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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 9 — Apr. 23, 2012
  • pp: 10320–10329
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Noise suppression using optimum filtering of OCs generated by a multiport encoder/decoder

Takahiro Kodama, Naoya Wada, Gabriella Cincotti, Xu Wang, and Ken-ichi Kitayama  »View Author Affiliations


Optics Express, Vol. 20, Issue 9, pp. 10320-10329 (2012)
http://dx.doi.org/10.1364/OE.20.010320


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Abstract

We propose a novel receiver configuration using an extreme narrow band-optical band pass filter (ENB-OBPF) to reduce the multiple access interference (MAI) and beat noises in an optical code division multiplexing (OCDM) transmission. We numerically and experimentally demonstrate an enhancement of the code detectability, that allows us to increase the number of users in a passive optical network (PON) from 4 to 8 without any forward error correction (FEC).

© 2012 OSA

1. Introduction

During the past decade, coherent OCs, where the encoding information is embedded in the phases of the OC spectrum and/or time chips, have been largely investigated in literature, as they present enhanced correlation properties, with respect to incoherent OCs, and larger spectral efficiency. Novel coherent time-spreading (TS) encoding systems have been demonstrated using only compact optical passive devices, a planar cost-effective multiport device has been designed and its prototypes have been used in many different packet switching and OCDM experiments. The multiport encoder/decoder (E/D) has the unique capability of simultaneously generating/processing multiple phase shift keying (PSK) OCs [4

4. G. Cincotti, N. Wada, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-part I: modeling and design,” J. Lightwave Technol. 24(1), 103–112 (2006). [CrossRef]

].

In OCDM coherent systems, MAI and beat noises are the main issues that limit the system performance and many techniques have been proposed to overcome these impairments [5

5. X. Wang and K. Kitayama, “Analysis of beat noise in coherent and incoherent time-spreading OCDMA,” J. Lightwave Technol. 22(10), 2226–2235 (2004). [CrossRef]

]. The spectral amplitude of conventional TS OCs, using for instance M-sequence or Gold codes, is almost constant over a broad interval of frequencies (as shown in Fig. 1
Fig. 1 Conventional TS-OC spectrums.
), so that the pulse width of autocorrelation signal is only a few picoseconds large; in this case, it is possible to reduce the influence of MAI and beat noises by using optical time gating [6

6. S. Etemad, T. Banwell, S. Galli, J. Jackel, R. Menendez, P. Toliver, J. Young, P. Delfyett, C. Price, and T. Turpin, “Optical-CDMA incorporating phase coding of coherent frequency bins: concept, simulation, experiments,” OFC 2004, FG5, LA, CA, USA, Feb. 2004.

,7

7. H. Sotobayashi, W. Chujo, and K. Kitayama, “1.6-b/s/Hz 6.4 Tb/s QPSK-OCDM/WDM (4OCDM x WDM x 40Gb/s) transmission experiment using optical hard thresholding,” IEEE Photon. Technol. Lett. 14(4), 555–557 (2002). [CrossRef]

] and optical thresholding [8

8. J. H. Lee, P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Reduction of interchannel interference noise in a two-channel grating-based OCDMA system using a nonlinear optical loop mirror,” IEEE Photon. Technol. Lett. 13(5), 529–531 (2001). [CrossRef]

10

10. T. Hamanaka, X. Wang, N. Wada, A. Nishiki, and K. Kitayama, “Ten-user truly asynchronous gigabit OCDMA transmission experiment with a 511-chip SSFBG en/decoder,” J. Lightwave Technol. 24(1), 95–102 (2006). [CrossRef]

]. On the other hand, the width of the autocorrelation signal of the PSK OCs generated by a multiport E/D is much broader and smoother, and it is not possible to use optical thresholding, unless we do not refer to a complete synchronous transmission.

