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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 23873–23884
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All-optical hash code generation and verification for low latency communications

Yvan Paquot, Jochen Schröder, Mark D. Pelusi, and Benjamin J. Eggleton  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 23873-23884 (2013)
http://dx.doi.org/10.1364/OE.21.023873


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Abstract

We introduce an all-optical, format transparent hash code generator 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 comparison 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 OSA

1. Introduction

Detection and correction of mistaken data is a critical function in information systems. Therefore, numerous error management techniques have been developed, including Forward Error Correction (FEC), checksums, cyclic redundancy checks and more generally hash functions [1

1. J. G. Proakis and M. Salehi, Digital Communications (McGraw-Hill Higher Education, 2008).

]. 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

2. A. A. Bruen and M. A. Forcinito, Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century (John Wiley & Sons, 2011).

]. 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 current telecommunication networks [3

3. D. Russell, The Principles of Computer Networking (Cambridge University Press, 1989).

] allowing coding gains of over 10 dB [4

4. T. Mizuochi, “Recent progress in forward error correction and its interplay with transmission impairments,” IEEE J. Select. Topics Quantum Electron . 12, 544–554 (2006). [CrossRef]

6

6. C. Xie, Y. Zhao, Z. Xiao, D. Chang, and F. Yu, “FEC for high speed optical transmission,” Proc. of SPIE-OSA-IEEE 8309, 83091R1 (2011).

]. These integrity 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

7. K. Azadet, E. Haratsch, and H. Kim, “Equalization and FEC techniques for optical transceivers,” IEEE J. Solid-State Circuits 37, 317–327 (2002). [CrossRef]

]. The intense processing operations required introduce constraints in terms of bandwidth, energy efficiency and latency [8

8. M. Freiberger, D. Templeton, and E. Mercado, “Low latency optical services,” in “National Fiber Optic Engineers Conference,” p. NTu2E.1 (OSA, Washington, D.C., 2012).

,9

9. Y. Miyata, K. Sugihara, W. Matsumoto, K. Onohara, T. Sugihara, K. Kubo, H. Yoshida, and T. Mizuochi, “A triple-concatenated FEC using soft-decision decoding for 100 Gb/s optical transmission,” in “Optical Fiber Communication Conference,” p. OThL3 (OSA, Washington, D.C., 2010).

]. An implementation of a hash function directly in the optical domain could significantly reduce these burdens. A recent report established the feasibility of a Semiconductor Optical Amplifiers (SOA) based hash encoder and decoder. However, the proposed scheme only works for On-Off Keying (OOK) signals of limited bandwidth [10

10. M. Suzuki and H. Uenohara, “Investigation of all-optical error detection circuit using SOA-MZI-based XOR gates at 10 Gbit/s,” Electron. Lett. 45, 224–225 (2009). [CrossRef]

,11

11. Y. Aikawa, S. Shimizu, and H. Uenohara, “Investigation of all-optical division processing using a SOA-MZI-based XOR gate for all-optical FEC with cyclic code,” Photonics in Switching 1, 3–5 (2010).

] and cannot be generalised to advanced modulation formats which are now used extensively in communication systems [12

12. P. Winzer and R. Essiambre, “Advanced optical modulation formats,” Proceedings of the IEEE 94, 952–985 (2006). [CrossRef]

].

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.

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 compared 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 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.

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

These four waves have phasors EH1, EH2, EP1 and EP2, amplitudes AH1, AH2 and AP1 = AP2 and wave vectors kH1, kH2, kP1 and 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 = AI1eI1 and EI2 = AI2eI2. The phase matching condition of FWM [16

16. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

] determines the wave vectors of the generated idlers kI1 = −kH1 + 2kP1 and kI2 = −kH2 + 2kP2. By developing the expression of the idler fields, one can deduce the phase relations of these idlers [17

17. J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express 17, 12555–12563 (2009). [CrossRef] [PubMed]

]:
ϕI1=ϕH1+2ϕP1=ϕH1+2ϕP
(5)
ϕI2=ϕH2+2ϕP2=ϕH2+2ϕP
(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 AI1AH1AP12 and AI2AH2AP22, the total idler field generated is
EItot=EI1+EI2=AI1eiϕI1+AI2eiϕI2(AH1eiϕH1+AH2eiϕH2)×ei.2ϕPabsolutephase offset
(7)
=(AH1AH2)eiϕH1
(8)
The absolute phase ϕP is 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 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.

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

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

18. T. Inoue and S. Namiki, “Pulse compression techniques using highly nonlinear fibers,” Laser & Photonics Review 2, 83–99 (2008). [CrossRef]

]. 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 and π2 phase shift in order to generate an 80 Gb/s QPSK signal [19

19. J. Yu and X. Zhou, “Multilevel modulations and digital coherent detection,” Optical Fiber Technology 15, 197–208 (2009). [CrossRef]

]. The 40 Gb/s BPSK signal is generated by bypassing the second modulator.

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.

