## LDPC coded OFDM over the atmospheric turbulence channel

Optics Express, Vol. 15, Issue 10, pp. 6336-6350 (2007)

http://dx.doi.org/10.1364/OE.15.006336

Acrobat PDF (2597 KB)

### Abstract

Low-density parity-check (LDPC) coded optical orthogonal frequency division
multiplexing (OFDM) is shown to significantly outperform LDPC coded on-off
keying (OOK) over the atmospheric turbulence channel in terms of both coding
gain and spectral efficiency. In the regime of strong turbulence at a bit-error
rate of 10^{-5}, the coding gain improvement of the LDPC coded
single-side band unclipped-OFDM system with 64 sub-carriers is larger than the
coding gain of the LDPC coded OOK system by 20.2dB for quadrature-phase-shift
keying (QPSK) and by 23.4dB for binary-phase-shift keying (BPSK).

© 2007 Optical Society of America

## 1. Introduction

1. X. Zhu and J. M. Kahn, “Free-space optical communication
through atmospheric turbulence channels,”
IEEE Trans. Commun. **50**, 1293–1300
(2002). [CrossRef]

4. M.-C. Jeong, J.-S. Lee, S.-Y. Kim, S.-W. Namgung, J.-H. Lee, M.-Y. Cho, S.-W. Huh, Y.-S. Ahn, J.-W. Cho, and J.-S. Lee, “8x10 Gb/s terrestrial optical
free-space transmission over 3.4 km using an optical
repeater,” IEEE Photon. Technol. Lett. **15**, 171–173
(2003). [CrossRef]

1. X. Zhu and J. M. Kahn, “Free-space optical communication
through atmospheric turbulence channels,”
IEEE Trans. Commun. **50**, 1293–1300
(2002). [CrossRef]

1. X. Zhu and J. M. Kahn, “Free-space optical communication
through atmospheric turbulence channels,”
IEEE Trans. Commun. **50**, 1293–1300
(2002). [CrossRef]

**50**, 1293–1300
(2002). [CrossRef]

**50**, 1293–1300
(2002). [CrossRef]

**50**, 1293–1300
(2002). [CrossRef]

^{-6}both MLSD and PSP require the electrical signal to noise ratio larger than 20 dB even in the weak turbulence regime. Such signal powers are unacceptably high for many applications, and novel modulation techniques for IM/DD FSO systems are needed. In this paper we show that orthogonal frequency division multiplexing (OFDM) combined with error control coding is a very good modulation format for FSO IM/DD systems.

7. Y. Wu and B. Caron, “Digital television terrestrial
broadcasting,” IEEE Commun. Mag. **32**, 46–52
(1994). [CrossRef]

8. Q. Pan and R. J. Green, “Bit-error-rate performance of
lightwave hybrid AM/OFDM systems with comparison with AM/QAM systems in the
presence of clipping impulse noise,” IEEE
Photon. Technol. Lett. **8**, 278–280
(1996). [CrossRef]

9. A. Kim, Y. Hun Joo, and Y. Kim, “60 GHz wireless communication
systems with radio-over-fiber links for indoor wireless
LANs,” IEEE Trans. Commun. Electron. **50**, 517–520
(2004). [CrossRef]

10. B. J. Dixon, R. D. Pollard, and S. Iezekiel, “Orthogonal frequency-division
multiplexing in wireless communication systems with multimode fiber
feeds,” IEEE Trans Microwave Theory Tech. **49**, 1404–1409
(2001). [CrossRef]

7. Y. Wu and B. Caron, “Digital television terrestrial
broadcasting,” IEEE Commun. Mag. **32**, 46–52
(1994). [CrossRef]

5. J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, “Shannon capacities and
error-correction codes for optical atmospheric trubulent
channels,” J. Opt. Net. **4**, 586–601
(2005). [CrossRef]

11. I. B. Djordjevic, O. Milenkovic, and B. Vasic, “Generalized low-density parity-check
codes for Optical Communication Systems,”
J. Lightwave Technol. **23**, 1939–1946
(2005). [CrossRef]

11. I. B. Djordjevic, O. Milenkovic, and B. Vasic, “Generalized low-density parity-check
codes for Optical Communication Systems,”
J. Lightwave Technol. **23**, 1939–1946
(2005). [CrossRef]

11. I. B. Djordjevic, O. Milenkovic, and B. Vasic, “Generalized low-density parity-check
codes for Optical Communication Systems,”
J. Lightwave Technol. **23**, 1939–1946
(2005). [CrossRef]

