Page 1

All-optical hash code generation and

verification for low latency

communications

Yvan Paquot,1∗Jochen Schr¨ oder,1Mark D. Pelusi1

and Benjamin J. Eggleton1

1Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS),

Institute of Photonics and Optical Science (IPOS)

School of Physics A28, University of Sydney, NSW 2006, Australia

* yvan@physics.usyd.edu.au

Abstract: We introduce an all-optical, format transparent hash code gen-

erator and a hash comparator for data packets verification with low latency

at high baudrate. The device is reconfigurable and able to generate hash

codes based on arbitrary functions and perform the comparison directly in

the optical domain. Hash codes are calculated with custom interferometric

circuits implemented with a Fourier domain optical processor. A novel

nonlinear scheme featuring multiple four-wave mixing processes in a single

waveguide is implemented for simultaneous phase and amplitude compar-

ison of the hash codes before and after transmission. We demonstrate the

technique with single polarisation BPSK and QPSK signals up to a data rate

of 80 Gb/s.

© 2013 Optical Society of America

OCIS codes: (060.1155) All-optical networks; (190.4380) Nonlinear optics, four-wave

mixing.

References and links

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Received 18 Jul 2013; revised 12 Sep 2013; accepted 14 Sep 2013; published 30 Sep 2013

7 October 2013 | Vol. 21, No. 20 | DOI:10.1364/OE.21.023873 | OPTICS EXPRESS 23873

Page 2

13. J. E. McGeehan, S. Kumar, and A. E. Willner, “Simultaneous optical digital half-subtraction and -addition using

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208 (2009).

20. M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion

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1.Introduction

Detection and correction of mistaken data is a critical function in information systems. There-

fore, numerous error management techniques have been developed, including Forward Error

Correction (FEC), checksums, cyclic redundancy checks and more generally hash functions [1].

The underlying principle of any hash method is the computation of a number as a signature of a

data packet mapping the original data to a value in a smaller mathematical space [2]. Identical

blocks of data yield the same hash code, while different ones should have different signatures,

heralding an error. In a transmission system, failure can be detected with high probability by

comparing the hash before and after propagation. With a higher degree of complexity, FEC

algorithms are able to repair corrupted data without re-transmission, and are in use in most cur-

renttelecommunicationnetworks[3]allowingcodinggainsofover10dB[4–6].Theseintegrity

check methods imply the transmission of some redundant information (i.e. the hash codes) and

usually result in increased latency and power consumption due to the required processing.

In the context of high bandwidth optical communications, these algorithms are part of the

Digital Signal Processing (DSP) performed at both the transmitter and the receiver [7]. The

intense processing operations required introduce constraints in terms of bandwidth, energy ef-

ficiency and latency [8,9]. An implementation of a hash function directly in the optical domain

could significantly reduce these burdens. A recent report established the feasibility of a Semi-

conductor Optical Amplifiers (SOA) based hash encoder and decoder. However, the proposed

scheme only works for On-Off Keying (OOK) signals of limited bandwidth [10,11] and cannot

be generalised to advanced modulation formats which are now used extensively in communi-

cation systems [12].

Here we introduce and demonstrate for the first time an all-optical, format transparent, hash

code verified transmission link comprising a low latency hash code generator and comparator.

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In this scheme, the hash code is generated using a Fourier domain optical processing opera-

tion on the data signal, while the hash code comparator is implemented via coherent optical

subtraction based on multiple Four Wave Mixing (FWM) processes in a nonlinear medium.

Data validation consists of comparing hash signals calculated before and after transmission.

In contrast to most electronic methods, which incorporate the hash codes into the bitstream or

packets, we transmit the codes on a separate wavelength channel thus avoiding the need for

sophisticated bit-rate adjustment, check symbol insertion and segmentation schemes. Experi-

ments are reported for a 40 Gb/s single channel Binary Phase Shift Keying (BPSK) signal and

a 80 Gb/s single channel Quadrature Phase Shift Keying (QPSK) signal. Our approach can be

easily scaled to higher symbol rates and modulation formats without modification. This work

represents a key result for ultra-low latency optical networks.

2. Principle

Hash based error detection codes require transmission of redundant information along with

the data. In most electronic systems it is concatenated to the payload of each data packet.