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 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.
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 configurations. 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 = ASeS 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 βj and offset in phase by ϕj according to the desired hash function equation. The field after propagation in arm j is Ej=1NASeiϕSβjattenuationeikΔLjdelayeiϕjphaseoffset. At the output of the device the delayed complex fields are passively combined resulting in:
EH=j=1NEj=ASeiϕSNj=1Nβjei(kΔLj+ϕj)
(9)
with 0 ≤ βj ≤ 1. Let us define νj=cΔLj being the frequency offset associated to the delay j such that kΔLj=2πννj. The amplitude transfer function is written
=|EH|2|ES|2=1N|j=1Nβjei(2π.ννj+ϕj)|2
(10)
=1N((j=1Nβjcos(2π.ννj+ϕj))2+(j=1Nβjsin(2π.ννj+ϕj))2)
(11)
and the phase transfer function is
ϕ=angle(EH)=atan(Im(EH)Re(EH))=atan(j=1Nβjsin(2π.ννj+ϕj)j=1Nβjcos(2π.ννj+ϕj))
(12)
The FD-POP allows for custom control of the spectral phase and amplitude with a resolution 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 configurations. The red trace corresponds to a 2-symbols packet with the hash definition HN = BN + BN+1e, where HN and BN are 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+13BN+2eiπ and HN=BN+BN+1+23BN+2eiπ. Other hash definitions can be obtained by choosing linear combinations of the BN with other coefficients and phases.

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.

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 described for the transmitter, while leaving the transmitted hash channel untouched. The relative 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.

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 amplification 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.
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.

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 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.
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.

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 channels encoded with a first phase modulator (PM) are split onto two arms. One passes through 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 set manually via the phase shifter and phase locking is maintained by placing the interferometric structure inside an enclosure to isolate it from vibrations and thermal drift.
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 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.
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. Tolerance to long distance transmission

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

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.

4.2. Extension of the method to higher symbol rates

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

20. M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightw. Technol. 26, 73–78 (2008). [CrossRef]

], 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 verification 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.

4.3. Latency

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.

4.4. Hash channel sampling for improved bandwidth efficiency

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

22. A. Ellis, J. Lucek, D. Pitcher, D. Moodie, and D. Cotter, “Full 10 × 10 Gbit/s OTDM data generation and demultiplexing using electroabsorption modulators,” Electron. Lett. 34, 1766–1767 (1998). [CrossRef]

] followed by a narrow-band filter or, for ultra high bandwidth OTDM signals, by nonlinear optical sampling [23

23. P. Andrekson, “Picosecond optical sampling using four-wave mixing in fibre,” Electron. Lett. 27, 1440–1441 (1991). [CrossRef]

, 24

24. H. Hansen Mulvad, L. Oxenløwe, M. Galili, A. Clausen, L. Gruner-Nielsen, and P. Jeppesen, “1.28 Tbit/s single-polarisation serial OOK optical data generation and demultiplexing,” Electron. Lett. 45, 280–281 (2009). [CrossRef]

]. The resulting lower bandwidth hash channel would be less subject to distortions and have better spectral efficiency.

4.5. Effect of dispersion

Also, solutions have been demonstrated for automatic compensation of fluctuations of multiple orders of dispersion using a FD-POP as tuneable compensator [25

25. Y. Paquot, J. Schröder, J. Van Erps, T. D. Vo, M. D. Pelusi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Single parameter optimization for simultaneous automatic compensation of multiple orders of dispersion for a 1.28 Tbaud signal,” Opt. Express 19, 25512–25520 (2011). [CrossRef]

]. 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. Phase relations

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.

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

Acknowledgments

The authors acknowledge the Australian Research Council (ARC) Centres of Excellences Program (Project CE110001018), Laureate Fellowship (Project FL120100029), Discovery Early Career Researcher Award (DECRA) (Project DE120101329) and an ARC Linkage grant with Finisar Australia (Project LP120100661).

References and links

1.

J. G. Proakis and M. Salehi, Digital Communications (McGraw-Hill Higher Education, 2008).

2.

A. A. Bruen and M. A. Forcinito, Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century (John Wiley & Sons, 2011).

3.

D. Russell, The Principles of Computer Networking (Cambridge University Press, 1989).

4.

T. Mizuochi, “Recent progress in forward error correction and its interplay with transmission impairments,” IEEE J. Select. Topics Quantum Electron . 12, 544–554 (2006). [CrossRef]

5.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Communications Magazine, 48–55 (2010). [CrossRef]

6.

C. Xie, Y. Zhao, Z. Xiao, D. Chang, and F. Yu, “FEC for high speed optical transmission,” Proc. of SPIE-OSA-IEEE 8309, 83091R1 (2011).

7.

K. Azadet, E. Haratsch, and H. Kim, “Equalization and FEC techniques for optical transceivers,” IEEE J. Solid-State Circuits 37, 317–327 (2002). [CrossRef]

8.