5. J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, “Shannon capacities and
error-correction codes for optical atmospheric trubulent
channels,” J. Opt. Net. **4**, 586–601
(2005). [CrossRef]

14. R. You and J. M. Kahn, “Average power reduction techniques
for multiple-subcarrier intensity-modulated optical
signals,” IEEE Trans. Commun. **49**, 2164–2171
(2001). [CrossRef]

## 2. FSO-OFDM transmission system

*B*bits. The

*B*bits in each group (frame) are subdivided into

*K*subgroups with the

*i*

^{th}subgroup containing

*b*bits,

_{i}*B*=∑

^{k}_{i=1}

*b*. The

_{i}*b*bits from the

_{i}*i*

^{th}subgroup are mapped into a complex-valued signal from a 2

*-point signal constellation such as quadrature-amplitude modulation (QAM), which is considered in this paper. The complex-valued signal points from*

^{bi}*K*subchannels are considered to be the values of the discrete Fourier transform (DFT) of a multicarrier OFDM signal (for more details see Ref. [6]). Therefore, the symbol length (the time between two consecutive OFDM symbols) in an OFDM system is

*T*=

*KT*

_{s}, where

*T*

_{s}is the symbol-interval length in an equivalent single-carrier system. By selecting

*K*, the number of subchannels, sufficiently large, the OFDM symbol interval can be made significantly larger than the dispersed pulse-width in a single-carrier system, resulting in an arbitrarily small intersymbol interference. Following the description given in Ref. [6], the complex envelope of a transmitted OFDM signal can be written as

*X*denotes the

_{i,k}*k*-th OFDM symbol in the

*i*-th subcarrier,

*w*(

*t*) is the window function, and

*f*

_{RF}is the RF carrier frequency. The duration of the OFDM symbol is denoted by

*T*, while

*T*

_{FFT}is the FFT sequence duration,

*T*

_{G}is the guard interval duration (the duration of cyclic extension), and

*T*

_{win}is the length of the windowing interval. The details of the resulting OFDM symbol are shown in Figs. 1(d)–1(e). The symbols are constructed as follows.

*N*

_{QAM}(=

*K*) consecutive input QAM symbols are zero-padded to obtain

*N*

_{FFT}(=2

*,*

^{m}*m*>1) input samples for inverse fast Fourier transform (IFFT), then

*N*

_{G}samples are inserted to create the guard interval

*T*

_{G}and finally the OFDM symbol is multiplied by the window function (raised cosine function is used in Ref. [6], but the Kaiser, Blackman-Harris and other window functions are also applicable).

*N*

_{G}/2 samples of the FFT frame (of duration

*T*

_{FFT}with

*N*

_{FFT}samples) as the prefix, and repeating the first

*N*

_{G}/2 samples (out of

*N*

_{FFT}) as the suffix. (Notice that windowing is more effective for smaller numbers of subcarriers.) After a D/A conversion and RF up-conversion, we convert the RF signal to the optical domain using one of two options: (i) for symbol rates up to 10 Gsymbols/s the OFDM signal directly modulates the DFB laser, and (ii) for symbol rates above 10 Gsymbols/s the OFDM signal drives the Mach-Zehnder modulator (MZM). The DC component [

*b*in Eq. (1)] is inserted to enable noncoherent recover of the QAM symbols. In the reminder of this Section three different OFDM schemes are presented.

### 2.1 Biased-OFDM single-side band scheme

*b*is sufficiently large so that when added to

*s*

_{OFDM}(

*t*) the resulting sum is non-negative. For illustrative purposes the DFB laser driving signal (which is identical to the MZM RF input signal of schemes B and C) is shown in Fig. 2(a). The main disadvantage of the B-OFDM scheme is the poor power efficiency.

### 2.2 Clipped-OFDM single-side band scheme

### 2.3 Unclipped-OFDM single-side band scheme

_{3}MZM in a fashion similar to that used in duobinary optical transmission. To avoid distortion due to clipping, the information bearing signal is transmitted by modulating the electrical field (instead of intensity modulation employed in the B-OFDM and C-OFDM schemes) so that the negative part of the OFDM signal is transmitted to the photodetector. Distortion introduced by the photodetector, caused by squaring, is successfully eliminated by proper filtering, and the recovered signal distortion is insignificant. Notice that U-OFDM is less power efficient than C-OFDM because the negative portion of the OFDM signal is transmitted and then discarded [see Fig. 2(c)]. For U-OFDM the detector nonlinearity is compensated by post-detection filters that reject (potentially useful) signal energy and compromise power efficiency. Despite this drawback we find that U-OFDM is still significantly more power efficient than B-OFDM. Note that the DC bias shifts the average of the C-OFDM signal towards positive values, while in the case of B-OFDM a much larger bias is needed to completely eliminate the negative portion of the signal. The MZM RF input signal for U-OFDM is shown in Fig. 2(c), and the recovered constellation diagram for 16-QAM SSB is shown in Fig. 2(g). The transmitted signal is recovered with negligible distortion.

