## Deep-space and near-Earth optical communications by coded orbital angular momentum (OAM) modulation |

Optics Express, Vol. 19, Issue 15, pp. 14277-14289 (2011)

http://dx.doi.org/10.1364/OE.19.014277

Acrobat PDF (1305 KB)

### Abstract

In order to achieve multi-gigabit transmission (projected for 2020) for the use in interplanetary communications, the usage of large number of time slots in pulse-position modulation (PPM), typically used in deep-space applications, is needed, which imposes stringent requirements on system design and implementation. As an alternative satisfying high-bandwidth demands of future interplanetary communications, while keeping the system cost and power consumption reasonably low, in this paper, we describe the use of orbital angular momentum (OAM) as an additional degree of freedom. The OAM is associated with azimuthal phase of the complex electric field. Because OAM eigenstates are orthogonal the can be used as basis functions for *N-*dimensional signaling. The OAM modulation and multiplexing can, therefore, be used, in combination with other degrees of freedom, to solve the high-bandwidth requirements of future deep-space and near-Earth optical communications. The main challenge for OAM deep-space communication represents the link between a spacecraft probe and the Earth station because in the presence of atmospheric turbulence the orthogonality between OAM states is no longer preserved. We will show that in combination with LDPC codes, the OAM-based modulation schemes can operate even under strong atmospheric turbulence regime. In addition, the spectral efficiency of proposed scheme is *N ^{2}/*log

_{2}

*N*times better than that of PPM.

© 2011 OSA

## 1. Introduction

1. B. Moision and J. Hamkins, “Deep-space optical communications downlink budget: modulation and coding,“ The Interplanetary Network Progress Report 42-154, April-June 2003 (Jet Propulsion Laboratory, Pasadena, California, 15 August 2003), pp. 1-28, http://ipnpr.jpl.nasa.gov/progress_report/42-154/154K.pdf.

5. H. Hemmati, “Interplanetary laser communications,” Optics & Photonics News **18**(11), 22–27 (2007). [CrossRef]

7. I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express **18**(24), 24722–24728 (2010). [CrossRef] [PubMed]

8. I. B. Djordjevic, “Orbital angular momentum (OAM) based LDPC-coded deep-space optical communication,” Proc. SPIE **7923**, 792306, 792306–792308 (2011) (invited paper). [CrossRef]

9. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. **94**(15), 153901 (2005). [CrossRef] [PubMed]

13. M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. **47**(4), A32–A42 (2008). [CrossRef] [PubMed]

14. M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory **50**(8), 1788–1793 (2004). [CrossRef]

17. J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. **53**(8), 1288–1299 (2005). [CrossRef]

*N*-dimensional OAM modulation (Sec. 2); and (iii) orthogonal OAM division multiplexing (Sec. 3), similar to OFDM [24]. We will also describe different approaches to deal with atmospheric turbulence induced OAM crosstalk including: (1) equalization; (2) OAM-time coding, which is analogous to the space-time coding; and (3) adaptive modulation and coding (AMC).

18. I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express **18**(24), 24722–24728 (2010). [CrossRef] [PubMed]

18. I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express **18**(24), 24722–24728 (2010). [CrossRef] [PubMed]

*N*-dimensional OAM-based coded modulation scheme suitable for deep-space and near-Earth applications. The OAM division multiplexing is described in Section 3. Different methods to re-establish the orthogonality of OAM modes, after transmission over atmospheric turbulence channels, are described in Section 4. We evaluate the suitability of OAM-based coded-modulation schemes for deep-space/near-Earth applications in Section 5. Section 6 is devoted to concluding remarks.