M. Freiberger, D. Templeton, and E. Mercado, “Low latency optical services,” in “National Fiber Optic Engineers Conference,” p. NTu2E.1 (OSA, Washington, D.C., 2012).

9.

Y. Miyata, K. Sugihara, W. Matsumoto, K. Onohara, T. Sugihara, K. Kubo, H. Yoshida, and T. Mizuochi, “A triple-concatenated FEC using soft-decision decoding for 100 Gb/s optical transmission,” in “Optical Fiber Communication Conference,” p. OThL3 (OSA, Washington, D.C., 2010).

10.

M. Suzuki and H. Uenohara, “Investigation of all-optical error detection circuit using SOA-MZI-based XOR gates at 10 Gbit/s,” Electron. Lett. 45, 224–225 (2009). [CrossRef]

11.

Y. Aikawa, S. Shimizu, and H. Uenohara, “Investigation of all-optical division processing using a SOA-MZI-based XOR gate for all-optical FEC with cyclic code,” Photonics in Switching 1, 3–5 (2010).

12.

P. Winzer and R. Essiambre, “Advanced optical modulation formats,” Proceedings of the IEEE 94, 952–985 (2006). [CrossRef]

13.

J. E. McGeehan, S. Kumar, and A. E. Willner, “Simultaneous optical digital half-subtraction and -addition using SOAs and a PPLN waveguide.” Opt. Express 15, 5543–5549 (2007). [CrossRef] [PubMed]

14.

J. Schröder, O. Brasier, J. VanErps, M. A. F. Roelens, S. Frisken, and B. J. Eggleton, “OSNR monitoring of a 1.28 Tbaud signal by interferometry inside a wavelength-selective switch,” J. Lightw. Technol. 29, 1542–1546 (2011). [CrossRef]

15.

J. Schröder, M. A. F. Roelens, L. B. Du, A. J. Lowery, S. Frisken, and B. J. Eggleton, “An optical FPGA: reconfigurable simultaneous multi-output spectral pulse-shaping for linear optical processing,” Opt. Express 21, 690–697 (2013). [CrossRef] [PubMed]

16.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

17.

J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express 17, 12555–12563 (2009). [CrossRef] [PubMed]

18.

T. Inoue and S. Namiki, “Pulse compression techniques using highly nonlinear fibers,” Laser & Photonics Review 2, 83–99 (2008). [CrossRef]

19.

J. Yu and X. Zhou, “Multilevel modulations and digital coherent detection,” Optical Fiber Technology 15, 197–208 (2009). [CrossRef]

20.

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightw. Technol. 26, 73–78 (2008). [CrossRef]

21.

B. Eggleton, T. Vo, R. Pant, J. Schroder, M. Pelusi, D. Yong Choi, S. Madden, and B. Luther-Davies, “Photonic chip based ultrafast optical processing based on high nonlinearity dispersion engineered chalcogenide waveguides,” Laser & Photonics Reviews 6, 97–114 (2012). [CrossRef]

22.

A. Ellis, J. Lucek, D. Pitcher, D. Moodie, and D. Cotter, “Full 10 × 10 Gbit/s OTDM data generation and demultiplexing using electroabsorption modulators,” Electron. Lett. 34, 1766–1767 (1998). [CrossRef]

23.

P. Andrekson, “Picosecond optical sampling using four-wave mixing in fibre,” Electron. Lett. 27, 1440–1441 (1991). [CrossRef]

24.

H. Hansen Mulvad, L. Oxenløwe, M. Galili, A. Clausen, L. Gruner-Nielsen, and P. Jeppesen, “1.28 Tbit/s single-polarisation serial OOK optical data generation and demultiplexing,” Electron. Lett. 45, 280–281 (2009). [CrossRef]

25.

Y. Paquot, J. Schröder, J. Van Erps, T. D. Vo, M. D. Pelusi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Single parameter optimization for simultaneous automatic compensation of multiple orders of dispersion for a 1.28 Tbaud signal,” Opt. Express 19, 25512–25520 (2011). [CrossRef]

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(060.1155) Fiber optics and optical communications : All-optical networks

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 18, 2013
Revised Manuscript: September 12, 2013
Manuscript Accepted: September 14, 2013
Published: September 30, 2013

Citation
Yvan Paquot, Jochen Schröder, Mark D. Pelusi, and Benjamin J. Eggleton, "All-optical hash code generation and verification for low latency communications," Opt. Express 21, 23873-23884 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23873


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References

  1. J. G. Proakis and M. Salehi, Digital Communications (McGraw-Hill Higher Education, 2008).
  2. A. A. Bruen and M. A. Forcinito, Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century (John Wiley & Sons, 2011).
  3. D. Russell, The Principles of Computer Networking (Cambridge University Press, 1989).
  4. T. Mizuochi, “Recent progress in forward error correction and its interplay with transmission impairments,” IEEE J. Select. Topics Quantum Electron. 12, 544–554 (2006). [CrossRef]
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