2. Analysis of the code detection performance

2.1 Numerical simulations

To evaluate the code detection performances, we have analyzed three different systems: without any filter, using a rectangular profile ENB-OBPF and with an ENB-OBPF obtained with an apodized fiber Bragg grating (FBG), as shown in Fig. 2(a)
Fig. 2 (a) Filtering characteristics of two ENB-OBPFs, with rectangular and apodized profile (b) Apodized filter shape (c) Architecture to evaluate the OC detection performance.
. The bandwidths of the rectangular and apodized filters have been chosen to fit with the main lobe of the autocorrelation spectrum (see Fig. 2(b)). The channel spacing of a 16-port device with 200GHz free spectral range (FSR) is 0.1nm, that almost equates the main lobe width of the autocorrelation spectrum [4

4. G. Cincotti, N. Wada, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-part I: modeling and design,” J. Lightwave Technol. 24(1), 103–112 (2006). [CrossRef]

]. The choice of an apodized FBG relies on its enhanced filtering features, with respect to standard FBG filters; also this device allows a flexible design of the optical transfer function and it is extremely compact so that it can be easily placed at the RN and OLT. The transfer function of apodized FBG filter is shown in Fig. 2(b). Figure 2(c) shows the architecture used to numerically evaluate the code performance: a 2ps pulse from a mode locked laser diode (MLLD) is sent to an optical switch (SW) that selects the input port k of the encoder. At the receiver output k’, we measure the autocorrelation signal if k’ = k, otherwise we detect the crosscorrelation signals. The two main parameters used to evaluate the system performance are the power contrast ratio (PCR) [12

12. N. Kataoka, N. Wada, X. Wang, G. Cincotti, A. Sakamoto, Y. Terada, T. Miyazaki, and K. Kitayama, “Field trial of duplex, 10Gbps x 8-user DPSK-OCDMA system using a single 16 x 16 multi-port encoder/decoder and 16-level phase-shifted SSFBG encoder/decoders,” J. Lightwave Technol. 27(3), 299–305 (2009). [CrossRef]

], i.e. the ratio between the average power of autocorrelation and crosscorrelation waveforms, and the ratio between the autocorrelation and crosscorrelation (ACP/CCP) peaks [4

4. G. Cincotti, N. Wada, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-part I: modeling and design,” J. Lightwave Technol. 24(1), 103–112 (2006). [CrossRef]

,11

11. G. Manzacca, M. S. Moreolo, and G. Cincotti, “Performance analysis of multidimensional codes generated/processed by a single planar device,” J. Lightwave Technol. 25(6), 1629–1637 (2007). [CrossRef]

]. Using the formulas of Refs [4

4. G. Cincotti, N. Wada, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-part I: modeling and design,” J. Lightwave Technol. 24(1), 103–112 (2006). [CrossRef]

,11

11. G. Manzacca, M. S. Moreolo, and G. Cincotti, “Performance analysis of multidimensional codes generated/processed by a single planar device,” J. Lightwave Technol. 25(6), 1629–1637 (2007). [CrossRef]

,12

12. N. Kataoka, N. Wada, X. Wang, G. Cincotti, A. Sakamoto, Y. Terada, T. Miyazaki, and K. Kitayama, “Field trial of duplex, 10Gbps x 8-user DPSK-OCDMA system using a single 16 x 16 multi-port encoder/decoder and 16-level phase-shifted SSFBG encoder/decoders,” J. Lightwave Technol. 27(3), 299–305 (2009). [CrossRef]

], we have calculated the PCR and ACP2/CCP2 ratio for different bandwidth values and different filtering shapes of the ENB-OBPF, that are shown in Fig. 3
Fig. 3 (a) ACP2/CCP2 at the decoder output #1 (b) PCR at the decoder output #1.
: we observe that the rectangular filter removes a large part of the autocorrelation signal. On the other hand, the apodized FBG filter has a narrower filter shape that better fits with the autocorrelation spectrum; at the same time, the FBG filter more efficiently eliminates the outband MAI.

