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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

A review of the information capacity of single-mode free-space optical communication

Baris I. Erkmen, Bruce E. Moision, Kevin M. Birnbaum

Published Feb 11, 2010• 11 citations
Publisher

Abstract

We provide a summary of the classical information capacity of single-mode free-space optical communication for pure-loss channels. We compare the capacities afforded by structured transmitters and receivers to that of the ultimate communication capacity dictated by the quantum nature of light, and we draw the following conclusions. The ultimate capacity can be achieved with classical coherent states (i.e., ideal laser light), but the capacity-achieving receiver (measurement) is yet to be determined. In photon-starved pure-loss channels, binary phase modulation in combination with the optimal receiver is near-capacity achieving, and more importantly, it is superior to on-off keying with either the optimal receiver (as yet to be determined) or with a photon-counter. Heterodyne detection approaches the ultimate capacity at high mean photon numbers.

DOI
10.1117/12.843542

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We provide a summary of the classical information capacity of single-mode free-space optical communication for pure-loss channels. We compare the capacities afforded by structured transmitters and receivers to that of the ultimate communication capacity dictated by the quantum nature of light, and we draw the following conclusions. The ultimate capacity can be achieved with classical coherent states (i.e., ideal laser light), but the capacity-achieving receiver (measurement) is yet to be determined. In photon-starved pure-loss channels, binary phase modulation in combination with the optimal receiver is near-capacity achieving, and more importantly, it is superior to on-off keying with either the optimal receiver (as yet to be determined) or with a photon-counter. Heterodyne detection approaches the ultimate capacity at high mean photon numbers.
Feature Issue on Optical Wireless Communications (OWC) The ultimate classical information capacity of multiple-spatial-mode, wideband optical communications in vacuum between soft-aperture transmit and receive pupils is considered. The ultimate capacity is shown to be achieved by coherent-state encoding and joint measurements over entire code words. This capacity is compared with the capacities realized with the same encoding and homodyne or heterodyne detection, which are single-channel-use measurements. Realistic background spectral-radiance values are used to obtain tight bounds on the capacity of single-spatial-mode, narrowband 1.55 μm wavelength free-space communications in the presence of background light.
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated codewords with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations (passive linear optics: beamsplitters and phase-shifters, second order nonlinear process (squeezers), along with homodyne or heterodyne detection measurements) and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communications, one has to incorporate non-Gaussian (i.e. higher order nonlinear) operations in the receiver.
Semiclassical models for multiple-user optical communication cannot assess the ultimate limits on reliable communication as permitted by the laws of physics. In all optical communications settings that have been analyzed within a quantum framework so far, the gaps between the quantum limit to the capacity and the Shannon limit for structured receivers become most significant in the low photon-number regime. Here, we present a quantum treatment of a multiple-transmitter multiple-receiver multi-spatial-mode free-space interference channel with diffraction-limited loss and a thermal background. We consider the performance of a laser-light (coherent state) encoding in conjunction with various detection strategies such as homodyne, heterodyne, and joint detection. Joint detection outperforms both homodyne and heterodyne detection whenever the channel exhibits “very strong” interference. We determine the capacity region for homodyne or heterodyne detection when the channel has “strong” interference, and we conjecture the existence of a joint detection strategy that outperforms the former two strategies in this case. Finally, we determine the Han-Kobayashi achievable rate regions for both homodyne and heterodyne detection and compare them to a region achievable by a conjectured joint detection strategy. In these latter cases, we determine achievable rate regions if the receivers employ a recently discovered minentropy quantum simultaneous decoder.
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated code words with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent-state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations [passive linear optics: beam splitters and phase shifters; second-order nonlinear optics (or active linear optics): squeezers, along with homodyne or heterodyne detection measurements] and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communication, one has to incorporate non-Gaussian, i.e., third- or higher-order nonlinear operations in the receiver. Finally we compare our Gaussian receiver limit with experimentally feasible non-Gaussian receivers and show that in the regime of low received photon flux, it is possible to overcome the Gaussian receiver limit by relatively simple non-Gaussian receivers based on photon counting.
When classical information is sent over a channel with quantum-state modulation alphabet, such as the free-space optical (FSO) channel, attaining the ultimate (Holevo) limit to channel capacity requires the receiver to make joint measurements over long codeword blocks. In recent work, we showed a receiver for a pure-state channel that can attain the ultimate capacity by applying a single-shot optical (unitary) transformation on the received codeword state followed by simultaneous (but separable) projective measurements on the single-modulation-symbol state spaces. In this paper, we study the ultimate tradeoff between photon efficiency and spectral efficiency for the FSO channel. Based on our general results for the pure-state quantum channel, we show some of the first concrete examples of codes and laboratory-realizable joint-detection optical receivers that can achieve fundamentally higher (superadditive) channel capacity than receivers that physically detect each modulation symbol one at a time, as is done by all conventional (coherent or direct-detection) optical receivers.
The information capacity of an optical channel under power constraints is ultimately limited by the quantum nature of transmitted signals. We discuss currently available and emerging photonic technologies whose combination can be shown theoretically to enable nearly quantum-limited operation of a noisy optical communication link in the photon-starved regime, with the information rate scaling linearly in the detected signal power. The key ingredients are quantum pulse gating to facilitate mode selectivity, photon-number-resolved direct detection, and a photon-efficient high-order modulation format such as pulse position modulation, frequency shift keying, or binary phase shift keyed Hadamard words decoded optically using structured receivers.