Repetition Rate Multiplication of Pseudorandom Bit Sequences

Abstract

We develop a method for the repetition rate multiplication by a factor of 2 n of pseudorandom bit sequences (PRBSs). It makes recursive use of an optical or-gate in feedback and ensures that the complexity of the resulting circuit is independent of the multiplication factor or the PRBS order to be rate multiplied. We employ an all-optical circuit comprising of two nonlinear fiber Sagnac interferometers and show error-free quadrupling of 12.5-Gb/s PRBSs to 50 Gb/s.

Full text

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456IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 7, APRIL 1, 2009
Repetition Rate Multiplication of Pseudorandom
Bit Sequences
Christos Kouloumentas, Christos Stamatiadis, Student Member, IEEE,
Panagiotis Zakynthinos, Student Member, IEEE, and Hercules Avramopoulos
Abstract—We develop a method for the repetition rate multipli-
cation by a factor of ? of pseudorandom bit sequences (PRBSs).
It makes recursive use of an optical OR-gate in feedback and en-
sures that the complexity of the resulting circuit is independent
of the multiplication factor or the PRBS order to be rate multi-
plied. We employan all-opticalcircuit comprisingoftwononlinear
fiber Sagnac interferometers and show error-free quadrupling of
12.5-Gb/s PRBSs to 50 Gb/s.
Index Terms—Feedback loop, nonlinear optical loop mirror,
nonlinear Sagnac interferometer, optical OR-gate, pseudorandom
bit sequence (PRBS), rate multiplication.
I. INTRODUCTION
A
ularly, as data repetition rates increase. This difficulty is related
to the cost and delay in the installation of the new electronics
test and measurement equipment and proves insurmountable
for less well endowed laboratories.
We take as an example bit-error-rate (BER) test sets. At
present the transition from 10- to 40-Gb/s data rates is taking
place necessitating the replacement of 10-Gb/s test sets. At the
same time, hero experiments are being performed at 160 and up
to 640 Gb/s [1], [2]. For these rates, all-electronic pattern gen-
eration for testing is not available. All-optical pseudorandom
bit sequence (PRBS) generation has been shown [3], [4] but an
all-optical BER system would require an all-optical error de-
tector that remains to be demonstrated, and in stand-alone form
it will not have the programming flexibility of electronic pattern
generators. Currently the only practical option is to optically
multiplex the pattern provided by electronic pattern generators,
in fiber “split-shift-and-recombine” bit interleavers. These
interleavers require
stages to obtain
of the low-rate PRBS [5]. This means that their complexity in
terms of components and adjustments scales with the number
of stages, while further rate increases require the addition of
more stages. It is, therefore, of interest to investigate whether
it is possible to rate multiply PRBSs, in a single-stage multi-
plier, independent of the multiplication factor. In the present
communication, we develop such a method.
recurring difficulty for lightwave technology research
groups is the need to upgrade testing infrastructures reg-
rate-multiplication
Manuscript received October 31, 2008; revised December 17, 2008. Cur-
rent version published March 18, 2009. This work was supported by the Euro-
pean Commission under the ICT EURO-FOS Network of Excellence (Contract
224402).
The authors are with the Photonics Communications Research Laboratory,
School of Electrical and Computer Engineering, National Technical University
of Athens, 15773 Athens, Greece (e-mail: ckou@mail.ntua.gr; cstamat@mail.
ntua.gr; zakynth@mail.ntua.gr; hav@mail.ntua.gr).
Color versions of one or more of the figures in this letter are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LPT.2009.2013330
Fig. 1. (a) PRBS rate multiplication concept. (b) Example of rate quadrupling
of the ? ? ? PRBS: the numbers indicate the tributary channel that the pulses
belongto.(c)FiberSagnacinterferometeroperatingasa2?2exchange-bypass
switch, and truth table in case of continuous “1s” at In1.
Our method uses an OR-gate in feedback configuration with
a delay through the feedback loop such that successive transits
build the multiplied PRBS. In this implementation, we use two
nonlinear fiber Sagnac loops, one as the OR-gate and the second
asthewavelengthconverter,andquadruplicatea12.5-Gb/s
PRBS to 50 Gb/s. The resulting PRBS was evaluated by de-
multiplexing its four interleaved 12.5-Gb/s tributary channels.
They were error-free and each exhibited less than 1.5-dB power
penalty compared to the input PRBS.