## 2. Deep-space and near-Earth optical Communications based on LDPC-coded OAM modulation

*N*-dimensional OAM coded modulation. The angular momentum,

**, of the classical electromagnetic field can be written as [19]**

*L***is the electric field intensity,**

*E***is the vector potential associated with magnetic field intensity**

*A***by**

*H**r*,

*ϕ*,

*z*) (

*r*denotes the radial distance from propagation axis,

*ϕ*denotes the azimuthal angle and

*z*denotes the propagation distance) as follows [10

10. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. **47**(13), 2414–2429 (2008). [CrossRef] [PubMed]

*w*(

*z*) =

*w*

_{0}[1 + (

*z*/

*z*

_{R})]

^{1/2}with

*w*

_{0}being the zero-order Gaussian radius at the waist,

*k*= 2π/λ is the propagation constant, and

*L*(⋅) is the associated Laguerre polynomial, with

^{l}_{p}*p*and

*l*representing the radial and azimuthal mode numbers, respectively. It can be seen from (2) that

*l*th mode of LG beam has the azimuthal angular dependence of the form exp(-j

*lϕ*), and consequently,

*l*is also called the azimuthal mode number (index). For

*l*= 0, field

*u*(

*r*,

*ϕ*,

*z*) becomes a zero-order Gaussian beam, that is the TEM

_{00}mode. For

*p*= 0,

*L*(⋅) = 1 for all

^{l}_{p}*l*s, so that the intensity of a LG mode is a ring of radius proportional to (|

*l*|)

^{1/2}, as illustrated in Fig. 1(a) . It can be shown [10

10. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. **47**(13), 2414–2429 (2008). [CrossRef] [PubMed]

*p*, the following principle of othogonality is satisfied:

*p*are mutually orthogonal and as such they can be used as basis functions for

*OAM modulation*. The number of OAM states to be used depends on atmospheric turbulence strength. For

*N*= 2

*L*+ 1, the corresponding OAM states can be indexed by

*l*where

*l*takes values in the set {-

*L*,-

*L*+ 1,…,-1,0,1,…,

*L*}. By increasing the number of dimensions (i.e., the number of OAM eigenstates), we can increase the aggregate data rate of the system.

*terrestrial*FSO communication [18

18. I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express **18**(24), 24722–24728 (2010). [CrossRef] [PubMed]

**18**(24), 24722–24728 (2010). [CrossRef] [PubMed]

*N*branches by using a power splitter (such as 1:

*N*star coupler) to feed

*N*Mach-Zehnder modulators (MZMs), each corresponding to one of the

*N*OAM modes. The mode demultiplexer can be implemented by propagating the multimode signal in opposite direction, as shown in Fig. 1(c). The

*j*th input to the

*j*th MZM,

*j*th coordinate of the signal to be modulated (see Fig. 1b). The output of mode multiplexer is expanded by telescope and transmitted towards remote destination. The OAM multiplexing is obtained by summing up

*N*independent streams per each OAM state into a single optical beam. Clearly, when OAM transmitter and receiver are implemented as shown in Fig. 1(b,c) we are not able to distinguish between OAM modes with azimuthal mode numbers of the same magnitude but of opposite sign. Nevertheless, distinguishable modes

*l*= 0,1,…,

*L*(for fixed

*p*) are still orthogonal. The mode detector shown in Fig. 1(e), instead of being implemented based on Fig. 1(c) it can be implemented based on integrated ring-shaped detector with

*N*-different p.i.n. regions to capture different

*l*-modes, as illustrated in Fig. 1(a) for

*p*= 0. Such a mode detector will have

*N*outputs that correspond to

*N*-projections along OAM modes. After this generic description of OAM based deep-space/near-Earth optical communication systems, we provide more details of OAM transmitter and receiver.