2.2 Experimental validation

Figure 4
Fig. 4 Experimental setup and results.
shows the experimental setup that we used to evaluate the MAI and beat noise effects. The MLLD at 1550 nm is driven at 9.95328 GHz and the pulse stream is down-converted to 622.08 MHz by a LN-IM, to reduce the bit rate and completely eliminate the inter symbol interference (ISI). The OBPF after LN-IM is use only to remove the amplified spontaneous emission (ASE) noise. A 3 dB coupler splits the bit stream in two signals, that are forwarded to the ports #1 and #3 of a 16x16 multiport E/D. Each PSK OCs is composed of 16 chips with 200 Gchip/s rate. By using two switches (SW), it has been possible to transmit a single OC or two OCs simultaneously, to measure the autocorrelation and the cross-correlation signals, respectively. In addition, the polarization controllers (PC) and the polarizers (Pol) were used to investigate the system performance in the worst case scenario, when the polarization states of two OCs are aligned.

At the receiver side, the signal is sent to a multiport E/D, and the output #1 is connected to an ENB-OBPF with 0.1 nm bandwidth at the center wavelength of 1551 nm, in the case of evaluation of the performance with a filter, or connected directly to the monitoring system. The resolutions of the optical spectrum analyzer are used 1 nm/div and 0.1 nm/div.

Insets (i, ii) of Fig. 4 show the cases without any filter and with the ENB-OBPF, respectively; The measured autocorrelation and the cross-correlation waveforms are shown in insets (a, b), respectively and they have the same scales, and insets (c, d) show the autocorrelation waveform when both OCs are transmitted, and the corresponding spectrum. An inspection of these figures confirms that the use of an ENB-OBPF largely reduces the MAI and beat noise effect. To increase the receiver sensitivity, it is necessary to filter the outband MAI noise, without degradating the autocorrelation signal; for this reason, a tradeoff is required: the apodized filter shape and width has been selected to fit with the main lobe of the autocorrelation signal, where the large part of the power of the matched signal is comprised.

3. Analysis of the system performance of a 10 Gbps, OCDM-PON

3.1 System configuration

3.2 Theoretical analysis

To analyze the system performance, we have numerically investigated a 10Gbps, 8 ONUs, on-off keying (OOK) OCDM-based PON system with paired multiport E/Ds, using data rate detection. In this case, the 8 ports pn = 2n-1 (n = 1-8) of a 16x16 multiport E/D are used, as shown in Fig. 6
Fig. 6 Architecture to evaluate the performance of a 8 ONU, 10Gbps, OCDM-based PON.
. Without considering dispersion effects, about 95% of the autocorrelation signal power of each bit is contained in one bit slot, so ISI effect is negligible. The autocorrelation signal Eac (t) can be expressed as
Eac(t)=M(f)Hki(f)Hik(f)G(f)exp(j2πf)dt
(1)
where M (f) is the transfer function of the optical source, Hki (f) and Hik’ (f) are the transfer functions of multiport E/D, and G (f) is the transfer function of the ENB-OBPF. A similar expression can be obtained for the optical field of the crosscorrelation signal
Ecc(t)=M(f)Hki(f)Hik'(f)G(f)exp(j2πf)dt
(2)
with k’≠k. The average power of the autocorrelation and crosscorrelation signals can be evaluated as
Pd=0Tb|Eac(t)|2dtPi=0Tb|Ecc(t)|2dt
(3)
where Tb is the bit duration time. Considering the scheme of Fig. 6, the decision signal Z can be calculated as
Z=Pd+i=2NPi+2i=2N0Tb|Eac(t)||Ecci(t)|cos[ϕac(t)ϕcci(t)]dt+2i=2N0Tb|Ecci(t)||Eccj(t)|cos[ϕcci(t)ϕccj(t)]dt+n(t)
(4)
where φac is the phase of the autocorrelation signal, Ecc-i exp(φcc-i) and Ecc-j exp(φcc-j) are the interfering signals, and ℜ is the photodetector responsibility and n is the Gaussian random signal, due to thermal and shot noises. In this expression, the first term is the matched signal, the second one is the MAI noise, the third and the fourth terms are the first and the second-order beat noises, respectively. The phase of the beat noise term is a random process; in our numerical evaluations, we considered only the first beat noise, assuming a Gaussian statistics, because the second beat noise does not affect the detection [16