II. OPERATING PRINCIPLE AND EXPERIMENTAL SETUP
Fig.1(a)showstheschemeinblockdiagramwiththe OR-gate
and the feedback loop whose purpose is to provide the specified
delay between the inputs of the OR-gate. According to the deci-
mation property of PRBSs, in order to achieve a multiplication
factor of
of a low-rate input PRBS, the length of the delay
mustbe
, whereis theperiod ofthis input PRBS[6]. For
1041-1135/$25.00 © 2009 IEEE
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KOULOUMENTAS et al.: REPETITION RATE MULTIPLICATION OF PSEUDORANDOM BIT SEQUENCES 457
Fig. 2. Experimental setup.
practical reasons, the feedback loop may have to be longer than
, in the general case
tive integer. The scheme effectively “folds” the
“split-shift-and-recombine” bit interleavers into a single stage
and builds the rate-multiplied PRBS after
the gate, thereafter reproducing it indefinitely.
Fig. 1(b) shows, as an example, the rate quadrupling of a
PRBS (1011100) with this concept. After the first OR op-
eration, the loop contains the input PRBS. In the next
transits through the gate, the pulses arriving through the feed-
back path are delayed with respect to the input PRBS by one
quarter of its period and are ORed with it, each time occupying
adjacent slots of the final bit stream. After a total of
operations or
transits through the feedback loop, the
rate-multiplied PRBS is created, containing
low rate PRBSs. The temporal window that was originally oc-
cupied by a single period of the low-rate PRBS is now occupied
by
periods of a PRBS of the same order but with
repetition rate. In Fig. 1(b), the four channels are indicated by
the numbers on top of the pulses. From that point onwards, the
OR-gate reproduces the same pattern and the circuit reaches a
steady-state. In principle this methodcan be appliedto any mul-
tiplication factor
or PRBS order.
In our implementation, the OR operation was obtained with
a 2
2 exchange-bypass switch [7], realized with a nonlinear
Sagnac loop as in Fig. 1(c). Depending on the control signal,
the switch operates in the bar or cross state. In the absence of
a control pulse, both inputs are mirrored out to their incoming
ports, whereas if a control pulse is present they are switched
over. As shown in the truth table of Fig. 1(c), if a stream of
“1s” enters In1, the result of the OR-operation between the other
input, In2, and the control signal appears at the Out2 port. Input
signals into ports In1 and In2 were the optical clock at the final
rate and wavelength
, and the low-rate PRBS at wavelength
, respectively. The control signal was the feedback stream.
Since the control signal must be at a different wavelength
from the inputs ator , the output signal in Out2 must be
wavelength converted before returning as feedback signal.
Fig. 2 shows the experimental setup. It consists of the signal
generation unit, the PRBS rate multiplier unit and the evalu-
ation stage. The outputs of two distributed-feedback (DFB)
laser diodes at
(1557 nm) and
ulated in an electroabsorption modulator (EAM) to provide
pulsetrains of 7 ps at 12.5 GHz. The pulsetrain at
a fiber Fabry–Pérot filter (FPF) with 50-GHz free-spectral
range (FSR) and finesse of 100. This output pulsetrain pro-
vided the 50-GHz optical clock signal and exhibited amplitude
, where is a nonnega-
stages of the
transits through
OR
interleaved,
higher
(1560 nm) were mod-
entered
modulation of about 1 dB. The second pulsetrain at
modulated in a Li:NbO electrooptical modulator (EOM) by
a
PRBS. The 50-GHz clock and the 12.5-Gb/s PRBS
were amplified in erbium-doped fiber amplifiers (EDFAs) and
entered SAGNAC1 as input signals. The nonlinear element was
180 m of highly nonlinear fiber (HNLF) with 1.21-ps/nm/km
dispersion and 10-W
km
of SAGNAC1, the signals at wavelengths
wavelength converted to
(1543 nm) in SAGNAC2. They
were separated with arrayed waveguide grating (AWG3), and
entered SAGNAC2 as control signals in a counterpropagating
configuration, with their relative timing preserved. The non-
linear element of SAGNAC2 was 260 m of the same type of
HNLF as in SAGNAC1. The average power of the control
signals at
and was limited by the available EDFAs
to 240 and 70 mW, respectively, and resulted in about 70%
switching of SAGNAC2. The wavelength-converted signal at
closed the feedback loop as control signal of SAGNAC1. It
was arranged to arrive delayed by
average power. The 50-Gb/s PRBS output was obtained from
AWG3 as the
output of the OR gate, and it was evaluated by
demultiplexing its four tributary channels.
