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Information Theory and Applications Workshop (ITA)

Approaching the ultimate limits of communication efficiency with a photon-counting detector

Baris I. Erkmen, Bruce E. Moision, Samuel J. Dolinar, Kevin M. Birnbaum, D. Divsalar

Published Feb 1, 2012• 3 citations
Publisher

Abstract

Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement is as of yet unknown, and it is also likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over classical- and nonclassical-state alphabets. We first review the state-of-the-art coherent on-off-keying (OOK) with a photon-counting measurement, illustrating its asymptotic inefficiency relative to the Holevo limit. We show that a commonly made Poisson approximation in thermal noise leads to unbounded photon information efficiencies, violating the conjectured Holevo limit. We analyze two binary-modulation architectures that improve upon the dimensional versus photon efficiency tradeoff achievable with conventional OOK. We show that at high photon efficiency these architectures achieve an efficiency tradeoff that differs from the best possible tradeoff-determined by the Holevo capacity-by only a constant factor. The first architecture we analyze is a coherent-state transmitter that relies on feedback from the receiver to control the transmitted energy. The second architecture uses a single-photon number-state source.

DOI
10.1109/ita.2012.6181832

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Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement is as of yet unknown, and it is also likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over classical- and nonclassical-state alphabets. We first review the state-of-the-art coherent on-off-keying (OOK) with a photon-counting measurement, illustrating its asymptotic inefficiency relative to the Holevo limit. We show that a commonly made Poisson approximation in thermal noise leads to unbounded photon information efficiencies, violating the conjectured Holevo limit. We analyze two binary-modulation architectures that improve upon the dimensional versus photon efficiency tradeoff achievable with conventional OOK. We show that at high photon efficiency these architectures achieve an efficiency tradeoff that differs from the best possible tradeoff-determined by the Holevo capacity-by only a constant factor. The first architecture we analyze is a coherent-state transmitter that relies on feedback from the receiver to control the transmitted energy. The second architecture uses a single-photon number-state source.
Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement scheme is as of yet unknown, and it is also likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over classical- and nonclassical-state alphabets. We analyze two binary modulation architectures that improve upon the dimensional versus photon efficiency tradeoff achievable with the state-of-the-art coherent-state on-off keying modulation. We show that at high photon efficiency these architectures achieve an efficiency tradeoff that differs from the best possible tradeoff--determined by the Holevo capacity--by only a constant factor. The first architecture we analyze is a coherent-state transmitter that relies on feedback from the receiver to control the transmitted energy. The second architecture uses a single-photon number-state source.
Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement is unknown, and likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over classical- and nonclassical-state alphabets. We first review state-of-the-art coherent on-off-keying (OOK) and pulse-position modulation (PPM) with a photon-counting measurement, illustrating its asymptotic inefficiency relative to the Holevo limit. Then we analyze two architectures that improve upon the dimensional versus photon efficiency tradeoff achievable with conventional OOK or PPM. We show that at high photon efficiency these architectures achieve an efficiency tradeoff that differs from the best possible tradeoff by only a constant factor. The first architecture is a coherent-state transmitter that relies on feedback from the receiver to control the transmitted energy. The second architecture uses a single-photon number-state source.
Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement scheme is as of yet unknown, and it is also likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over classical- and nonclassical-state alphabets. We analyze two binary-modulation architectures that improve upon the dimensional versus photon efficiency tradeoff achievable with the state-of-the-art coherent-state on-off keying modulation. We show that at high photon efficiency these architectures achieve an efficiency tradeoff that differs from the best possible tradeoff--determined by the Holevo capacity--by only a constant factor. The first architecture we analyze is a coherent-state transmitter that relies on feedback from the receiver to control the transmitted energy. The second architecture uses a single-photon number-state source.
It is well known that ideal free-space optical communication at the quantum limit can have unbounded photon information efficiency (PIE), measured in bits per photon. High PIE comes at a price of low dimensional information efficiency (DIE), measured in bits per spatio-temporal-polarization mode. If only temporal modes are used, then DIE translates directly to bandwidth efficiency. In this paper, the DIE vs. PIE tradeoffs for known modulations and receiver structures are compared to the ultimate quantum limit, and analytic approximations are found in the limit of high PIE. This analysis shows that known structures fall short of the maximum attainable DIE by a factor that increases linearly with PIE for high PIE. The capacity of the Dolinar receiver is derived for binary coherent-state modulations and computed for the case of on off keying (OOK). The DIE vs. PIE tradeoff for this case is improved only slightly compared to OOK with photon counting. An adaptive rule is derived for an additive local oscillator that maximizes the mutual information between a receiver and a transmitter that selects from a set of coherent states. For binary phase-shift keying (BPSK), this is shown to be equivalent to the operation of the Dolinar receiver. The Dolinar receiver is extended to make adaptive measurements on a coded sequence of coherent state symbols. Information from previous measurements is used to adjust the a priori probabilities of the next symbols. The adaptive Dolinar receiver does not improve the DIE vs. PIE tradeoff compared to independent transmission and Dolinar reception of each symbol.
An ideal intensity-modulated photon-counting channel can achieve unbounded photon information efficiencies (PIEs). However, a number of limitations of a physical system limit the practically achievable PIE. In this paper, we discuss several of these limitations and illustrate their impact on the channel. We show that, for the Poisson channel, noise does not strictly bound PIE, although there is an effective limit, as the dimensional information efficiency goes as e[overline] e PIE beyond a threshold PIE. Since the Holevo limit is bounded in the presence of noise, this illustrates that the Poisson approximation is invalid at large PIE for any number of noise modes. We show that a finite transmitter extinction ratio bounds the achievable PIE to a maximum that is logarithmic in the extinction ratio. We show how detector jitter limits the ability to mitigate noise in the PPM signaling framework. We illustrate a method to model detector blocking when the number of detectors is large, and illustrate mitigation of blocking with spatial spreading and altering. Finally, we illustrate the design of a high photon efficiency system using state-of-the-art photo-detectors and taking all these effects into account.
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.