*K*different bit streams coming from different information sources are encoded using (

*n*,

*k*) (

_{m}*m*= 1,…,

*K*) LDPC codes, as shown in the Fig. 1(d). The outputs of the encoders are interleaved by the

*K*×

*n*block interleaver. The block interleaver accepts bits from the encoders row-wise and outputs bits column-wise to the mapper, which accepts

*K*bits at each time instance

*i*. The mapper determines the corresponding

*M*-ary signal constellation point by

^{N}*M*is the number of amplitude levels per OAM state and

*C*is the normalization constant. The set {Φ

_{N}_{1}, Φ

_{2},…,Φ

_{N}} represents a set of

*N*orthogonal OAM basis functions, while with

*φ*

_{i}_{,}

*we denoted OAM modulation coordinates of*

_{j}*i*th constellation point. The signals are then modulated, mode multiplexed and sent over the deep-space or near-Earth optical channel (see Fig. 1).

*N*to be used is determined by the desired final rate and current channel conditions. The simplest OAM-based coded modulation scheme with direct detection can be described by the following set of constellation points for

*N*= 3 and

*M*= 2 {(0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1)}. The

*N*-dimensional signal constellation can be obtained as the

*N*-dimensional Cartesian product of a one-dimensional signal constellation originating from non-negative pulse-amplitude modulation (PAM). At the receiver side (see Fig. 1(d)), after OAM demodulation (or mode demultiplexing) and photodetection, the outputs of the

*N*branches of the demodulator are sampled at the symbol rate, and the corresponding samples, after analog-to-digital conversion, are forwarded to the

*a posteriori*probability (APP) demapper. The orthogonality among OAM modes in realistic deep-space and near-Earth optical communication systems can be re-established by various MIMO and equalization techniques, as discussed in Section 4. The APP demapper provides the bit LLRs required for iterative LDPC decoding (see Fig. 1e). The

*l*th branch in Fig. 1(f) represents the projection along

*l*th OAM state (coordinate). Let

*R**denote the received constellation point, and*

_{i}

*S*_{0}denote the reference constellation point. The superscript (

*l*) (

*l*= -

*L*,…,-1,0,1…,

*L*) is used to denote the

*l*th OAM coordinate. When the deep-space/near-Earth optical communication system is based on

*N*-dimensional transmitter and receiver shown in Fig. 1(c,d), then the corresponding signal constellation point is defined as

*P*(

*R**|*

_{i}

*S**) denote the conditional probabilities that are estimated by collection of OAM crosstalk histograms, obtained by propagating sufficiently long training sequence over the deep-space/near-Earth optical channel, while*

_{i}*P*(

**) denotes**

*S**a priori*probability of symbol

**. The symbol log-likelihood ratios (LLRs) can be calculated by**

*S**c*the

_{j}*j*th bit in the observed symbol

**binary representation**

*S***= (**

*c**c*

_{0},

*c*

_{1},…,

*c*

_{b}_{-1}) (

*b*is the number of bits needed to represent the symbol

**). The prior symbol LLRs for the next iteration are determined by**

*S**L*(

*c*) = log[

_{j}*P*(

*c*= 0)/

_{j}*P*(

*c*= 1)], the prior symbol LLRs become

_{j}*L*(

*c*

^{(in)}

*) [*

_{j}*L*(

*c*

^{(out)}

*)] to denote the LDPC decoder input (output). The bit LLRs*

_{j}*L*(

*c*) are determined from symbol LLRs by

_{j}*j*th bit reliability is calculated as the logarithm of the ratio of a probability that

*c*= 0 and probability that

_{j}*c*= 1. In the nominator, we perform the summation over all symbols

_{j}**having 0 at the observed position**

*S**j*, while in the denominator over all symbols

**having 1 at the same position**

*S**j*. With

*L*(

_{a}*c*) we denoted the prior (extrinsic) information determined from the APP demapper. The inner summation in (13) is performed over all bits of symbol

_{k}**, selected in the outer summation, for which**

*S**c*= 0,

_{k}*k*≠

*j*. The bit LLRs are forwarded to LDPC decoders, which provide extrinsic bit LLRs for demapper according to (12), and are used as inputs to (11) as the prior information.

