## Performance of short-range non-line-of-sight LED-based ultraviolet communication receivers

Optics Express, Vol. 18, Issue 12, pp. 12226-12238 (2010)

http://dx.doi.org/10.1364/OE.18.012226

Acrobat PDF (1566 KB)

### Abstract

Utilizing an empirical path loss model proposed in the first paper of a two-part series, the bit error rate performance of short-range non-line-of-sight ultraviolet communication receivers is analyzed. Typical photodetector models and modulation formats are considered. Our results provide semi-analytical prediction of the achievable communication performance as a function of system and channel parameters, and serve as a basis for system design.

© 2010 OSA

## 1. Introduction

1. M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. **8**(2), 302–309 (2002). [CrossRef]

2. V. Adivarahan, Q. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285 nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AlN/sapphire templates,” Jpn. J. Appl. Phys. **46**(23), L537– L539 (2007). [CrossRef]

4. M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. **8**(2), 302–309 (2002). [CrossRef]

5. Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. **46**(5), 67–73 (2008). [CrossRef]

6. M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A **8**(12), 1964–1972 (1991). [CrossRef]

9. Z. Xu, H. Ding, B. M. Sadler, and G. Chen, “Analytical performance study of solar blind non-line-of-sight ultraviolet short-range communication links,” Opt. Lett. **33**(16), 1860–1862 (2008). [CrossRef] [PubMed]

10. H. Ding, G. Chen, A. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Comm. **27**(9), 1535–1544 (2009). [CrossRef]

11. G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express **17**(5), 3929–3940 (2009). [CrossRef] [PubMed]

11. G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express **17**(5), 3929–3940 (2009). [CrossRef] [PubMed]

10. H. Ding, G. Chen, A. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Comm. **27**(9), 1535–1544 (2009). [CrossRef]

11. G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express **17**(5), 3929–3940 (2009). [CrossRef] [PubMed]

**17**(5), 3929–3940 (2009). [CrossRef] [PubMed]

## 2. System architecture and NLOS UV channel path loss model

*θ*and

_{1}*θ*are the transmitter (Tx) and receiver (Rx) apex angles, and

_{2}*ϕ*and

_{1}*ϕ*are the Tx full beam divergence angle and Rx field of view (FOV), respectively. For the purposes of this paper,

_{2}*ϕ*and

_{1}*ϕ*are fixed to be 10° and 30°, respectively [11

_{2}**17**(5), 3929–3940 (2009). [CrossRef] [PubMed]

*r*.

*V*is referred to as the optical common volume, and

*r*and

_{1}*r*are the distances of the common volume to the Tx and Rx, respectively.In order to characterize the system performance, we utilize the channel model to predict received optical power, and incorporate stochastic models for the detector and noise sources. We ignore atmospheric turbulence effects, which are generally negligible for ranges on the order of a few hundred meters or less. We model the photodetector output as a Poisson point process with the counting rate λ determined by the instantaneous received optical power such that

_{2}*λ*,

_{S}= ηP_{r}/(hν) = ηP_{t}/(Lhν). η*P*,

_{r}*h*,

*ν*,

*P*, and

_{t}*L*denote the quantum efficiency of the detector including optical filter and photodetector, received power, Planck’s constant, the frequency of the optical field, transmitted power and path loss, respectively. In particular, path loss

*L*can be used to predict the received power given the transmission power.

12. G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express **16**(19), 15059–15068 (2008). [CrossRef] [PubMed]

**17**(5), 3929–3940 (2009). [CrossRef] [PubMed]

*ξ*are unknown non-linear functions of the apex angles (cf. Figure 1). These parameters are summarized in Tables 1 and 2 below.

## 3. Ideal photon counting receiver performance

*k*per pulse time out of each modulation symbol period, which also complies with a Poisson distribution with photon arrival rate

_{1}*λ*. The probability is given by Eq. (2) where

*λ = λ*when the signal is present and

_{S}+ λ_{b}*λ = λ*when signal is absent, and

_{b}*λ*denotes the background radiation photon count rate. Although the ozone layer in the upper atmosphere absorbs most of the radiation in the deep UV, there remains some background radiation, some percentage of which will leak through the optical filter.

