Deep-space optical communication links operate under severely limited signal power, approaching the photon-starved regime that requires a receiver capable of measuring individual incoming photons. This makes the photon information efficiency (PIE), i.e., the number of bits that can be retrieved from a single received photon, a relevant figure of merit to characterize data rates achievable in deep-space scenarios. We review theoretical PIE limits assuming a scalable modulation format, such as pulse position modulation (PPM), combined with a photon counting direct detection receiver. For unrestricted signal bandwidth, the attainable PIE is effectively limited by the background noise acquired by the propagating optical signal. The actual PIE limit depends on the effectiveness of the noise rejection mechanism implemented at the receiver, which can be improved by the nonlinear optical technique of quantum pulse gating. Further enhancement is possible by resorting to photon number resolved detection, which improves discrimination of PPM pulses against weak background noise. The results are compared with the ultimate quantum mechanical PIE limit implied by the Gordon–Holevo capacity bound, which takes into account general modulation formats as well as any physically permitted measurement techniques.
We identify the maximum attainable transmission rate of a noisy optical link employing the pulse position modulation (PPM) format with direct detection. We show that for a fixed background noise level it is possible to achieve the information rate directly proportional to the average detected signal power in the photon-starved regime. This implies inverse-square scaling with the distance, presenting a qualitative improvement over previously obtained estimates that scaled as the inverse of the fourth power of the distance. The necessary ingredients to achieve the improved mode of operation are the unrestricted optimization of the PPM order and the complete decoding of detection events to extract information from sequences containing multiple counts within one PPM frame. Importantly, information efficiency equivalent to high-order PPM formats can be attained using signals with uniformly distributed optical power processed with recently proposed structured optical receivers.
We investigate theoretically the efficiency of deep-space optical communication in the presence of background noise. With decreasing average signal power spectral density, a scaling gap opens up between optimized simple-decoded pulse position modulation and generalized on-off keying with direct detection. The scaling of the latter follows the quantum mechanical capacity of an optical channel with additive Gaussian noise. Efficient communication is found to require a highly imbalanced distribution of instantaneous signal power. This condition can be alleviated through the use of structured receivers which exploit optical interference over multiple time bins to concentrate the signal power before the detection stage.
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