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Optica Laser Congress (ASSL, LAC, LS&C)

Ultimate Limits on Photon and Spectral Efficient Communication through Atmospheric Turbulence

Jeffrey H. Shapiro, Nivedita Chandrasekaran, Ligong Wang

Published Jan 1, 2013• 1 citation
Publisher

Abstract

Bounds on the ergodic classical and private capacities for optical communication through turbulence are presented, showing that high photon and spectral efficiencies can be achieved simultaneously in the near-field power transfer regime.
DOI
10.1364/lsc.2013.ltu1b.2

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Ultimate Limits on Photon and Spectral Efficient Communication through Atmospheric Turbulence

Jeffrey H. Shapiro, Nivedita Chandrasekaran, Ligong Wang

Abstract: Bounds on the ergodic classical and private capacities for optical communication through turbulence are presented, showing that high photon and spectral efficiencies can be achieved simultaneously in the near-field power transfer regime. © 2013 Optical Society of America OCIS codes: (060.2605) Free-space optical communication; (010.1330) Atmospheric turbulence.

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Vacuum-propagation optical communication with high photon efficiency (many bits/photon) and high spectral efficiency (many bits/s ·Hz) requires operation in the near-field power transfer regime with a large number of spatial modes. For terrestrial propagation paths, however, the effects of atmospheric turbulence must be factored into the photon and spectral efficiency assessments. In Part I of this study [N. Chandrasekaran and J. H. Shapiro, “Photon Information Efficient Communication Through Atmospheric Turbulence-Part I: Channel Model and Propagation Statistics,” J. Lightw. Technol., vol. 32, no. 6, pp. 1075-1087, Mar. 2014], modal-transmissivity statistics were derived for the turbulent channel that depend solely on the mutual coherence function of the atmospheric Green's function, and these bounds were evaluated for ~ 200 spatial-mode systems whose transmitters used either focused-beam (FB), Hermite-Gaussian (HG), or Laguerre-Gaussian (LG) modes and whose receivers either did or did not employ adaptive optics. This Part II paper derives upper and lower bounds for the ergodic Holevo capacities of classical and private information transmission over the multiple spatial-mode turbulent channel that can be evaluated from Part I's transmissivity statistics. Also included are bounds on the ergodic capacity for on-off keying encoding and direct detection. It is shown that: 1) adaptive optics are not necessary to realize high photon information efficiency and high spectral efficiency simultaneously; 2) an FB-mode system with perfect adaptive optics outperforms its HG-mode and LG-mode counterparts; and 3) the converse is true when adaptive optics are not employed.
Optical communication with high photon-efficiency (many bits/photon) and high spectral efficiency (SE) (many bits/s-Hz) cannot be achieved unless multiple spatial modes are employed. For vacuum propagation, it is known that achieving 10 bits/photon and 5 bits/s-Hz requires 189 low-loss spatial modes at the ultimate Holevo limit and 4500 such modes at the Shannon limit for on-off keying with direct detection. For terrestrial propagation paths, however, atmospheric turbulence corrupts multiple spatial-mode operation. This paper derives power-transmissivity bounds and average intermodal crosstalks for the turbulent channel that depend solely on the mutual coherence function of the atmospheric Green's function. These statistics are then evaluated for ~ 200 spatial-mode systems whose transmitters use either focused-beam, Hermite-Gaussian (HG), or Laguerre-Gaussian (LG) modes and whose receivers either do or do not employ adaptive optics. It is shown that: (1) adaptive optics are not necessary for achieving both high photon information efficiency (PIE) and high SE; (2) systems employing HG or LG modes achieve the same capacities through turbulence; and (3) the orbital angular momentum carried by LG modes does not provide turbulence immunity. In the companion paper [N. Chandrasekaran, J. H. Shapiro, and L. Wang, “Photon Information Efficient Communication Through Atmospheric Turbulence-Part II: Bounds on Ergodic Classical and Private Capacities,” J. Lightw. Technol., vol. 32, no. 6, pp. 1088-1097, Mar. 2014], the transmissivity bounds are used to quantify the turbulence-induced loss in PIE versus SE performance for these mode sets.
Free-space optical communication systems potentially gain many dBs over RF systems. There is no upper limit on the theoretically achievable photon efficiency when the system is quantum-noise-limited: a) Intensity modulations plus photon counting can achieve arbitrarily high photon efficiency, but with sub-optimal spectral efficiency. b) Quantum-ideal number states can achieve the ultimate capacity in the limit of perfect transmissivity. Appropriate error correction codes are needed to communicate reliably near the capacity limits. Poisson-modeled noises, detector losses, and atmospheric effects must all be accounted for: a) Theoretical models are used to analyze performance degradations. b) Mitigation strategies derived from this analysis are applied to minimize these degradations.
We investigate modulation and coding techniques that approach the fundamental limits of communication and key distribution over optical channels, in the regime of simultaneously high photon and bandwidth efficiencies. First, we develop a simple and robust system design for free-space optical communication that incorporates pulse-position modulation (PPM) over multiple spatial degrees of freedom in order to achieve high photon and spectral efficiency. Further, in the context of key distribution, we determine the optimal rate using a Poisson source of entangled photon pairs and photon detectors, and show how to approach it using PPM parsing of the detected photon stream.