*a*(

*t*)|

^{2}denotes the intensity fluctuation due to atmospheric turbulence, and

*R*denotes the photodiode responsivity. The signal after RF down-conversion and appropriate filtering, can be written as

*h*(

_{e}*t*) is the impulse response of the low-pass filter (having the transfer function

*H*(j

_{e}*ω*)),

*n*(

*t*) is electronic noise in the receiver, commonly modeled as a Gaussian process,

*k*

_{RF}denotes the RF downconversion factor, and the * is the convolution operator. Finally, after the A/D conversion and cyclic extension removal, the transmitted signal is demodulated by the FFT algorithm. The soft outputs of the FFT demodulator are used to estimate the bit reliabilities that are fed to four identical LDPC iterative decoders based on the sum-product algorithm [15].

16. R. Hui, B. Zhu, R. Huang, C. T. Allen, K. R. Demarest, and D. Richards, “Subcarrier multiplexing for
highspeed optical transmission,” J.
Lightwave Technol. **20**, 417–427
(2002). [CrossRef]

## 3. An atmospheric turbulence model

**50**, 1293–1300
(2002). [CrossRef]

5. J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, “Shannon capacities and
error-correction codes for optical atmospheric trubulent
channels,” J. Opt. Net. **4**, 586–601
(2005). [CrossRef]

*L*

_{0}, is transferred without loss to eddies of decreasing size down to sizes of a few millimeters characterized by the inner scale

*l*

_{0}. The inner scale represents the cell size at which energy is dissipated by viscosity. The refractive index varies randomly across the different turbulent eddies and causes phase and amplitude perturbations to a propagating optical wave front. Turbulence can also cause random drifts of optical beams–a phenomenon usually referred to as wandering – and can induce beam focusing. In our study it is assumed that the outer scale is infinite, and that the inner scale is zero; however, it straightforward to extend this analysis to the case of non-zero inner scale [2

2. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the
irradiance probability density function of a laser beam propagating through
turbulent media,” Opt. Eng. **40**, 1554–1562
(2001). [CrossRef]

**4**, 586–601
(2005). [CrossRef]

**4**, 586–601
(2005). [CrossRef]

*k*= 2π/λ is the optical wave number, λ is the wavelength,

*L*is the propagation distance, and

*C*

_{n}^{2}is the refractive index structure parameter, which we assume to be constant for horizontal paths. Although the Rytov variance represents the scintillation index of an unbounded plane wave in the weak turbulence regime, it can also been used as an intuitive measure of turbulence strength that brings together all relevant physical parameters. Throughout the paper we often refer to

*σ*simply as the turbulence strength. The refractive index structure parameter

_{R}*C*

_{n}^{2}varies from about 10

^{-17}m

^{-2/3}for very weak turbulence to about 10

^{-13}m

^{-2/3}for strong turbulence [1

**50**, 1293–1300
(2002). [CrossRef]

**4**, 586–601
(2005). [CrossRef]

2. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the
irradiance probability density function of a laser beam propagating through
turbulent media,” Opt. Eng. **40**, 1554–1562
(2001). [CrossRef]

2. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the
irradiance probability density function of a laser beam propagating through
turbulent media,” Opt. Eng. **40**, 1554–1562
(2001). [CrossRef]

*I*is the signal intensity,

*Γ*(∙) is the gamma function, and

*K*(∙) is the modified Bessel function of the second kind and order

_{α-β}*α-β*.