In our method however, the original data channel remains unchanged while the hash code is

transmitted on a parallel wavelength channel as depicted on Fig. 1. At the receiver side, integrity

of the data is checked by comparing the hash code from before to the one after transmission via

all-optical signal subtraction.

Data

Modulator

Optical

source

Data

Transmission

Detector

packet

Hash

calculation

Hash

calculation

=

?

Error signal

Hash

generator

Hash

comparator

Error signal

hash

data

hash

data

Fig. 1. Principle of the all-optical hash key verified link. Hash codes are generated inside

the transmitter and communicated through the network along with the data in an adjacent

channel. At the receiver side, hash codes are recalculated from the data channel and com-

pared to the transmitted hash. On the diagram, red components indicate optical devices and

green the electrical domain.

The functional diagram in Fig. 2 illustrates the successive transformations of the optical

channels. The same data is encoded onto two phase locked WDM channels. One channel is

kept as it is, while the other is used as a base for computing the hash signal (Hash 1) in a first

hash generator device. Both channels are then propagated through the link. At the receiver, the

comparison is performed by calculating the hash (Hash 2) from the received data channel using

the same hash function and combining it with Hash 1 and two phase-locked pump waves. The

four waves, occupying different wavelengths, are sent through a nonlinear medium to carry out

the hash comparison. Upon nonlinear propagation, the two hash channels are translated to the

same wavelength channel (Idler) by degenerate FWM with the two pump waves. If the relative

phase between the hash channels is set to π, the wavelength conversion will result in a coherent

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subtraction, i.e. if the hash codes are the same, then destructive interference cancels the optical

power at the translated wavelength. A transmission error causing the hash codes to differ would

unbalance the interference term and trigger a spike at the idler wavelength, producing an error

signal which can be extracted by bandpass filtering.

Hash 1

Hash 2

Hash 1

Data

Duplicate

data

Pumps

Error

signal

Filter

Idler

Transmission

link

Transmitter Receiver - error detection

Hash

generator

Hash

generator

+ phase

control

Nonlinear mixing

Fig. 2. Functional diagram. Arrows aligned with a same horizontal level represent signals

at a same wavelength.

The hash code of an N-symbol packet is calculated by multiplying N successive symbols

with custom weight and sign coefficients and coherently adding them. Such an operation can

be realized using a multipath interferometric circuit (MIC) with tuneable phase offset and at-

tenuation, represented on the right part of Fig. 5. The sign of the coefficients is controlled by the

relative phase of the different interferometric arms, while the weight can be set via attenuation.

We use a Fourier Domain Programmable Optical Processor (FD-POP) configured as a custom

MIC by implementing the corresponding phase and amplitude transfer functions. Unlike pre-

vious methods [10,13], this is compatible with advanced modulation formats and allows for

easily reconfiguring packet length and the hash function without any physical change to the

setup. Wavelength selective delay, phase control and attenuation are implemented in the FD-

POP [14,15], as detailed in section 3. The resulting hash signal takes the form of a multilevel

phase- and amplitude-coded channel at same rate as the data. Note that, because the hash code

is generated from N data symbols, its required bandwidth can be reduced to 1/Nth of this value

by sampling, as further explained in section 4.

In contrast to previous systems that only allowed for comparing binary intensity coded sig-

nals, our hash comparator enables simultaneous comparison of multi-level phase and amplitude

encoding. A more detailed explanation of the scheme is depicted in Fig. 3. The two phase-

locked hash channels to be compared (Eqs (1) and (2)) are co-propagated with two pumps

separated by half their spectral separationΔν

2(Eqs (3) and (4)).

EH1ei2πνH1t

EH2ei2π(νH1+Δν)t

EP1ei2πνP1t

EP2ei2π(νP1+Δν

EH1

EH2

EP1

EP2

=

(1)

(2)

(3)

=

=

=

2)t

(4)

These four waves have phasors EH1, EH2, EP1and EP2, amplitudes AH1, AH2and AP1=

AP2and wave vectors kH1, kH2, kP1and kP2. As a consequence of the choice of frequency

separations, first order FWM products of the pairs Hash 1 - Pump 1 and Hash 2 - Pump 2 appear

at same frequency to add up coherently and have phasors EI1= AI1eiφI1and EI2= AI2eiφI2. The

phase matching condition of FWM [16] determines the wave vectors of the generated idlers

kI1= −kH1+2kP1and kI2= −kH2+2kP2. By developing the expression of the idler fields, one

can deduce the phase relations of these idlers [17]:

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φI1

φI2

=

=

−φH1+2φP1= −φH1+2φP

−φH2+2φP2= −φH2+2φP

(5)

(6)

Where the two phase locked pumps have been set with equal phases φP1=φP2=φP. In order

to operate coherent subtraction, the hash signals are set with opposite phases φH2= φH1+π.