was
parameter. At the output port
andwere
with 620-mW
III. RESULTS AND DISCUSSION
Fig. 3(a)-(b) illustrates traces and eye-diagrams of the
12.5-Gb/s input
PRBS obtained after the EOM and
the 50-Gb/s output PRBS after AWG3, and reveals that the
correct pattern was obtained. Fig. 4(a) shows traces of the
four 12.5-Gb/s interleaved PRBSs after demultiplexing with an
EAM, and the complete 50-Gb/s PRBS depicted with the same
trigger signal. The four channels have the same pattern form as
the input PRBS. They were obtained by successively delaying
the signal in the EAM by 20 ps each time. Union of the four
12.5-Gb/s traces yields the 50-Gb/s sequence on the bottom of
Fig. 4(a). In Fig. 4(b), we present the BER curves obtained for
the low-rate PRBS as back-to-back (B-2-B) measurement and
the four 12.5-Gb/s channels after demultiplexing. Error-free
operation was achieved for all channels with power penalty of
less than1.5 dB relativeto theinput PRBS, and less than 0.3-dB
variation between them. The primary reason for this penalty
was the 1-dB modulation in the FPF generated clock signal and
the insufficient power provided by the amplifier in the control
signal of SAGNAC2. In combination, these two constraints did
not allow for effective signal regeneration in the circuit. As
a result the optical signal-to-noise ratio degradation by 5 dB
of the 50-Gb/s PRBS signal compared to the input 12.5-Gb/s
signal could not be corrected. By modifying the feedback
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458IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 7, APRIL 1, 2009
Fig. 3. (a) and (b) Traces and eye-diagrams of input 12.5 Gb/s and rate multi-
plied 50-Gb/s PRBS.
Fig. 4. (a) Traces of the four tributary channels after demultiplexing. Bottom
trace is the 50-Gb/s PRBS. (b) BER curves of four tributary channels and input,
B-2-B, 12.5-Gb/s PRBS. BER data of output 12.5-Gb/s PRBS obtained from
quadrupled 3.125-Gb/s PRBS is also shown with empty circle curve.
delay, the circuit was also used for the rate multiplication of the
PRBS from 12.5 Gb/s to 50 and 25 Gb/s, and similar
results were obtained. To verify that the PRBS generated at
the aggregate rate is also error-free, we have quadruplicated a
3.125 Gb/s
PRBS. The optical signal generator unit of
Fig. 2 was modified to provide directly the 12.5-GHz optical
clock signal and the 3.125-Gb/s PRBS pattern. This ensured
a good quality optical clock signal and enough power to fully
switch the SAGNAC gates. The BER curve with the open
circles of Fig. 4(b) shows a power penalty of only 0.2 dB of the
rate multiplied output PRBS, compared to the 12.5-Gb/s optical
PRBS obtained directly from the electronic PRBS generator
(B-2-B).
The circuit was stable for characterization when care was
taken to prevent temperature fluctuations in the laboratory and
to protect the polarizationsensitive parts from random airdrifts.
Error-free operation could be sustained provided that variations
in the delay of its feedback path were within
timum value.
1 ps of the op-
TABLE I
INDICATIVE REQUIRED LENGTHS OF THE FEEDBACK LOOP (IN METERS)
To explore the versatility of our method, we investigated the
feedback delay required to obtain other PRBS orders and mul-
tiplication factors. Table I summarizes indicative delay lengths
formultiplicationofseveral10-Gb/sPRBSorderstoavarietyof
finalbitrates.Itwasobtainedontheassumptionthata5-nsprop-
agationdelaycorrespondsto1-mfiberlength.TableIshowsthat
multiplication of orders up to 15 can be easily accommodated
up to 640 Gb/s. Moreover, the parameter
can be chosen so that the lengths for the PRBS orders in the
same multiplication factor family lie in close proximity. The
down-scaling of the required delay as the multiplication factor
increases, enables the multiplication of the
640 Gb/s with a realistic length of about 2621.44 m. Again,
can be appropriately modified to allow for the required delays
of all PRBS orders to lie in close proximity. Finally, for higher
repetitionratemultiplicationfactors,thepowerrequirementsfor
the SAGNAC gates are expected to remain the same, provided
that the duty-cycle of the optical pulses at the final rate is also
retained.
in
PRBS to
IV. CONCLUSION
We have demonstrated a method to rate-multiply a PRBS by
a factor of
that makes recursive use of an optical OR-gate in
feedback. A circuit comprising of two nonlinear fiber Sagnac
interferometers was used to obtain error-free quadrupling of
12.5-Gb/s PRBSs to 50 Gb/s.
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