*α*and

*β*are parameters of the PDF describing the scintillation experienced by plane waves, and in the case of zero-inner scale (

*l*

_{0}= 0) are given by [2

**40**, 1554–1562
(2001). [CrossRef]

*σ*

_{R}^{2}is the Rytov variance as given in (4). The PDF parameters α and β represent the effective number of large-scale and small-scale cells, respectively [2

**40**, 1554–1562
(2001). [CrossRef]

**40**, 1554–1562
(2001). [CrossRef]

_{R}=0.6). The atmospheric turbulence changes the symmetry of clusters from circular for AWGN channel to elliptic (see Fig. 3). Both C-OFDM and U-OFDM schemes are more immune to the atmospheric turbulence than the B-OFDM scheme. The U-OFDM system is only slightly more immune to the atmospheric turbulence than C-OFDM scheme. It appears that the better power efficiency of C-OFDM compensates the distortion introduced by clipping. The reason is simple. The average launched power is fixed for all three OFDM schemes meaning that more energy per bit is allocated in the C-OFDM scheme (because the power in DC bias is lower), and as a consequence the scheme is more immune to electrical noise. Higher immunity to electrical noise may result in slightly better BER performance of the C-OFDM scheme when compared to the U-OFDM scheme (see Section 5).

## 4. Block-circulant LDPC codes and iterative decoding

**23**, 1939–1946
(2005). [CrossRef]

13. O. Milenkovic, I. B. Djordjevic, and B. Vasic, “Block-circulant low-density
parity-check codes for optical communication
systems,” J. Sel. Top. Quantum Electron. **10**, 294–299
(2004). [CrossRef]

12. I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical
communication systems,” IEEE Photon.
Technol. Lett. **17**, 2224–2226
(2005). [CrossRef]

**, of a regular block-circulant LDPC code can be written as**

*H***are selected as elements from the following set**

*H**p*is a prime, and

*θ*is the primitive element of the finite field GF(

*p*

^{2}). The structure of the parity-check matrix of a block-circulant code facilitates a low-complexity decoder implementation because it is highly regular and only the dimension of the permutation matrix

*P*and the exponents are to be stored. The decoder is based on an efficient realization of the sum-product algorithm given in Ref. [15]. Bit reliabilities fed to the iterative decoder are calculated as explained below.

**50**, 1293–1300
(2002). [CrossRef]

**4**, 586–601
(2005). [CrossRef]

*r*

_{I}is the in-phase demodulator sample, and

*r*

_{Q}is the quadrature demodulator sample, then the

*symbol*log-likelihood ratio (LLR) is calculated as

*s*

_{I}and

*s*

_{Q}are the coordinates of a transmitted signal constellation point and AWGN variance (σ

^{2}) is determined from the required electrical signal-to-noise ratio (SNR) per bit

*E*

_{b}/

*N*

_{o}

*P*

_{o}is the normalized received power [6], and

*s*denotes the QAM symbol in the

_{i,k}*k*-th subcarrier channel of the

*i*-th OFDM frame. (With

*M*we denote the number of points in the corresponding constellation diagram.) Notice that the definition of electrical SNR per bit, common in digital communications [Eq. (8)] (see Refs. [6] and [17]), is different from that used in Refs. [1

**50**, 1293–1300
(2002). [CrossRef]

**4**, 586–601
(2005). [CrossRef]

*E*

_{s}/

*N*

_{0}is equal to the bit energy-to-noise density ratio

*E*

_{b}/

*N*

_{0}multiplied by the number of bits per symbol which is typically large. For example, for an OFDM system with 256 sub-carriers using BPSK,

*E*

_{s}/

*N*

_{0}is about 24 dB larger than

*E*

_{b}/

*N*

_{0}. One must be careful when comparing OFDM system BER performance with OOK, not to confuse the bit energy-to-noise density ratio (

*E*

_{b}/

*N*

_{0}) with symbol energy-to-noise density ratio (

*E*

_{s}/

*N*

_{0}). For more details on OFDM principles the interested reader is referred to Ref. [6], and for more details on comparison of different modulation schemes to Ref. [17].

*bit likelihoods*, provided to the iterative decoder, are calculated from the symbol LLRs, λ(

*s*), as

^{*}(

*x*,

*y*)= log(e

*+e*

^{x}*), is applied recursively [18] max*

^{y}^{*}(

*x*,

*y*)=max(

*x*,

*y*)+log(1+e

^{-|x-y|}). Notice that the correction factor log(1 +

*e*

^{-|x-y|}) in max

^{*}-operator for high-speed applications can be either tabulated or even omitted, without significant degradation in performance [18].