Given that the degenerate FWM products amplitudes verify the relations AI1∝ AH1A2

AI2∝ AH2A2

EI1+EI2= AI1eiφI1+AI2eiφI2∝?AH1e−iφH1+AH2e−iφH2?

=(AH1−AH2)e−iφH1

The absolute phase φPis not relevant for the error signal and can be omitted. The subtraction in

the complex space implies that the total intensity at idlers frequency cancels only if AH1=AH2.

Any mismatch between the hash signals translates into an idler spike signalling an error. This

P1and

P2, the total idler field generated is

EItot

=

× ei.2φP

? ?? ?

absolute phase offset

(7)

(8)

Hash

signals

Δʋ

Pumps

Δʋ/2

Idlers

ɸP1 ɸP2

f

ɸH1 ɸH2

Idlers

Amplitude

and phase

control

(3)

Hash 1

Hash 2

Pumps

BPF

Fig. 3. Principle of the all optical coherent signal comparator. Left: hash signals to be com-

pared are copropagated with pumps through a third-order nonlinear medium after relative

phase and amplitude adjustment. Inset: Two simultaneous FWM-based wavelength shifting

processes occur inside the nonlinear medium. Two pumps with half the frequency spacing

of the hash signals bring both idlers to the same wavelength. Initial configuration of the

signals with opposite phases (represented by arrows facing in opposite directions) causes

the idlers to interfere destructively so as to cancel the total idler product when both hash

are equal. Mismatch between hash codes causes an idler spike. Bandpass filtering (BPF) of

the total idler extracts the error signal.

requires Hash 1 and Hash 2 to be phase locked (which is automatically the case if the two

initial copies of the signal come from the same broadband source) and Pump 1 and Pump 2 to

be phase locked. Importantly no phase relation is required between the hash channels and the

two pumps.

3.Experiment and results

The experimental setup is shown in Fig. 4. The signal is generated from a mode-locked fibre

laser that delivers a 40 GHz pulse train (2 ps full width at half maximum) at 1550 nm. The

spectrum is broadened inside a highly nonlinear fibre (HNLF) and filtered to obtain a quasi-

flat comb spectrum over a bandwidth of 6 nm [18]. The pulse train is then encoded using two

successive phase modulators driven by two independent pseudo-random bit sequences (PRBS)

of either 64 bits (Figs. 6 and 8) or 231−1 bits (Fig. 10) and biased to deliver a π andπ

shift in order to generate an 80 Gb/s QPSK signal [19]. The 40 Gb/s BPSK signal is generated

by bypassing the second modulator.

The hash is calculated by coherent addition of N successive symbols with custom phase and

amplitude offsets. This could be performed in an integrated MIC with calibrated phase shifts

2phase

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SMF

50m

DCF

20m

40GHz flat

frequency

comb

6 nm bandwidth

PM

ɸ=π

PRBS

data

Clock

40GHz

EDFA

PC

EDFA

BPF

5 nm

PC

HNLF

30m

EDFA

PBS

Delay

BPF

70 GHz

EDFA

BPF

300 mW

FD-

POP

Pre-transmission

hash code

generation

Post-transmission

hash

+ Phase control

FD-

POP

Sampling

scope

Detector

Pumps

PM

ɸ=π/2

Hash

comparator

Fig. 4. Experimental setup. A wideband flat frequency comb is QPSK-encoded with two

successive phase modulators (PM). Hash keys are calculated before and after transmission

inside Fourier-domain programmable optical processors (FD-POP). Combination with a

pump pulse train and wavelength-selective phase control by the second FD-POP conditions

the signals for coherent hash comparison inside a 30 m section of highly nonlinear fibre

(HNLF). PM: phase modulator ; BPF: bandpass filter.

and attenuations on each arm illustrated on the right of Fig. 5. Here we use a more flexible

solution based on a FD-POP. The effect of the linear MIC is fully represented by its spectral

phase and amplitude transfer function programmed into the FD-POP device.

