDM), DMT is a baseband multicarrier modulation technique that is already widely employed in copper-based digital subscriber lines (DSL) systems such as asymmetrical DSL (ADSL) and very high data rate DSL (VDSL). By dividing a high-speed serial data stream into multiple parallel low-speed sub-streams and transmitting them simultaneously using different frequencies, DMT can be used to efficiently combat various signal impairments such as dispersion and narrowband interference. Due to the use of intensity-modulation and direct-detection (IM/DD) in low-cost optical systems, where only the intensity of light is modulated and not the phase, the application of DMT is different from standard electrical systems. Characteristics such as high crest factor, which is the ratio of the peak to root-mean-square amplitude value of the DMT signal, and clipping have different consequences and are studied in this thesis. After an introduction to the principles of DMT and rate-adaptive bit-loading, an analytical model of the optical IM/DD channel for short-range optical communications is presented. Making use of this model, the theoretical capacity of such a channel is derived for both a Gaussian and a first-order low-pass electrical-to-electrical channel response by means of the water-filling method. It is found that the crest factor of the modulation signal plays a dominant role in defining the capacity of the optical IM/DD channel. Furthermore, by including characteristics of DMT modulation such as clipping and quantization, it is shown that the calculated capacity values can be refined and optimum parameters for DMT transmission over an optical IM/DD channel exist. Following this, the optimum clipping values and number of subcarriers for maximizing DMT transmission performance over an optical IM/DD channel are investigated. It is shown that the optimum clipping value, which depends on various system parameters such as receiver noise power and modulation order, can be determined by using an analytical expression. In the case of the number of subcarriers, larger values generally lead to better performance when DMT with bit-loading is used. Additionally, various experiments to explore the system limits of DMT techniques have been performed and the results for POF, MMF, and optical wireless are presented. It is shown that record bit-rates of up to 47 Gbit/s can be achieved using DMT. Finally, an efficient way to implement DMT is presented, together with results regarding the implementation of a real-time DMT transmission system operating at 1.25 Gbit/s. System complexity issues of real-time hardware implementation are also discussed, showing that pipelining and parallelization are essential in high-speed designs, adding to the need of extra hardware resources. Moreover, it is verified that for DMT, the Fast Fourier Transform (FFT) operations require most hardware resources. After the presentation of some alternative modulation techniques such as pulse-amplitude-modulated DMT (PAM-DMT), which also were investigated by the author, this thesis ends with the conclusions and some recommendations for further research work
End-to-end Deep Learning of Optical Fiber Communications
In this paper, we implement an optical fiber communication system as an
end-to-end deep neural network, including the complete chain of transmitter,
channel model, and receiver. This approach enables the optimization of the
transceiver in a single end-to-end process. We illustrate the benefits of this
method by applying it to intensity modulation/direct detection (IM/DD) systems
and show that we can achieve bit error rates below the 6.7\% hard-decision
forward error correction (HD-FEC) threshold. We model all componentry of the
transmitter and receiver, as well as the fiber channel, and apply deep learning
to find transmitter and receiver configurations minimizing the symbol error
rate. We propose and verify in simulations a training method that yields robust
and flexible transceivers that allow---without reconfiguration---reliable
transmission over a large range of link dispersions. The results from
end-to-end deep learning are successfully verified for the first time in an
experiment. In particular, we achieve information rates of 42\,Gb/s below the
HD-FEC threshold at distances beyond 40\,km. We find that our results
outperform conventional IM/DD solutions based on 2 and 4 level pulse amplitude
modulation (PAM2/PAM4) with feedforward equalization (FFE) at the receiver. Our
study is the first step towards end-to-end deep learning-based optimization of
optical fiber communication systems.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog
Ultra Wideband Communications: from Analog to Digital
Ultrabreitband-Signale (Ultra Wideband [UWB]) können einen
signifikanten Nutzen im Bereich drahtloser Kommunikationssysteme haben. Es
sind jedoch noch einige Probleme offen, die durch Systemdesigner und
Wissenschaftler gelöst werden müssen. Ein Funknetzsystem mit einer derart
großen Bandbreite ist normalerweise auch durch eine große Anzahl an
Mehrwegekomponenten mit jeweils verschiedenen Pfadamplituden
gekennzeichnet. Daher ist es schwierig, die zeitlich verteilte Energie
effektiv zu erfassen. Außerdem ist in vielen Fällen der naheliegende
Ansatz, ein kohärenter Empfänger im Sinne eines signalangepassten Filters
oder eines Korrelators, nicht unbedingt die beste Wahl. In der vorliegenden
Arbeit wird dabei auf die bestehende Problematik und weitere
Lösungsmöglichkeiten eingegangen.