## 5. Simulation Results

_{R}=0.6) [see Fig. 4(a)] the coding gain improvement of LDPC coded FSO-OFDM system with 64 sub-carriers over the LDPC encoded FSO OOK system is 8.47 dB for QPSK and 9.66 dB for BPSK, at the BER of 10

^{-5}. For strong turbulence (σ

_{R}=3.0) [see Fig. 4(b)] the coding gain improvement of the LDPC coded FSO-OFDM system over the LDPC coded FSO OOK system is 20.24 dB for QPSK and 23.38 dB for BPSK. In both cases the block-circulant [13

13. O. Milenkovic, I. B. Djordjevic, and B. Vasic, “Block-circulant low-density
parity-check codes for optical communication
systems,” J. Sel. Top. Quantum Electron. **10**, 294–299
(2004). [CrossRef]

_{R}=0.6), is given in Fig. 5. The C-OFDM scheme slightly outperforms the U-OFDM scheme. Both C-OFDM and U-OFDM schemes outperform the B-OFDM scheme by approximately 1.5dB at BER of 10

^{-5}.

**50**, 1293–1300
(2002). [CrossRef]

**50**, 1293–1300
(2002). [CrossRef]

*d*is the distance between points

_{ij}*P*and

_{i}*P*.

_{j}*B*denotes the log-amplitude covariance function:

_{x}*X*is the log-amplitude fluctuation. The joint temporal distribution of

*n*intensity samples (

*I*

_{1}

*I*

_{2}…,

*I*) is given by Ref. [1

_{n}**50**, 1293–1300
(2002). [CrossRef]

_{X}is the covariance matrix of intensity samples:

^{2}

_{X}denotes the variance of the log-normally distributed amplitude, which for plane wave can be approximated as Ref. [20]

*k*, propagation length

*L*, and the refractive index structure parameter

*C*were introduced earlier.

_{n}*T*is the time interval between observations, which corresponds to the OFDM symbol period; while τ

_{0}is the

*coherence time*. Notice that expressions (12)–(13) are valid in the

*weak*turbulence regime. In the same regime the covariance function (11) is found to be exponential for both plane and spherical waves [20]

_{0}are in the range from 10μs to 10ms.

_{X}is set to 0.6 (notice that σ

_{X}is different from Rytov standard deviation σ

_{R}used earlier, and for horizontal paths σ

_{X}~0.498σ

_{R}). It is clear from Fig. 6 that LDPC-coded OFDM with or without interleaver provides excellent performance improvement even in the presence of temporal correlation. The BER performance can further be improved by using the interleaver with larger interleaving degree than that used in Fig. 6 (the star curve), at the expense of increasing encoder/decoder complexity. Notice the on-off keying (OOK) modulation scheme enters BER floor for this value of standard deviation (σ

_{X}=0.6), and even advanced FEC is not able to help too much. However, LDPC-coded OOK is able to operate properly at lower standard deviations σ

_{X}.

## 6. Conclusion

^{-5}) ranging from 8.47 dB in the regime of weak turbulence (for QPSK) to 23.38 dB in the regime of strong turbulence (for BPSK) compared to LDPC-coded OOK, (ii) significant spectral efficiency improvement, (iii) no channel equalization is required, and (iv) a simple FFT is used for modulating and demodulating. To further improve spectral efficiency, the FSO-OFDM SSB transmission scheme may be combined with sub-carrier multiplexing.

## Acknowledgments

## References and Links

1. | X. Zhu and J. M. Kahn, “Free-space optical communication
through atmospheric turbulence channels,”
IEEE Trans. Commun. |

2. | M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the
irradiance probability density function of a laser beam propagating through
turbulent media,” Opt. Eng. |

3. | X. Zhu and J. M. Kahn, “Markov chain model in
maximum-likelihood sequence detection for free-space optical communication
through atmospheric turbulence channels,”
J. Lightwave Technol. |

4. | M.-C. Jeong, J.-S. Lee, S.-Y. Kim, S.-W. Namgung, J.-H. Lee, M.-Y. Cho, S.-W. Huh, Y.-S. Ahn, J.-W. Cho, and J.-S. Lee, “8x10 Gb/s terrestrial optical
free-space transmission over 3.4 km using an optical
repeater,” IEEE Photon. Technol. Lett. |

5. | J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, “Shannon capacities and
error-correction codes for optical atmospheric trubulent
channels,” J. Opt. Net. |

6. | R. Van Nee and R. Prasad, |

7. | Y. Wu and B. Caron, “Digital television terrestrial
broadcasting,” IEEE Commun. Mag. |

8. | Q. Pan and R. J. Green, “Bit-error-rate performance of
lightwave hybrid AM/OFDM systems with comparison with AM/QAM systems in the
presence of clipping impulse noise,” IEEE
Photon. Technol. Lett. |