16. G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance analysis of a multiport encoder/decoder in OCDMA scenario,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1415–1421 (2007). [CrossRef]

]. To investigate the system performance in the worst-case scenario, with the largest values of the MAI and beat noises, we assume that all the users are transmitting simultaneously and synchronously a logic “1”, except for desired ONU, that transmits both “0” and “1”. We also assume that all the signals have the same polarization. The beat noise variance has the following expression:
σbeat2=2πi=2N02π0TbEac2(t)Ecci2(t)cos2θidtdθi
(5)
where θi is a random variable with a uniform distribution between 0 and 2π. σ02 and σ12 are the total noise variance corresponding to logic bits “0” and “1”, respectively
σ02=σth2+σMAI2σ12=σbeat2+σsh2+σMAI2
(6)
and σth2,and σsh2 are the thermal and shot noise variances, respectively
σth2=4kBTBRRLσsh2=2eBRPd(1+i=1mPiPd)
(7)
Here kB is Boltzmann constant, T is the temperature, BR is the receiver bandwidth, e is the electron charge, and RL is the load resistance. If the power level received at the PD is low, σth2 is dominant, and increasing the power, σbeat2of “1” transmission becomes dominant. Therefore, the beat and shot noises which are generated by MAI can be neglected for the case data “0” transmission. The error probabilities for an incorrect recognition are
Pe(1|0)=12erfc[Pd(Ithi=2NPiPd)2σ0]Pe(0|1)=12erfc[Pd(1+i=2NPiPdIth)2σ1]
(8)
where Ith is the detection threshold, and the BER is given by
BER=Pr(0)dataPe(1|0)+Pr(1)dataPe(0|1)=14(erfc[Pd(Ithi=2NPiPd)2σ0]+erfc[Pd(1+i=2NPiPdIth)2σ1])
(9)
where Pr(0)data, and Pr(1)data are the probability of transmitting “0” or “1”.

3.3 Comparison of BER performances

4. Conclusions

We have demonstrated that an optimum filtering of the OC generated by a multiport E/D allows us to largely reduce the MAI and beat noise effects in label processing and OCDM transmission, with a drastic improvement of the code detection performance. We have also shown that this new architecture allows us to increase from 4 to 8 the number of simultaneous ONUs transmitting in a 10 Gbps OCDM-based PON, based on paired multiport E/Ds. The proposed technique can also be used to enhance the performances of systems with larger bit rate.

Acknowledgment

The authors would like to thank B. Dai of Heriot-Watt University for his kind cooperation. X. Wang acknowledges the support of Royal Society International Joint Project. This work was also supported by the Osaka University Scholarship for Short-term Overseas Research Activities 2011.

References and links

1.

K. Kitayama and M. Murata, “Versatile optical code-based MPLS for circuit, burst, and packet switchings,” J. Lightwave Technol. 21(11), 2753–2764 (2003). [CrossRef]

2.

N. Kataoka, N. Wada, G. Cincotti, K. Kitayama, and T. Miyazaki, “A novel multiplexed optical code label processing with huge number of address entry for scalable optical packet switched network,” ECOC 2007, Tu.3.2.3, Berlin, Germany, Sep. 2007.

3.

P. R. Prucnal, Optical Code Division Multiple Access: Fundamentals and Applications (Taylor Francis Inc, 2005).

4.

G. Cincotti, N. Wada, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-part I: modeling and design,” J. Lightwave Technol. 24(1), 103–112 (2006). [CrossRef]

5.

X. Wang and K. Kitayama, “Analysis of beat noise in coherent and incoherent time-spreading OCDMA,” J. Lightwave Technol. 22(10), 2226–2235 (2004). [CrossRef]

6.

S. Etemad, T. Banwell, S. Galli, J. Jackel, R. Menendez, P. Toliver, J. Young, P. Delfyett, C. Price, and T. Turpin, “Optical-CDMA incorporating phase coding of coherent frequency bins: concept, simulation, experiments,” OFC 2004, FG5, LA, CA, USA, Feb. 2004.