Im ersten Abschnitt geht es um „Impulse Radio UWB”-Systeme mit
niedriger Datenrate. Bei diesen Systemen kommt ein inkohärenter Empfänger
zum Einsatz. Inkohärente Signaldetektion stellt insofern einen
vielversprechenden Ansatz dar, als das damit aufwandsgünstige und robuste
Implementierungen möglich sind. Dies trifft vor allem in Anwendungsfällen
wie den von drahtlosen Sensornetzen zu, wo preiswerte Geräte mit langer
Batterielaufzeit nötigsind. Dies verringert den für die Kanalschätzung
und die Synchronisation nötigen Aufwand, was jedoch auf Kosten der
Leistungseffizienz geht und eine erhöhte Störempfindlichkeit gegenüber
Interferenz (z.B. Interferenz durch mehrere Nutzer oder schmalbandige
Interferenz) zur Folge hat.
Um die Bitfehlerrate der oben genannten Verfahren zu bestimmen, wurde
zunächst ein inkohärenter Combining-Verlust spezifiziert, welcher
auftritt im Gegensatz zu kohärenter Detektion mit Maximum Ratio Multipath
Combining. Dieser Verlust hängt von dem Produkt aus der Länge des
Integrationsfensters und der Signalbandbreite ab.
Um den Verlust durch inkohärentes Combining zu reduzieren und somit die
Leistungseffizienz des Empfängers zu steigern, werden verbesserte
Combining-Methoden für Mehrwegeempfang vorgeschlagen. Ein analoger
Empfänger, bei dem der Hauptteil des Mehrwege-Combinings durch einen
„Integrate and Dump”-Filter implementiert ist, wird für UWB-Systeme
mit Zeit-Hopping gezeigt. Dabei wurde die Einsatzmöglichkeit von dünn
besetzten Codes in solchen System diskutiert und bewertet. Des Weiteren
wird eine Regel für die Code-Auswahl vorgestellt, welche die Stabilität
des Systems gegen Mehrnutzer-Störungen sicherstellt und gleichzeitig den
Verlust durch inkohärentes Combining verringert.
Danach liegt der Fokus auf digitalen Lösungen bei inkohärenter
Demodulation. Im Vergleich zum Analogempfänger besitzt ein
Digitalempfänger einen Analog-Digital-Wandler im Zeitbereich gefolgt von
einem digitalen Optimalfilter. Der digitale Optimalfilter dekodiert den
Mehrfachzugriffscode kohärent und beschränkt das inkohärente Combining
auf die empfangenen Mehrwegekomponenten im Digitalbereich. Es kommt ein
schneller Analog-Digital-Wandler mit geringer Auflösung zum Einsatz, um
einen vertretbaren Energieverbrauch zu gewährleisten. Diese Digitaltechnik
macht den Einsatz langer Analogverzögerungen bei differentieller
Demodulation unnötig und ermöglicht viele Arten der digitalen
Signalverarbeitung. Im Vergleich zur Analogtechnik reduziert sie nicht nur
den inkohärenten Combining-Verlust, sonder zeigt auch eine stärkere
Resistenz gegenüber Störungen. Dabei werden die Auswirkungen der
Auflösung und der Abtastrate der Analog-Digital-Umsetzung analysiert. Die
Resultate zeigen, dass die verminderte Effizienz solcher
Analog-Digital-Wandler gering ausfällt. Weiterhin zeigt sich, dass im
Falle starker Mehrnutzerinterferenz sogar eine Verbesserung der Ergebnisse
zu beobachten ist. Die vorgeschlagenen Design-Regeln spezifizieren die
Anwendung der Analog-Digital-Wandler und die Auswahl der Systemparameter in
Abhängigkeit der verwendeten Mehrfachzugriffscodes und der Modulationsart.