*N*OAM orthogonal modes, we employ the in-phase (I) and quadrature (Q) components so that the corresponding space is 2

*N*-dimensional. On the other hand, when four-dimensional modulator is used, with two coordinates being I- and Q-coordinates in x-polarization and two coordinates being I- and Q-coordinates in y polarization, the corresponding space is 4

*N*-dimensional. The 4

*N*-dimensional scheme allows even 4

*N*-bits to be transmitted per single symbol, which represents an energy-efficient communication scheme. However, the complexity of such receiver might be too high even for near-Earth applications. The one-dimensional coherent detection scheme seems to be a good compromise between optical link energy-efficiency and receiver complexity. In Fig. 2(c), we show the receiver configuration with coherent detection that assumes that one-dimensional MZMs are used. One laser is used to detect all coordinates, whose output is used as an input to 1:

*N*power splitter. The output of balanced detector

*n*(

*n*= 0,1,…,

*N*-1) provides the projection along OAM state

*n*. This coherent detection receiver scheme; composed of mode-demultiplexer, balanced coherent detectors, power splitter and local laser; can be integrated on a single chip using hybrid opto-electronic integrated circuit (OEIC) technology.

20. I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Generalized OFDM (GOFDM) for ultra-high-speed optical transmission,” Opt. Express **19**(7), 6969–6979 (2011). [CrossRef] [PubMed]

21. H. G. Batshon and I. B. Djordjevic, “Beyond 240 Gb/s per wavelength optical transmission using coded hybrid subcarrier/amplitude/ phase/polarization modulation,” IEEE Photon. Technol. Lett. **22**(5), 299–301 (2010). [CrossRef]

20. I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Generalized OFDM (GOFDM) for ultra-high-speed optical transmission,” Opt. Express **19**(7), 6969–6979 (2011). [CrossRef] [PubMed]

5. H. Hemmati, “Interplanetary laser communications,” Optics & Photonics News **18**(11), 22–27 (2007). [CrossRef]

5. H. Hemmati, “Interplanetary laser communications,” Optics & Photonics News **18**(11), 22–27 (2007). [CrossRef]

## 3. Orthogonal OAM division multiplexing

*K*bits at time instance

*i*from the (

*K*×

*n*) interleaver column-wise and determines the corresponding

*M*-ary (

*M*= 2

*) signal constellation point (*

^{K}*ϕ*

_{I}

*,*

_{,i}*ϕ*

_{Q}

*) assuming a two-dimensional (2D) constellation such as*

_{,i}*M*-ary PSK or

*M*-ary QAM. The coordinates correspond to in-phase (I) and quadrature (Q) components of

*M*-ary 2D constellation. The 2D constellation points, after serial-to-parallel (S/P) conversion, are used as the inputs to I/Q modulators of OAM transmitters shown in Fig. 3(a). On the receiver side, upon OAM demultiplexing and detection as shown in Fig. 3(b), the soft estimates of symbols

*k*th OAM state are forwarded to the APP demapper, which determines the symbol LLRs. The soft symbol estimates in the

*k*th OAM state

## 4. Compensation of OAM crosstalk introduced by atmospheric turbulence

### OAM Channel Model

**[**

*x*=*x*

_{1}

*x*

_{2}…

*x*]

_{N}^{T}is transmitted vector with

*i*th complex number component being the in-phase/quadrature (I/Q) signal constellation point transmitted using

*i*th OAM state;

**[**

*y*=*y*

_{1}

*y*

_{2}…

*y*]

_{N}^{T}is the received vector;

**[**

*w*=*w*

_{1}

*w*

_{2}…

*w*]

_{N}^{T}is the vector of noise samples; and

**represents the channel matrix with rank(**

*H***) =**

*H**N*that corresponds to the number of OAM states not experiencing fading (due to atmospheric turbulence). The channel matrix coefficients can be determined by using a training sequence. The OAM FSO channel model (14) is similar to a wireless communication MIMO model [25