_{b}*M*-PPM is an orthogonal modulation which transmits a pulse in one of

*M*slot positions. With narrower pulse duration time

*T*and the number of noise photons per second

_{p}*N*depending on the operating conditions, it is desirable to minimize the noise photon count

_{n}*λ*for improved signal detection performance as long as the peak power constraint of the light source is met. More specifically, the bit error probability is given by Eq. (5) [15

_{b}= N_{n}T_{p}15. S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. **17**(6), 670–676 (1969). [CrossRef]

*N*typically varies over zero to 14.5 kHz from night time to noon [12

_{n}12. G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express **16**(19), 15059–15068 (2008). [CrossRef] [PubMed]

*T*by increasing the order of the PPM modulation to achieve a very small value of

_{p}*λ*. As

_{b}*λ*approaches zero, Eq. (5) then evolves into

_{b}*P*, which appears the same as the limiting case for OOK. However, the expression of

_{e-PPM}= exp(-λ_{S})/2*λ*for

_{s}*M*-PPM becomes

*λ*. Therefore, for a given bit error probability requirement or equivalently the same

_{s}= (ηP_{t}log_{2}M)/(LR_{b}hυ)*λ*,

_{s}*M*-PPM can achieve a data rate of

*log*times that of OOK. In Section 5 we use Eqs. (3) and (5) to illustrate the range-rate performance tradeoffs.

_{2}M## 4. Performance of PMT/APD based receivers with thermal noise

### 4.1 Statistical modeling of the photodetector output

*k*in response to the primary photoelectrons

_{2}*k*. The number of secondary photoelectrons is described by the probability mass function in Eq. (6) [13]where

_{1}*P*(

_{k1}*k*) is the primary photoelectron probability described by Eq. (2), and

_{1}*P*(

_{k2}*k*|

_{2}*k*) is the conditional probability of the secondary photoelectrons given

_{1}*k*. There has been a rich amount of literature since the 1960s on modeling

_{1}*P*(

_{k2}*k*) for PMT and APD photodetectors. For brevity, we provide only the main results here.

_{2}*C*is the normalizing factor, and

*ζ*is the PMT spreading factor that describes the variance of PMT gain

*A*.

*P*follows Eq. (8) [16

_{k2}(k_{2})16. R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Dev. **19**(6), 703–713 (1972). [CrossRef]

17. J. Conradi, “The distribution of gains in uniformly multiplying avalanche photodiodes: experimental,” IEEE Trans. Electron. Dev. **19**(6), 713–718 (1972). [CrossRef]

*F*is the excess noise factor jointly determined by the ionization factor

*γ*and gain

*A*. For PMT and APD cases,

*F*is given by

*1 + ζ*and

^{2}*γA + [2-(1/A)](1-γ),*respectively. With the typical values of

*ζ*= 0.1 and

*γ*= 0.028,

*F*takes the values 1.01 and 4.7343 [13] for a PMT and APD (with gain 100), respectively.

*ν*from

*z*takes the form in Eq. (9) where

*n*is the thermal noise normal random variable and

*v*is the output current of the detector. The noise realization can usually be described by a zero mean Gaussian random variable with variance given by Eq. (10) [18

18. K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. **53**(9), 1455–1461 (2005). [CrossRef]

*w*here

*k*and

_{e}, T^{o}*R*denote the Boltzmann constant, the receiver temperature (Kelvin), and the load resistance.

_{L}*T*is the pulse interval for pulse-based modulation such as OOK and PPM.

_{p}*k*shifts the

_{2}*v*by changing the mean of

*n*to the form of Eq. (11) where

*k*is a random variable, leading to a random mean. Conditioned on the average count of primary photoelectrons per pulse, denoted as

_{2}*λ*, the conditional density of

*z, p*is the average of the continuous Gaussian distribution over the secondary photoelectron probability given by Eq. (12) [13]In the above,

_{z}(z|λ),*G*(

*z*,

*a*,

*b*) denotes the pdf of the Gaussian random variable

*z*with mean

*a*and variance

*b*.

*P*is given in Eq. (7) for a PMT, and in Eq. (8) for an APD.

_{k2}(j)^{5}~10

^{8}, such that a probability accumulation will have a corresponding high computational complexity. So, as an alternative, we directly model the random gain effect with the thermal noise, as proposed in [15

15. S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. **17**(6), 670–676 (1969). [CrossRef]

*A*} to be independent and identically distributed (i.i.d.) random variables representing the multiplication gain for each photoelectron. Then

_{i}*z*can be written as Eq. (13) Approximating the random gain as a Gaussian random variable,

*z*is the summation of

*k*Gaussian random variables each with mean

_{1}*Ae*and variance

*(F-1)(Ae)*, plus noise

^{2}*n*with zero mean and variance as given in Eq. (10). Conditioned on the primary photon arrival rate which is typically moderate,