Wir zeigen, wie unter Anwendung erweiterter Modulationsverfahren die
Leistungseffizienz verbessert werden kann und schlagen ein Verfahren zur
Unterdrückung schmalbandiger Störer vor, welches auf Soft Limiting
aufbaut. Durch die Untersuchungen und Ergebnissen zeigt sich, dass
inkohärente Empfänger in UWB-Kommunikationssystemen mit niedriger
Datenrate ein großes Potential aufweisen.
Außerdem wird die Auswahl der benutzbaren Bandbreite untersucht, um einen
Kompromiss zwischen inkohärentem Combining-Verlust und Stabilität
gegenüber langsamen Schwund zu erreichen. Dadurch wurde ein neues Konzept
für UWB-Systeme erarbeitet: wahlweise kohärente oder inkohärente
Empfänger, welche als UWB-Systeme Frequenz-Hopping nutzen. Der wesentliche
Vorteil hiervon liegt darin, dass die Bandbreite im Basisband sich deutlich
verringert. Mithin ermöglicht dies einfach zu realisierende digitale
Signalverarbeitungstechnik mit kostengünstigen Analog-Digital-Wandlern.
Dies stellt eine neue Epoche in der Forschung im Bereich drahtloser
Sensorfunknetze dar.
Der Schwerpunkt des zweiten Abschnitts stellt adaptiven Signalverarbeitung
für hohe Datenraten mit „Direct Sequence”-UWB-Systemen in den
Vordergrund. In solchen Systemen entstehen, wegen der großen Anzahl der
empfangenen Mehrwegekomponenten, starke Inter- bzw.
Intrasymbolinterferenzen. Außerdem kann die Funktionalität des Systems
durch Mehrnutzerinterferenz und Schmalbandstörungen deutlich beeinflusst
werden. Um sie zu eliminieren, wird die „Widely Linear”-Rangreduzierung
benutzt. Dabei verbessert die Rangreduzierungsmethode das
Konvergenzverhalten, besonders wenn der gegebene Vektor eine sehr große
Anzahl an Abtastwerten beinhaltet (in Folge hoher einer Abtastrate).
Zusätzlich kann das System durch die Anwendung der R-linearen Verarbeitung
die Statistik zweiter Ordnung des nicht-zirkularen Signals vollständig
ausnutzen, was sich in verbesserten Schätzergebnissen widerspiegelt.
Allgemeine kann die Methode der „Widely Linear”-Rangreduzierung auch in
andern Bereichen angewendet werden, z.B. in „Direct
Sequence”-Codemultiplexverfahren (DS-CDMA), im MIMO-Bereich, im Global
System for Mobile Communications (GSM) und beim Beamforming.The aim of this thesis is to investigate key issues encountered in the
design of transmission schemes and receiving techniques for Ultra Wideband
(UWB) communication systems. Based on different data rate applications,
this work is divided into two parts, where energy efficient and robust
physical layer solutions are proposed, respectively.
Due to a huge bandwidth of UWB signals, a considerable amount of multipath
arrivals with various path gains is resolvable at the receiver. For low
data rate impulse radio UWB systems, suboptimal non-coherent detection is a
simple way to effectively capture the multipath energy. Feasible techniques
that increase the power efficiency and the interference robustness of
non-coherent detection need to be investigated. For high data rate direct
sequence UWB systems, a large number of multipath arrivals results in
severe inter-/intra-symbol interference. Additionally, the system
performance may also be deteriorated by multi-user interference and
narrowband interference. It is necessary to develop advanced signal
processing techniques at the receiver to suppress these interferences.