25. S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. **16**(8), 1451–1458 (1998). [CrossRef]

29. I. B. Djordjevic, L. Xu, and T. Wang, “PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation,” Opt. Express **16**(19), 14845–14852 (2008). [CrossRef] [PubMed]

29. I. B. Djordjevic, L. Xu, and T. Wang, “PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation,” Opt. Express **16**(19), 14845–14852 (2008). [CrossRef] [PubMed]

### OAM crosstalk compensation by equalization

*i*th OAM detector output can be represented as a finite impulse response (FIR) filter. That is, the channel model (15) is similar to an intersymbol interference (ISI) model so that various channel equalization techniques [26–30] can be used to compensate for OAM crosstalk including a feed-forward equalizer (FFE), decision-feedback equalizer (DFE), maximum-likelihood sequence detector (MLSD), and a turbo equalizer.

### OAM-time coding

25. S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. **16**(8), 1451–1458 (1998). [CrossRef]

29. I. B. Djordjevic, L. Xu, and T. Wang, “PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation,” Opt. Express **16**(19), 14845–14852 (2008). [CrossRef] [PubMed]

*N*

_{s}symbols, which is true for multi-gigabit transmission, the OAM FSO channel inputs and outputs are matrices, with dimensions corresponding to space-coordinate (the number of OAM modes) and time-coordinate (the number of symbol intervals). This can be modeled by

*N*is the number of OAM modes. Let us observe an OAM-time code in which the receiver has the knowledge of the channel matrix

**. Under maximum-likelihood (ML) detection, the optimum transmit matrix is obtained by the following minimization:**

*H*### Adaptive modulation and coding (AMC)

31. I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express **17**(20), 18250–18262 (2009). [CrossRef] [PubMed]

33. M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express **18**(3), 1820–1832 (2010). [CrossRef] [PubMed]

## 5. Performance analysis

*N*-dimensional (ND) OAM modulation versus PPM. On horizontal axis we use average number of photons per dimension (in dB-scale) so that ND-OAM and PPM can be compared. The results of simulations shown in Figs. 4-6 are obtained for Poisson deep-space optical channel model for the average number of background photons of 0.1. We assume that residual crosstalk on a given OAM mode is given by

*n*

_{x}= 0.1. From Fig. 4 it is clear that as we increase the number of dimensions, the improvement of ND-OAM over PPM is larger. The improvement (measured at BER of 10

^{−6}) ranges from 0.67 dB for

*N*= 2 to 2.81 dB for

*N*= 8. Moreover, the spectral efficiency

*S*of ND-OAM is

_{E}*T*we denoted the signaling interval (reciprocal of a symbol rate). For the same number of dimensions (

_{s}*M*=

*N*), the spectral efficiency of ND-OAM is

*N*

^{2}/log

_{2}

*N*times better. For example, for

*M*=

*N*= 8, the spectral efficiency of ND-OAM is 21.334 times better.

_{R}see [6].) For

*N*= 8, the degradation in performance ranges from 2.02 dB in medium turbulence regime to 2.87 dB in strong turbulence regime (at BER of 10

^{−6}).

10. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. **47**(13), 2414–2429 (2008). [CrossRef] [PubMed]

*M*= 2 and

*N*≥2 can operate even in strong turbulence regime for reasonable high SCNRs, as shown in Fig. 7.

## 6. Concluding remarks

*N*-dimensional OAM modulation, and orthogonal OAM division multiplexing. We demonstrate by Monte Carlo simulations, over the atmospheric turbulence channels, that proposed schemes can operate under strong atmospheric turbulence and provide dramatic improvement in throughput. We have shown that the improvement of ND-OAM over PPM, for the same number of dimensions, (measured at BER of 10

^{−6}) ranges from 0.67dB for

*N*= 2 to 2.81 dB for

*N*= 8. Moreover, the spectral efficiency, for the same number of dimensions, of ND-OAM is

*N*

^{2}/log

_{2}

*N*times better. The proposed OAM-based schemes, therefore, represent the excellent candidates for next generation deep-space and near-Earth optical communications. In addition to next generation deep-space/near-Earth optical communication enabling technologies, we have described different approaches to deal with atmospheric turbulence induced OAM crosstalk including equalization, OAM-time coding, and adaptive modulation and coding.