*z*is essentially a summation of Gaussian random variables and

*p*is thus found to follow Eq. (14) In this equation,

_{z}(z|λ)*P*assumes the form of Eq. (2), and

_{k1}(j)*σ*

^{2}involves the contributions from thermal noise and the random gain effect of the photodetector, which is

*F*for PMT or APD,

*σ*

^{2}takes the following forms in Eq. (15), respectively

### 4.2 Receiver performance

*P*and

_{1}*P*are probabilities of transmitting information “1” and “0”, respectively. Assume

_{0}*P*= 0.5. The optimal detection threshold z

_{1}= P_{0}*to minimize*

_{th}*P*can be found by setting the derivative to zero as

_{e_OOK}*dP*, leading to Eq. (17) Given the pdf of

_{e_OOK}/dz_{th}= 0*z*in Eq. (14), an equation for the optimal

*z*will be a mixture of summation and integral. Since a closed form for the optimal

_{th}*z*is not attainable, a numerical solution will be used. Using Eq. (14) for

_{th}*p*and applying the following identitythe error probability in Eq. (16) can be written in a compact form as Eq. (18)

_{z}(z)*M*-PPM) is widely employed as a pulse-based modulation option, where the receiver is based on the maximum likelihood method by comparing the outputs of different slot positions without a need for the threshold. The probability of correct detection for M-PPM is given by Eq. (19) which is the probability that the slot containing the signal arrival has the most significant value exceeding all other slots within each PPM word. This results in the error probability

*P*. Combining our results, the correct detection probability can be expressed as Eq. (20) [15

_{e_PPM}= 0.5M/(M-1)(1-P_{D})15. S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. **17**(6), 670–676 (1969). [CrossRef]

*erf*(

*x*) is the error function defined asThese analytical results will be evaluated numerically to demonstrate NLOS UV communication receiver performance.

## 5. Numerical analysis

### 5.1 Rate-range tradeoffs with a photon counting receiver

12. G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express **16**(19), 15059–15068 (2008). [CrossRef] [PubMed]

^{−3}. We see that small pointing angles provide substantially higher data rates, with generally more than 1 Mbps improvement at 100 meters. At large pointing angles, rates of tens of kbps are indicated. This illustrates that while strict pointing is not needed at high noise levels, some knowledge of directionality enhances the communications via lowering the pointing angles and thus the path loss. When the noise condition significantly improves for solar blind operation such that

*λ*0, both OOK and 4-PPM performance improves as shown in Fig. 3 . 4-PPM yields twice the data rate of OOK for a given range when

_{b}=*λ*0, as predicted earlier. However, we observe that the data rate performance is more sensitive to noise at large pointing angles by noticing that the data rate increases significantly as

_{b}=*λ*reduces. For example, at 100m and (40°,40°) pointing, the rate under OOK almost doubles, and 4-PPM has about a 1.5 times data rate increase. This is because the path loss is high and communication performance is then more sensitive to noise, whereas for small angles the path loss is reduced and the data rate shows less sensitivity to noise.

_{b}*M*-PPM for

*M*= (4,8,16). We show small and large angle cases for a fixed range. With moderate background noise,

*M*-PPM outperforms OOK. Again, performance is very sensitive to pointing due to significant path loss variation. With a small angle geometry, for example (20°, 20°), a data transfer rate up to 2Mbps is possible with an error rate of 10

^{−3}using 16-PPM, while a (40°, 40°) link barely allows for a rate of 50kbps.

### 5.2 PMT/APD receiver performance with fixed gain

^{4}and 250, respectively, and we assume the APD and PMT have the same detection area and quantum efficiency.

^{−3}error probability at 70 meters. We comment that the relatively poorer performance is due to the excess noise with the APD gain that raises the error floor, as well as the limited APD multiplication capability. We address this further in the next sub-section in terms of gain optimization.

^{−3}for most geometries. Comparing with Fig. 5, the data rate increase with 4-PPM versus OOK is evident for both detector types. A cross-comparison between PMT and APD in both Figs. 5 and 6 also validates the PMT as an effective solution to provide a viable communication link with large pointing angles.

### 5.3 Improving the performance with detector gain control

^{4}. The extent of BER improvement differs with pointing geometry, with the most gain occurring for the smaller pointing angles. For very large gain, the error performance is significantly better at small angles. For the APD, the BER first decreases with increasing gain, but then increases beyond a certain gain point. The variation is more pronounced for smaller pointing angles, and an optimal gain exists in each case. The optimal gain point tends to shift to a larger value as the pointing angles increase. The optimal gain is around 150 for (10°,10°), and approaches 300 for the (40°,40°) pointing case. Overall the PMT shows much better detection performance than the APD. A high gain PMT based receiver is practically feasible for the cases considered. For the APD based receiver, excess noise from random gain fluctuation significantly degrades performance, and an automatic gain control mechanism can be incorporated to adjust the APD bias voltage.