ɸ3

ɸ2

ɸ1

filter

phase

control

delay

Hash

channel

generation

Adjacent

channel

pass

filter

−40

−30

−20

−10

0

Attenuation [dB]

−50050100150200

−5

0

5

f [GHz]

φ[rad]

Hash channel

generation

Adjacent channel

pass

attenu-

ation

β3

β2

β1

ES

Ej

EH

Fig. 5. Hash code generation by Fourier domain optical processing. Left: power and phase

transfer functions programmed in the FD-POP. The spectral profiles applied to the data

signal reproduce the characteristics of a multipath interferometric circuit (MIC) coherently

adding successive bits. Blue, green and red traces correspond to different MIC configura-

tions. The other channel is left untouched through a bandpass filter transfer function. Right:

equivalent MIC implemented in the FD-POP.

The pass channel of the wavelength selective MIC is transmitted through a flat top bandpass

filter with constant phase. The hash channel results from equal splitting of the field ES= ASeiφS

into N arms, each delayed by an integer number of symbol lengths ΔLj= (j −1)ΔLsymbol

(j indexes the arms). Before recombination of the arms, each path is attenuated by βjand offset

in phase by φjaccording to the desired hash function equation. The field after propagation in

attenuation

????

fields are passively combined resulting in:

arm j is Ej=

1

√NASeiφS

?

βj

delay

? ?? ?

eikΔLj

phase offset

????

eiφj.

At the output of the device the delayed complex

EH=

N

∑

j=1

Ej=ASeiφS

√N

N

∑

j=1

?

βjei(kΔLj+φj)

(9)

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with 0≤βj≤1. Let us define νj=

that kΔLj= 2πν

c

ΔLjbeing the frequency offset associated to the delay j such

νj. The amplitude transfer function is written

H

=

|EH|2

|ES|2=1

1

N

N

?????

N

∑

j=1

?

βje

i

?

2π.ν

νj+φj

??????

2

(10)

=

⎛

⎝

?

N

∑

j=1

?

βjcos

?

2π.ν

νj+φj

??2

+

?

N

∑

j=1

?

βjsin

?

2π.ν

νj+φj

??2⎞

⎠(11)

and the phase transfer function is

φ = angle(EH) = atan

?Im(EH)

Re(EH)

?

= atan

⎛

⎝∑N

j=1

?βjsin

?

2π.ν

?

νj+φj

?

∑N

j=1

?βjcos

2π.ν

νj+φj

?

⎞

⎠

(12)

The FD-POP allows for custom control of the spectral phase and amplitude with a resolu-

tion of 5 GHz. Implementation of the transfer functions of Eqs. (11) and (12) realizes the

hash key function. Figure 5 shows examples of spectral transfer functions for various MIC

BPSK : BN - BN+1

BPSK : BN - BN+1 - BN+2

1

3

QPSK : BN - BN+1 - BN+2

1

3

QPSK : BN - BN+1

50

0

8

Time [ps]

Power [mW]6

4

2

40 302010

Fig. 6. Experimental intensity plots of the hash codes for BPSK (first and second columns)

and QPSK (third and fourth columns) signals. Information encoded in the phase of the hash

signals is not represented. Time traces (top row) and eye diagrams (bottom) of the 64 bits

patterns are measured with a sampling oscilloscope. Blues traces show simulation results

for the corresponding bit patterns.

configurations. The red trace corresponds to a 2-symbols packet with the hash definition

HN= BN+BN+1eiπ, where HNand BNare the optical field amplitudes of the hash and data

at symbol N. The green and blue traces correspond to 3-symbols packets with hash definitions

respectively HN= BN+BN+1eiπ+1

definitions can be obtained by choosing linear combinations of the BNwith other coefficients

and phases.