7.

H. Sotobayashi, W. Chujo, and K. Kitayama, “1.6-b/s/Hz 6.4 Tb/s QPSK-OCDM/WDM (4OCDM x WDM x 40Gb/s) transmission experiment using optical hard thresholding,” IEEE Photon. Technol. Lett. 14(4), 555–557 (2002). [CrossRef]

8.

J. H. Lee, P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Reduction of interchannel interference noise in a two-channel grating-based OCDMA system using a nonlinear optical loop mirror,” IEEE Photon. Technol. Lett. 13(5), 529–531 (2001). [CrossRef]

9.

Z. Jiang, D. S. Seo, S. D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Four user, 2.5-Gb/s, spectrally coded OCDMA system demonstration using low-power nonlinear processing,” J. Lightwave Technol. 23(1), 143–158 (2005). [CrossRef]

10.

T. Hamanaka, X. Wang, N. Wada, A. Nishiki, and K. Kitayama, “Ten-user truly asynchronous gigabit OCDMA transmission experiment with a 511-chip SSFBG en/decoder,” J. Lightwave Technol. 24(1), 95–102 (2006). [CrossRef]

11.

G. Manzacca, M. S. Moreolo, and G. Cincotti, “Performance analysis of multidimensional codes generated/processed by a single planar device,” J. Lightwave Technol. 25(6), 1629–1637 (2007). [CrossRef]

12.

N. Kataoka, N. Wada, X. Wang, G. Cincotti, A. Sakamoto, Y. Terada, T. Miyazaki, and K. Kitayama, “Field trial of duplex, 10Gbps x 8-user DPSK-OCDMA system using a single 16 x 16 multi-port encoder/decoder and 16-level phase-shifted SSFBG encoder/decoders,” J. Lightwave Technol. 27(3), 299–305 (2009). [CrossRef]

13.

S. Yoshima, N. Nakagawa, N. Kataoka, N. Suzuki, M. Noda, M. Nogami, J. Nakagawa, and K. Kitayama, “10Gb/s-based PON over OCDMA uplink burst transmission using SSFBG encoder/multi-port decoder and burst-mode receiver,” J. Lightwave Technol. 28(4), 365–371 (2010). [CrossRef]

14.

S. Yoshima, Y. Tanaka, N. Kataoka, N. Wada, J. Nakagawa, and K. Kitayama, “Full-duplex 10G-TDM-OCDMA-PON system using only a pair of en/decoder,” ECOC 2010, Tu.3.B.6, Torino, Italy, Sep. 2010.

15.

X. Wang, N. Wada, G. Cincotti, T. Miyazaki, and K. Kitayama, “Demonstration of over 128-Gb/s-capacity (12-user/spl times/10.71-Gb/s/user) asynchronous OCDMA using FEC and AWG-based multiport optical encoder/decopders,” IEEE Photon. Technol. Lett. 18(15), 1603–1605 (2006). [CrossRef]

16.

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance analysis of a multiport encoder/decoder in OCDMA scenario,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1415–1421 (2007). [CrossRef]

OCIS Codes
(060.4230) Fiber optics and optical communications : Multiplexing
(060.4510) Fiber optics and optical communications : Optical communications
(080.1238) Geometric optics : Array waveguide devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 2, 2012
Revised Manuscript: April 16, 2012
Manuscript Accepted: April 16, 2012
Published: April 19, 2012

Citation
Takahiro Kodama, Naoya Wada, Gabriella Cincotti, Xu Wang, and Ken-ichi Kitayama, "Noise suppression using optimum filtering of OCs generated by a multiport encoder/decoder," Opt. Express 20, 10320-10329 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-10320