2. B. Moision and J. Hamkins, “Coded modulation for the deep-space optical channel: serially concatenated pulse-position modulation,“ The Interplanetary Network Progress Report 42-161 (Jet Propulsion Laboratory, Pasadena, California, 15 May 2005), pp. 1-25, http://ipnpr.jpl.nasa.gov/progress_report/42-161/161T.pdf.

*N*= 8, and at the same time improve spectral efficiency 21 times (also for

*N*= 8), indicating that the proposed scheme is a promising candidate for next generation deep‐space and near-Earth optical communications.

## Acknowledgments

## References and links

1. | B. Moision and J. Hamkins, “Deep-space optical communications downlink budget: modulation and coding,“ The Interplanetary Network Progress Report 42-154, April-June 2003 (Jet Propulsion Laboratory, Pasadena, California, 15 August 2003), pp. 1-28, http://ipnpr.jpl.nasa.gov/progress_report/42-154/154K.pdf. |

2. | B. Moision and J. Hamkins, “Coded modulation for the deep-space optical channel: serially concatenated pulse-position modulation,“ The Interplanetary Network Progress Report 42-161 (Jet Propulsion Laboratory, Pasadena, California, 15 May 2005), pp. 1-25, http://ipnpr.jpl.nasa.gov/progress_report/42-161/161T.pdf. |

3. | F. Xu, M.-A. Khalighi, and S. Bourennane, “Coded PPM and multipulse PPM and iterative detection for free-space optical links,” J. Opt. Commun. Netw. |

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5. | H. Hemmati, “Interplanetary laser communications,” Optics & Photonics News |

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

7. | I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express |

8. | I. B. Djordjevic, “Orbital angular momentum (OAM) based LDPC-coded deep-space optical communication,” Proc. SPIE |

9. | C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. |

10. | J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. |

11. | J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. |

12. | G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express |

13. | M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. |

14. | M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory |

15. | S. Lin and D. J. Costello, |

16. | I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol. |

17. | J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. |

18. | I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express |

19. | J. D. Jackson, |

20. | I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Generalized OFDM (GOFDM) for ultra-high-speed optical transmission,” Opt. Express |

21. | H. G. Batshon and I. B. Djordjevic, “Beyond 240 Gb/s per wavelength optical transmission using coded hybrid subcarrier/amplitude/ phase/polarization modulation,” IEEE Photon. Technol. Lett. |

22. | H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. |

23. | I. B. Djordjevic and H. G. Batshon, “Generalized hybrid subcarrier/amplitude/phase/polarization LDPC-coded modulation based FSO Networking,” in |

24. | W. Shieh and I. B. Djordjevic, |

25. | S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. |

26. | A. Goldsmith, |

27. | D. Tse and P. Viswanath, |

28. | T. M. Duman and A. Ghrayeb, |

29. | I. B. Djordjevic, L. Xu, and T. Wang, “PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation,” Opt. Express |

30. | J. G. Proakis, |

31. | I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express |

32. | I. B. Djordjevic, “Adaptive modulation and coding for communication over the atmospheric turbulence channels,” in |

33. | M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express |

**OCIS Codes**

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(040.1880) Detectors : Detection

(060.4080) Fiber optics and optical communications : Modulation

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

(120.6085) Instrumentation, measurement, and metrology : Space instrumentation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: June 1, 2011

Revised Manuscript: June 27, 2011

Manuscript Accepted: June 29, 2011

Published: July 11, 2011

**Citation**

Ivan B. Djordjevic, "Deep-space and near-Earth optical communications by coded orbital angular momentum (OAM) modulation," Opt. Express **19**, 14277-14289 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14277

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