The calculated hash keys using the above functions for 40 Gb/s BPSK and 80 Gb/s QPSK

signals made of 64 symbols are shown on Fig. 6. Changing the hash parameters leads to dif-

ferent hash sequences for the same initial signal. In this experiment, hash key and data signal

are transmitted through a short fibre link made of 50 m of SMF and 20 m of DCF. Note that

the time traces and eye diagrams represent only the intensity of the hash channel. Information

is also contained in its phase, which is not shown in the traces but is taken into account by the

3BN+2eiπand HN= BN+BN+1+2

3BN+2eiπ. Other hash

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coherent signal comparator. Noise is mostly introduced in the signal generation by the phase

modulator delivering theπ

In order to compare the hash key calculated from the transmitted signal to the input signal

hash we use a second FD-POP at the end of the link. The FD-POP calculates the receiver hash

key from the transmitted data channel using the same phase and amplitude transfer function as

describedforthetransmitter,whileleavingthetransmittedhashchanneluntouched.Therelative

phase between the transmitted hash channel and the hash calculated from the transmitted data

signal is adjusted to π by the FD-POP to result in coherent subtraction.

2phase shift.

-10

-30

-50

-70

154815531558

Wavelength [nm]

Power [dBm]

Hash 1Hash 2

Pump 1 Pump 2

Idlers

Δʋ

Δʋ/2

H1 - H2 (no error)

H1 - H2 (all errors)

H1 - H2 (1 error)

Fig. 7. Experimental optical spectrum at the HNLF output. Insert: the total idler cancels out

for identical hash and not if they differ. Solid: both hash signals equal ; dotted: one error

every 512 symbols ; dashed: hash functions different for both signals.

The pump pulse train is coupled to a second input port of the FD-POP and shaped to obtain

a dual pump configuration with half the spectral separation of the hash signals. The hash and

pump inputs are combined inside the FD-POP to form the input of the comparator. After am-

plification to a total optical power of 300mW and out-of-band noise filtering, nonlinear mixing

occurs in a 30 m span of HNLF. The signals both have powers 10 dB lower than the pumps.

Figure 7 shows the output spectrum measured after the HNLF for three configurations: solid

green: the two hash functions are identical, resulting in idler output power at zero level due to

coherent subtraction (H1−H2); dashed black: the hash functions are programmed differently

at the receiver and the emitter, resulting in unbalanced coherent subtraction and therefore output

pulses indicating errors ; dotted blue: the hash functions are equal, but one bit every 512 bits

presents an error that triggers an idler spike at the comparator output. However, the effect on

the spectrum is barely noticeable in the last case, due to the low duty cycle (1/512) of the error

pulses.

Error detection is performed in the time domain, by narrow band (70 GHz) spectral filtering

at the frequency of the first order FWM products (detailed in the inset), to extract the idler.

After amplification, the hash verification signal is viewed on a sampling scope with 65 GHz

bandwidth.

The amplitude of the error signal translates to the degree of mismatch between the hash

keys and the degree of packet reliability within the limit of small errors. Indeed a small phase

and amplitude offset applied to one symbol causes a proportional change in the hash function.

Note however, that stronger perturbations or changes to multiple symbols have very small, but

nonzero, probability of cancelling out in the hash calculation.

Figure 8 relates the comparator output to the spectrum of the extracted idler for an 80 Gb/s

QPSK data. When both hash functions are generated using the same parameters before and

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2

0

Time [ns]

Power [mW]

6

4

2

1.61.2 0.80.4

Fig. 8. Time traces of the error signal after bandpass filtering of the idler. Top: Idler channel

filtered out. Bottom left: both hash signals equal. Bottom right: hash signals different. Hash

code mismatch is reflected by a nonzero error signal after optical subtraction.

after transmission, the mismatch signal after the comparator is constant zero, reporting no error

(bottom left). If the hash signals are generated with different hash functions on both generators,

the output is nonzero heralding transmission errors (bottom right) at every symbol.

Figure 9 shows a variation of the setup introduced in Fig. 4 in order to create localized errors

in the data signal in the case of BPSK encoding with 231−1 PRBS data. The two replicate

channelsencoded withafirstphasemodulator(PM)aresplitontotwoarms.Onepassesthrough

a second phase modulator driven by a separate pattern generator operating a π phase shift to

one bit every 512 symbols. The other arm is delayed and adjusted in phase with a phase shifter

(PS) to exactly match the path lengths of the interferometer. Both paths are recombined inside

the first FD-POP operating the hash calculation by assigning the two wavelength channels to

different ports of the device. This structure keeps the two data channels identical, except for

introducing a one symbol error every 512 symbols. The relative phase between the two paths is

setmanuallyviathephaseshifterandphaselockingismaintainedbyplacingtheinterferometric

structure inside an enclosure to isolate it from vibrations and thermal drift.