9. | A. Kim, Y. Hun Joo, and Y. Kim, “60 GHz wireless communication
systems with radio-over-fiber links for indoor wireless
LANs,” IEEE Trans. Commun. Electron. |

10. | B. J. Dixon, R. D. Pollard, and S. Iezekiel, “Orthogonal frequency-division
multiplexing in wireless communication systems with multimode fiber
feeds,” IEEE Trans Microwave Theory Tech. |

11. | I. B. Djordjevic, O. Milenkovic, and B. Vasic, “Generalized low-density parity-check
codes for Optical Communication Systems,”
J. Lightwave Technol. |

12. | I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical
communication systems,” IEEE Photon.
Technol. Lett. |

13. | O. Milenkovic, I. B. Djordjevic, and B. Vasic, “Block-circulant low-density
parity-check codes for optical communication
systems,” J. Sel. Top. Quantum Electron. |

14. | R. You and J. M. Kahn, “Average power reduction techniques
for multiple-subcarrier intensity-modulated optical
signals,” IEEE Trans. Commun. |

15. | H. X. Yu, E. Eleftheriou, D.-M. Arnold, and A. Dholakia, “Efficient implementations of the
sum-product algorithm for decoding of LDPC
codes,” in Proc. IEEE Globecom 2001 |

16. | R. Hui, B. Zhu, R. Huang, C. T. Allen, K. R. Demarest, and D. Richards, “Subcarrier multiplexing for
highspeed optical transmission,” J.
Lightwave Technol. |

17. | J. G. Proakis |

18. | W. E. Ryan, “Concatenated convolutional codes and
iterative decoding,” in |

19. | C.-C. Lin, K.-L. Lin, H.-Ch. Chang, and C.-Y. Lee, “A 3.33Gb/s (1200,720) low-density
parity check code decoder,” in Proc.
ESSCIRC |

20. | L. C. Andrews and R.L. Philips, |

21. | N. Levinson, “The Wiener RMS error criterion in
filter design and prediction,” J. Math.
Phys. |

22. | J. Durbin, “Efficient estimation of parameters
in moving-average models,” Biometrica |

23. | Wood A.T.A. and Chan G., “Simulation of stationary Gaussian
processes in [0,1] |

**OCIS Codes**

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(060.4080) Fiber optics and optical communications : Modulation

(060.4230) Fiber optics and optical communications : Multiplexing

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Atmospheric and ocean optics

**History**

Original Manuscript: February 7, 2007

Revised Manuscript: April 30, 2007

Manuscript Accepted: April 30, 2007

Published: May 8, 2007

**Citation**

Ivan B. Djordjevic, Bane Vasic, and Mark A. Neifeld, "LDPC coded OFDM over the atmospheric turbulence channel," Opt. Express **15**, 6336-6350 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-10-6336

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### References

- X. Zhu and J. M. Kahn, "Free-space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002). [CrossRef]
- M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001). [CrossRef]
- X. Zhu and J. M. Kahn, "Markov chain model in maximum-likelihood sequence detection for free-space optical communication through atmospheric turbulence channels," J. Lightwave Technol. 51, 509-516 (2003).
- M.-C. Jeong, J.-S. Lee, S.-Y. Kim, S.-W. Namgung, J.-H. Lee, M.-Y. Cho, S.-W. Huh, Y.-S. Ahn, J.-W. Cho, and J.-S. Lee, "8x10 Gb/s terrestrial optical free-space transmission over 3.4 km using an optical repeater," IEEE Photon. Technol. Lett. 15, 171-173 (2003). [CrossRef]
- J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric trubulent channels," J. Opt. Netw. 4, 586-601 (2005). [CrossRef]
- R. Van Nee and R. Prasad, OFDM Wireless Multimedia Communications, (Artech House, Boston 2000).
- Y. Wu and B. Caron, "Digital television terrestrial broadcasting," IEEE Commun. Mag. 32, 46-52 (1994). [CrossRef]
- Q. Pan and R. J. Green, "Bit-error-rate performance of lightwave hybrid AM/OFDM systems with comparison with AM/QAM systems in the presence of clipping impulse noise," IEEE Photon. Technol. Lett. 8, 278-280 (1996). [CrossRef]
- A. Kim, Y. Hun Joo, and Y. Kim, "60 GHz wireless communication systems with radio-over-fiber links for indoor wireless LANs," IEEE Trans. Commun. Electron. 50, 517-520 (2004). [CrossRef]
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