Part I of this thesis deals with the co-design of signaling schemes and
receiver architectures in low data rate impulse radio UWB systems based on
non-coherent detection.● We analyze the bit error rate performance of
non-coherent detection and characterize a non-coherent combining loss,
i.e., a performance penalty with respect to coherent detection with maximum
ratio multipath combining. The thorough analysis of this loss is very
helpful for the design of transmission schemes and receive techniques
innon-coherent UWB communication systems.● We propose to use optical
orthogonal codes in a time hopping impulse radio UWB system based on an
analog non-coherent receiver. The “analog” means that the major part of
the multipath combining is implemented by an integrate and dump filter. The
introduced semi-analytical method can help us to easily select the time
hopping codes to ensure the robustness against the multi-user interference
and meanwhile to alleviate the non-coherent combining loss.● The main
contribution of Part I is the proposal of applying fully digital solutions
in non-coherent detection. The proposed digital non-coherent receiver is
based on a time domain analog-to-digital converter, which has a high speed
but a very low resolution to maintain a reasonable power consumption.
Compared to its analog counterpart, itnot only significantly reduces the
non-coherent combining loss but also offers a higher interference
robustness. In particular, the one-bit receiver can effectively suppress
strong multi-user interference and is thus advantageous in separating
simultaneously operating piconets.The fully digital solutions overcome the
difficulty of implementing long analog delay lines and make differential
UWB detection possible. They also facilitate the development of various
digital signal processing techniques such as multi-user detection and
non-coherent multipath combining methods as well as the use of advanced
modulationschemes (e.g., M-ary Walsh modulation).● Furthermore, we
present a novel impulse radio UWB system based on frequency hopping, where
both coherent and non-coherent receivers can be adopted. The key advantage
is that the baseband bandwidth can be considerably reduced (e.g., lower
than 500 MHz), which enables low-complexity implementation of the fully
digital solutions. It opens up various research activities in the
application field of wireless sensor networks.
Part II of this thesis proposes adaptive widely linear reduced-rank
techniques to suppress interferences for high data rate direct sequence UWB
systems, where second-order non-circular signals are used. The reduced-rank
techniques are designed to improve the convergence performance and the
interference robustness especially when the received vector contains a
large number of samples (due to a high sampling rate in UWB systems). The
widely linear processing takes full advantage of the second-order
statistics of the non-circular signals and enhances the estimation
performance. The generic widely linear reduced-rank concept also has a
great potential in the applications of other systems such as Direct
Sequence Code Division Multiple Access (DS-CDMA), Multiple Input Multiple
Output (MIMO) system, and Global System for Mobile Communications (GSM), or
in other areas such as beamforming
Unsupervised ANN-Based Equalizer and Its Trainable FPGA Implementation
In recent years, communication engineers put strong emphasis on artificial
neural network (ANN)-based algorithms with the aim of increasing the
flexibility and autonomy of the system and its components. In this context,
unsupervised training is of special interest as it enables adaptation without
the overhead of transmitting pilot symbols. In this work, we present a novel
ANN-based, unsupervised equalizer and its trainable field programmable gate
array (FPGA) implementation. We demonstrate that our custom loss function
allows the ANN to adapt for varying channel conditions, approaching the
performance of a supervised baseline. Furthermore, as a first step towards a
practical communication system, we design an efficient FPGA implementation of
our proposed algorithm, which achieves a throughput in the order of Gbit/s,
outperforming a high-performance GPU by a large margin.Comment: accepted for publication at Joint European Conference on Networks and
Communications & 6G Summit (EuCNC/6G Summit), Gothenburg, Sweden, 6 - 9 June
202
Spectrally-efficient 168 Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers
Due to their simple and cost-effective transceiver architecture, single-polarization and single-photodiode based direct-detection (DD) systems offer advantages for metropolitan area network and data-center interconnect applications. Single-sideband subcarrier modulation (SSB SCM) signaling with direct detection has the potential to achieve high information spectral density (ISD) but its performance can be significantly degraded by signal-signal beat interference (SSBI). The recently proposed Kramers-Kronig (KK) digital signal processing (DSP) scheme is effective in eliminating the SSBI penalty. Through the use of the KK scheme, we achieved 4 × 168 Gb/s wavelength division multiplexing DD SSB 64-QAM Nyquist-SCM signal transmission over 80 km of uncompensated standard single-mode fiber at a net ISD of up to 4.61 (b/s)/Hz. The joint optimization of the optical carrier-to-signal power ratio (CSPR) and the KK algorithm sampling rate is described
An investigation into a DSP implementation of partial response signaling for 4800 bits per second full-duplex data communications over M.1020 telephone lines
Includes bibliographical references.This thesis investigates high-speed digital transmission over a conditioned, voice-grade telephone circuit (M.1020), using a technique known as partial response signaling, or PRS. In particular, the case where 4800 bps, full-duplex transmission is required in a CCI'PT V. 22 type format is investigated. The main v.22 criterion to be adhered to, is that frequency-division multiplexing (FDM) is to be used as the means of separating thetransmit and receive channels. The carrier frequencies should be 1200 Hz and 2400 Hz respectively. The investigation concerns the modulation and demodulation sections only
Design and implementation of low complexity adaptive optical OFDM systems for software-defined transmission in elastic optical networks
Due to the increasing global IP traffic and the exponential growing demand for broadband services, optical networks are experimenting significant changes. Advanced modulation formats are being implemented at the Digital Signal Processing (DSP) level as key enablers for high data rate transmission. Whereas in the network layer, flexi Dense Wavelength-Division Multiplexing (DWDM) grids are being investigated in order to efficiently use the optical spectrum according to the traffic demand. Enabling these capabilities makes high data rate transmission more feasible. Hence, introducing flexibility in the system is one of the main goals of this thesis. Furthermore, minimizing the cost and enhancing the Spectral Efficiency (SE) of the system are two crucial issues to consider in the transceiver design.
This dissertation investigates the use of Optical Orthogonal Frequency Division Multiplexing (O-OFDM) based either on the Fast Fourier Transform (FFT) or the Fast Hartley Transform (FHT) and flexi-grid technology to allow high data rate transmission over the fiber. Different cost-effective solutions for Elastic Optical Networks (EON) are provided.
On the one hand, Direct Detection (DD) systems are investigated and proposed to cope with present and future traffic demand. After an introduction to the principles of OFDM and its application in optical systems, the main problems of such modulation is introduced. In particular, Peak-to-Average Power Ratio (PAPR) is presented as a limitation in OFDM systems, as well as clipping and quantization noise. Hence, PAPR reduction techniques are proposed to mitigate these impairments. Additionally, Low Complexity (LC) PAPR reduction techniques based on the FHT have also been presented with a simplified DSP.
On the other hand, loading schemes have also been introduced in the analyzed system to combat Chromatic Dispersion (CD) when transmitting over the optical link. Moreover, thanks to Bit Loading (BL) and Power Loading (PL), flexible and software-defined transceivers can be implemented maximizing the spectral efficiency by adapting the data rate to the current demand and the actual network conditions. Specifically, OFDM symbols are created by mapping the different subcarriers with different modulation formats according to the channel profile. Experimental validation of the proposed flexible transceivers is also provided in this dissertation. The benefits of including loading capabilities in the design, such as enabling high data rate and software-defined transmission, are highlighted.Degut al creixement del tràfic IP i de la demanda de serveis de banda ampla, les xarxes òptiques estan experimentant canvis significatius. Els formats avançats de modulació, implementats a nivell de processat del senyal digital, habiliten la transmissió a alta velocitat. Mentre que a la capa de xarxa, l'espectre òptic es dividit en ranures flexibles ocupant l'ample de banda necessari