40GHz flat

frequency

comb

6 nm bandwidth

PM

PRBS

data

Clock

40GHz

EDFA

PC

BPF

5 nm

Pre-transmission

hash code

generation

PM

Delay

PS

Error

FD-

POP

Channel

with error

Clean

channel

Fig. 9. Variation of the signal generator to create localized errors in a BPSK signal. The

two replicate channels are split onto two arms, one being affected by a π phase shift of one

bit period every 512 symbols. Both paths are recombined into the first FD-POP acting as a

wavelength selective switch. PM: phase modulator ; PS: phase shifter.

A single bit error yield idlers mismatch in the comparator at the symbols that have different

hash keys. For a hash function calculated for data packets made of N symbols, the error signal

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Page 10

exhibits N spikes, due to the fact that all of the N hash keys involving the mistaken bit are

altered. Figure 10 shows the comparator output for a single bit error when data packets contain

3 bits (N=3). Similarly, a single bit error during transmission in a real system would change the

hash code of the data channel, leading to a spike at the comparator output.

No error

-60

Power [dB] -40

-50

1557.0 1556.3Wavelength [nm]

Fig. 10. Time traces of the error signal after bandpass filtering of the idler in the case of a

single error. Top: Idler channel filtered out. Bottom left: both hash signals equal (no error).

Bottom right: a single error causes a spike in the error signal.

4. Discussion

4.1.

In order to verify the validity of the technique for propagation through a longer path, we im-

plemented the system on a 40 Gb/s OOK link made of 20.72 km of SMF and a matching

spool of DCF (340 ps/nm) as presented on the left diagram of Fig. 11. Residual dispersion was

further compensated inside the end-of-link FD-POP by applying an additional quadratic spec-

tral phase. The hash key channel was configured for 3-bit packets according to the equation

HN= BN−BN+1+1

The only concern related to the addition of the mid-haul link was a slow scale timing drift

between the transmitted signal and the pump (that follows another path) due to ambient tem-

perature fluctuations. In our setup, the pump and signals were found to be significantly desyn-

chronized within a period of about 10 s. This issue, however, would not show up in a real system

where the pump pulse train would be generated based on a clock recovery module from the re-

ceived signal. Importantly, the coherent comparator is not affected by the phase drift between

hash and pump channels as mentioned in the principle section.

Figure 11 features the optical spectrum of the idlers and the corresponding eye diagrams

for two cases. The solid green trace shows the destructive interference between idlers when

transmitted and received hashes are equal and no error occurs. The dashed black trace marks

the increase in total idler power when the comparator is unbalanced by configuring both hashes

with different settings, which is equivalent to errors occurring at every bit. The corresponding

time trace of the error signal, measured with a sampling oscilloscope, still comprises symbols

apparently without error (error signal at zero), which is due to the fact that the data packets are

formed of only three bits. Hence there is still a high probability of having equal hash keys for

different signals.

Tolerance to long distance transmission

3BN+2.

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Page 11

2

0

Time [ns]

Power [mW]

6

4

1

0.8 0.60.4 0.1

Fig. 11. Hash key verified link of 20.72 km. Left: composition of the link. Right: Idler chan-

nel filtered out in case of both equal (green) and different (black) hash function definitions.

The corresponding eye diagrams show the error signal in the time domain.

4.2.

The potential for high baudrate operation enabled by the ultra fast reaction time of Kerr effect

exploited in the comparator offers a solution for error management at symbol rates inaccessible

to electronics.

Our implementation of the hash generator is particularly well-suited for ultra high baudrate

OTDM signals. The delay of our FD-POP is limited to about 50 ps [20], which at 40 Gbaud

only allows hash calculation for packets of up to 3 symbol (note that this still corresponds to

a bit-length of 6 in case of QPSK). However, increasing the symbol rate to 640 Gbaud, for

example, would enable processing of packets of up to 32 symbols. Also hash code based verifi-

cation of an OTDM channel only requires one instance of the hash generation and comparison

infrastructure, while WDM systems would need separate hash comparators for all channels.