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References

  1. K. Kitayama and M. Murata, “Versatile optical code-based MPLS for circuit, burst, and packet switchings,” J. Lightwave Technol.21(11), 2753–2764 (2003). [CrossRef]
  2. N. Kataoka, N. Wada, G. Cincotti, K. Kitayama, and T. Miyazaki, “A novel multiplexed optical code label processing with huge number of address entry for scalable optical packet switched network,” ECOC 2007, Tu.3.2.3, Berlin, Germany, Sep. 2007.
  3. P. R. Prucnal, Optical Code Division Multiple Access: Fundamentals and Applications (Taylor Francis Inc, 2005).
  4. G. Cincotti, N. Wada, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-part I: modeling and design,” J. Lightwave Technol.24(1), 103–112 (2006). [CrossRef]
  5. X. Wang and K. Kitayama, “Analysis of beat noise in coherent and incoherent time-spreading OCDMA,” J. Lightwave Technol.22(10), 2226–2235 (2004). [CrossRef]
  6. S. Etemad, T. Banwell, S. Galli, J. Jackel, R. Menendez, P. Toliver, J. Young, P. Delfyett, C. Price, and T. Turpin, “Optical-CDMA incorporating phase coding of coherent frequency bins: concept, simulation, experiments,” OFC 2004, FG5, LA, CA, USA, Feb. 2004.
  7. H. Sotobayashi, W. Chujo, and K. Kitayama, “1.6-b/s/Hz 6.4 Tb/s QPSK-OCDM/WDM (4OCDM x WDM x 40Gb/s) transmission experiment using optical hard thresholding,” IEEE Photon. Technol. Lett.14(4), 555–557 (2002). [CrossRef]
  8. J. H. Lee, P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Reduction of interchannel interference noise in a two-channel grating-based OCDMA system using a nonlinear optical loop mirror,” IEEE Photon. Technol. Lett.13(5), 529–531 (2001). [CrossRef]
  9. Z. Jiang, D. S. Seo, S. D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Four user, 2.5-Gb/s, spectrally coded OCDMA system demonstration using low-power nonlinear processing,” J. Lightwave Technol.23(1), 143–158 (2005). [CrossRef]
  10. T. Hamanaka, X. Wang, N. Wada, A. Nishiki, and K. Kitayama, “Ten-user truly asynchronous gigabit OCDMA transmission experiment with a 511-chip SSFBG en/decoder,” J. Lightwave Technol.24(1), 95–102 (2006). [CrossRef]
  11. G. Manzacca, M. S. Moreolo, and G. Cincotti, “Performance analysis of multidimensional codes generated/processed by a single planar device,” J. Lightwave Technol.25(6), 1629–1637 (2007). [CrossRef]
  12. N. Kataoka, N. Wada, X. Wang, G. Cincotti, A. Sakamoto, Y. Terada, T. Miyazaki, and K. Kitayama, “Field trial of duplex, 10Gbps x 8-user DPSK-OCDMA system using a single 16 x 16 multi-port encoder/decoder and 16-level phase-shifted SSFBG encoder/decoders,” J. Lightwave Technol.27(3), 299–305 (2009). [CrossRef]
  13. S. Yoshima, N. Nakagawa, N. Kataoka, N. Suzuki, M. Noda, M. Nogami, J. Nakagawa, and K. Kitayama, “10Gb/s-based PON over OCDMA uplink burst transmission using SSFBG encoder/multi-port decoder and burst-mode receiver,” J. Lightwave Technol.28(4), 365–371 (2010). [CrossRef]
  14. S. Yoshima, Y. Tanaka, N. Kataoka, N. Wada, J. Nakagawa, and K. Kitayama, “Full-duplex 10G-TDM-OCDMA-PON system using only a pair of en/decoder,” ECOC 2010, Tu.3.B.6, Torino, Italy, Sep. 2010.
  15. X. Wang, N. Wada, G. Cincotti, T. Miyazaki, and K. Kitayama, “Demonstration of over 128-Gb/s-capacity (12-user/spl times/10.71-Gb/s/user) asynchronous OCDMA using FEC and AWG-based multiport optical encoder/decopders,” IEEE Photon. Technol. Lett.18(15), 1603–1605 (2006). [CrossRef]
  16. G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance analysis of a multiport encoder/decoder in OCDMA scenario,” IEEE J. Sel. Top. Quantum Electron.13(5), 1415–1421 (2007). [CrossRef]

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