segons la demanda de tràfic. La transmissió a alta velocitat és fa més tangible un cop habilitades totes aquestes funcionalitats. D'aquesta manera un dels principals objectius d'aquesta tesis es introduir flexibilitat al sistema. A demés, minimitzar el cost i maximitzar l'eficiència espectral del sistema són també dos aspectes crucials a considerar en el disseny del transmissor i receptor. Aquesta tesis investiga l'ús de la tecnologia Optical Orthogonal Frequency Division Multiplexing (OFDM) basada en la transformada de Fourier (FFT) i la de Hartley (FHT) per tal de dissenyar un sistema flexible i capaç de transmetre a alta velocitat a través de la fibra òptica. Per tant, es proposen diferent solucions de baix cost vàlides per a utilitzar en xarxes òptiques elàstiques. En primer lloc, s'investiguen i es proposen sistemes basats en detecció directa per tal de suportar la present i futura demanda. Després d'una introducció dels principis d' OFDM i la seva aplicació als sistemes òptics, s'introdueixen alguns dels problemes d'aquesta modulació. En particular, es presenten el Peak-to-Average Power Ratio (PAPR) i els sorolls de clipping i de quantizació com a limitació dels sistemes OFDM. S'analitzen tècniques de reducció de PAPR per tal de reduir l'impacte d'aquests impediments. També es proposen tècniques de baixa complexitat per a reduir el PAPR basades en la FHT. Finalment, s'utilitzen algoritmes d'assignació de bits i de potència, Bit Loading (BL) i Power Loading (PL), per tal de combatre la dispersió cromàtica quan es transmet pel canal òptic. Amb la implementació dels algoritmes de BL i PL, es poden dissenyar transmissors i receptors flexibles adaptant la velocitat a la demanda del moment i a les actuals condicions de la xarxa. En particular, els símbols OFDM es creen mapejant cada portadora amb un format de modulació diferent segons el perfil del canal. El sistema és validat experimentalment mostrant les prestacions i els beneficis d'incloure flexibilitat per tal de facilitar la transmissió a alta velocitat i cobrir les necessitats de l'Internet del futurDebido al crecimiento del tráfico IP y de la demanda de servicios de banda ancha, las redes ópticas están experimentando cambios significativos. Los formatos avanzados de modulación, implementados a nivel de procesado de la señal digital, habilitan la transmisión a alta velocidad. Mientras que en la capa de red, el espectro óptico se divide en ranuras flexibles ocupando el ancho de banda necesario según la demanda de tráfico. La transmisión a alta velocidad es más tangible una vez habilitadas todas estas funcionalidades. De este modo uno de los principales objetivos de esta tesis es introducir flexibilidad en el sistema. Además, minimizar el coste y maximizar la eficiencia espectral del sistema son también dos aspectos cruciales a considerar en el diseño del transmisor y receptor.
Esta tesis investiga el uso de la tecnologia Optical Orthogonal Frequency Division Multiplexing (OFDM) basada en la transformada de Fourier (FFT) y en la de Hartley (FHT) con tal de diseñar un sistema flexible y capaz de transmitir a alta velocidad a través de la fibra óptica. Por lo tanto, se proponen distintas soluciones de bajo coste válidas para utilizar en redes ópticas elásticas.
En primer lugar, se investigan y se proponen sistemas basados en detección directa con tal de soportar la presente y futura demanda. Después de una introducción de los principios de OFDM y su aplicación en los sistemas ópticos, se introduce el principal problema de esta modulación. En particular se presentan el Peak-to-Average Power Ratio (PAPR) y los ruidos de clipping y cuantización como limitaciones de los sistemas OFDM. Se analizan técnicas de reducción de PAPR con tal de reducir el impacto de estos impedimentos. También se proponen técnicas de baja complejidad para reducir el PAPR basadas en la FHT.
Finalmente, se utilizan algoritmos de asignación de bits y potencia, Bit Loading (BL) y Power Loading (PL), con tal de combatir la dispersión cromática cuando se transmite por el canal óptico. Con la implementación de los algoritmos de BL y PL, se pueden diseñar transmisores y receptores flexibles adaptando la velocidad a la demanda del momento y a las actuales condiciones de la red. En particular, los símbolos OFDM se crean mapeando cada portadora con un formato de modulaci_on distinto según el perfil del canal. El sistema se valida experimentalmente mostrando las prestaciones y los beneficios de incluir flexibilidad con tal de facilitar la transmisión a alta velocidad y cubrir las necesidades de Internet del futuro
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