Extension of the method to higher symbol rates

4.3.

The latency introduced by our system is primarily determined by the 150 ns propagation time

throughthe30mofHNLF.Thislatencycanbealmostentirelyremovedbyeitherunwindingthe

HNLFsothatitispartofthetransmissionlinkorbyreplacingitbyanon-chipnonlinearity[21].

We acknowledge the fact that DSP based error correction mechanisms provide much more

sophisticated solutions. However, these introduce significant latency that can be removed by

using the all-optical method proposed in this work.

Latency

4.4.

In the experiment described in this paper, the hash channel has the same bandwidth as the

data channel because a hash code is generated at every symbol period. However, it can be

downsampled to 1/N of the original baudrate to keep only one hash code per data packet made

of N symbols, which is enough for error detection. This could be done for example, by sampling

the hash with an electro-absorption modulator [22] followed by a narrow-band filter or, for ultra

high bandwidth OTDM signals, by nonlinear optical sampling [23, 24]. The resulting lower

bandwidth hash channel would be less subject to distortions and have better spectral efficiency.

Hash channel sampling for improved bandwidth efficiency

4.5.

Residual chromatic dispersion can cause timing misalignment of the symbols in the data and

hashchannelstransmittedatdifferentwavelengths.Tocounterthis,theFD-POPprovidesaflex-

ible way to compensate for group velocity dispersion as well as higher orders of dispersion, at

the same time as they apply the hash phase masks [20]. This is the method used in our 20.72 km

Effect of dispersion

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Page 12

link transmission to remove the residual delay due to imprecise dispersion compensation by the

DCF section.

Also, solutions have been demonstrated for automatic compensation of fluctuations of multi-

ple orders of dispersion using a FD-POP as tuneable compensator [25]. In presence of strongly

varying dispersion, the FD-POP devices already used for the hash function generation can be

feedback-controlled to cancel dispersion in real time.

4.6.

The comparator requires the received data and hash signals to be phase locked. This condition

is automatically verified provided that the hash is generated from the signal itself and that both

channels propagate along the same path of fibres and amplifiers. Although the pumps involved

in the comparator must also be phase locked, no phase condition is required between signals

and pumps.

However, accidental desynchronization of the two channels or introduction of phase noise

in long amplified links may degrade the action of the comparator. A perturbation Δφ of the

relative phase between hash and data channels would introduce a maximum power inaccuracy

in the error signal of the order ofIADD

2

power when the phase relation is set in the adder configuration (φH1= φH2). A dependence

of the total idler power of this type has effectively been measured when sweeping the relative

phase over a 2π range (Fig. 12). In the case of our demonstration of a 20.72 km link reported

in paragraph 4.1, no effect of phase noise could be observed and the extinction ratio of the

coherent subtracter was similar to the one measured for the back-to-back transmission.

Phase relations

(1−cos(Δφ)), where IADDis the maximum total idler

−3−2−10123

0

0.005

0.01

0.015

∆φ[rad]

Idler inaccuracy [mW]

measurement

theory

Fig. 12. Theoretical and experimental inaccuracy in the hash subtraction as functions of the

phase perturbation between the two hash signals. The measurement was realized by feeding

two equal signals in the coherent comparator and sweeping over their relative phase.

5.Conclusion

We have shown flexible generation of hash keys using a linear optical device for high band-

width optical signals encoded with complex modulation formats. Comparison of hash keys

before and after transmission is implemented by coherent all-optical subtraction via a novel

dual FWM scheme. This scheme is to be considered as a compromise between the high latency

introduced by DSP FEC operation and a latency free link without error detection. The method

is demonstrated with an 80 Gb/s QPSK signal.

Acknowledgments

The authors acknowledge the Australian Research Council (ARC) Centres of Excellences Pro-

gram (Project CE110001018), Laureate Fellowship (Project FL120100029), Discovery Early

Career Researcher Award (DECRA) (Project DE120101329) and an ARC Linkage grant with

Finisar Australia (Project LP120100661).

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Received 18 Jul 2013; revised 12 Sep 2013; accepted 14 Sep 2013; published 30 Sep 2013

7 October 2013 | Vol. 21, No. 20 | DOI:10.1364/OE.21.023873 | OPTICS EXPRESS 23884