## 6. Conclusions and future work

## Acknowledgements

## References and links

1. | M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. |

2. | V. Adivarahan, Q. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285 nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AlN/sapphire templates,” Jpn. J. Appl. Phys. |

3. | W. S. Ross and R. S. Kennedy, “An investigation of atmospheric optically scattered non-line-of-sight communication links,” Army Research Office Project Report, Research Triangle Park, NC, January 1980. |

4. | M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. |

5. | Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. |

6. | M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A |

7. | G. A. Shaw, A. M. Siegel, J. Model, and M. L. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE |

8. | Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proceedings of IEEE Intl. Conf. on Acoustics, Speech, and Signal Proc. (IEEE, 2007). |

9. | Z. Xu, H. Ding, B. M. Sadler, and G. Chen, “Analytical performance study of solar blind non-line-of-sight ultraviolet short-range communication links,” Opt. Lett. |

10. | H. Ding, G. Chen, A. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Comm. |

11. | G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express |

12. | G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express |

13. | R. M. Gagliardi, and S. Karp, |

14. | Q. He, B. M. Sadler, and Z. Xu, “On the achievable performance of non-line of sight ultraviolet communications,” Proceedings of OSA Optics & Photonics Congress: Applications of Lasers for Sensing and Free Space Communications (OSA, 2010). |

15. | S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. |

16. | R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Dev. |

17. | J. Conradi, “The distribution of gains in uniformly multiplying avalanche photodiodes: experimental,” IEEE Trans. Electron. Dev. |

18. | K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. |

19. | S. Alexander, |

**OCIS Codes**

(060.4510) Fiber optics and optical communications : Optical communications

(060.2605) Fiber optics and optical communications : Free-space optical communication

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: December 14, 2009

Revised Manuscript: March 27, 2010

Manuscript Accepted: April 12, 2010

Published: May 25, 2010

**Citation**

Qunfeng He, Zhengyuan Xu, and Brian M. Sadler, "Performance of short-range non-line-of-sight LED-based ultraviolet communication receivers," Opt. Express **18**, 12226-12238 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-12-12226

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### References

- M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8(2), 302–309 (2002). [CrossRef]
- V. Adivarahan, Q. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285 nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AlN/sapphire templates,” Jpn. J. Appl. Phys. 46(23), L537– L539 (2007). [CrossRef]
- W. S. Ross and R. S. Kennedy, “An investigation of atmospheric optically scattered non-line-of-sight communication links,” Army Research Office Project Report, Research Triangle Park, NC, January 1980.
- M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8(2), 302–309 (2002). [CrossRef]
- Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008). [CrossRef]
- M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A 8(12), 1964–1972 (1991). [CrossRef]
- G. A. Shaw, A. M. Siegel, J. Model, and M. L. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE 5417, 250–261 (2004). [CrossRef]
- Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proceedings of IEEE Intl. Conf. on Acoustics, Speech, and Signal Proc. (IEEE, 2007).
- Z. Xu, H. Ding, B. M. Sadler, and G. Chen, “Analytical performance study of solar blind non-line-of-sight ultraviolet short-range communication links,” Opt. Lett. 33(16), 1860–1862 (2008). [CrossRef] [PubMed]
- H. Ding, G. Chen, A. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Comm. 27(9), 1535–1544 (2009). [CrossRef]
- G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express 17(5), 3929–3940 (2009). [CrossRef] [PubMed]
- G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express 16(19), 15059–15068 (2008). [CrossRef] [PubMed]
- R. M. Gagliardi and S. Karp, Optical Communications, 2nd ed. (John Wiley & Sons, 1995).
- Q. He, B. M. Sadler, and Z. Xu, “On the achievable performance of non-line of sight ultraviolet communications,” Proceedings of OSA Optics & Photonics Congress: Applications of Lasers for Sensing and Free Space Communications (OSA, 2010).
- S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. 17(6), 670–676 (1969). [CrossRef]
- R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Dev. 19(6), 703–713 (1972). [CrossRef]
- J. Conradi, “The distribution of gains in uniformly multiplying avalanche photodiodes: experimental,” IEEE Trans. Electron. Dev. 19(6), 713–718 (1972). [CrossRef]
- K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. 53(9), 1455–1461 (2005). [CrossRef]
- S. Alexander, Optical Communication Receiver Design (SPIE Optical Engineering Press, 1997.

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