The Discrete-Time Poisson Channel at Low Input Powers

Lapidoth, Amos; Shapiro, Jeffrey H.; Venkatesan, Vinodh; Wang, Ligong

doi:10.1109/tit.2011.2134430

Cited by 56 publications

(74 citation statements)

References 6 publications

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“…The capacity of this channel-the Poisson channel-was studied in [3,4], and the regime of low average photon numbers was studied in [17]. For our purposes of performance comparison, we need a more precise scaling law of rate performance, which the following lemma states.…”

Section: Coded Transmissions and Capacity Resultsmentioning

confidence: 99%

“…Finally, we would like to note that even though we believe that the receiver structure described in Conjecture 5 (a collective-measurement multi-mode generalization of the Dolinar receiver) is ineffective in attaining capacity that is any better than what ideal direct detection alone can, this type of all-optical pre-processing can immensely lessen the peak-power requirements compared to the high-peak-power OOK modulation that must be used by the direct-detection receiver to attain rate performance as stated in (17). An example of such a receiver was described in [21], using which a binary-phase-shift-keying modulation (which has the minimum possible peak power in the E 1 regime) could achieve the same rate scaling as in (17).…”

Section: Conjecturementioning

confidence: 93%

“…An example of such a receiver was described in [21], using which a binary-phase-shift-keying modulation (which has the minimum possible peak power in the E 1 regime) could achieve the same rate scaling as in (17). The scheme in [21] uses a passive linearmode mixing on the codeword symbols, but does not use any local signals prior to detection.…”

Section: Conjecturementioning

confidence: 99%

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Capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control

2017

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We study the problem of designing optical receivers to discriminate between multiple coherent states using coherent processing receivers-i.e., one that uses arbitrary coherent feedback control and quantum-noise-limited direct detection-which was shown by Dolinar to achieve the minimum error probability in discriminating any two coherent states. We first derive and re-interpret Dolinar's binary-hypothesis minimum-probability-of-error receiver as the one that optimizes the information efficiency at each time instant, based on recursive Bayesian updates within the receiver. Using this viewpoint, we propose a natural generalization of Dolinar's receiver design to discriminate M coherent states each of which could now be a codeword, i.e., a sequence of N coherent states each drawn from a modulation alphabet. We analyze the channel capacity of the pure-loss optical channel with a general coherent-processing receiver in the low-photon number regime and compare it with the capacity achievable with direct detection and the Holevo limit (achieving the latter would require a quantum joint-detection receiver). We show compelling evidence that despite the optimal performance of Dolinar's receiver for the binary coherent-state hypothesis test (either in error probability or mutual information), the asymptotic communication rate achievable by such a coherent-processing receiver is only as good as direct detection. This suggests that in the infinitelylong codeword limit, all potential benefits of coherent processing at the receiver can be obtained by designing a good code and direct detection, with no feedback within the receiver.Over time t ∈ [0, T ), consider a coherent-state input of constant amplitude S to a pure-loss optical channel, where S ∈ C, and |S| 2 T is the mean photon number. Coherent state is the quantum description of light generated by an ideal laser. In a noise-free environment, if one uses an ideal quantum-noise-limited photon counter to receive this optical signal, the output of the photon counter is a Poisson point process, with rate λ = |S| 2 over the time period [0, T ), indicating arrivals of individual photons. Clearly, one can generalize from a constant input to an arbitrary temporal-mode shape of the coherentstate pulse S(t), t ∈ [0, T ), which if detected with an ideal photon counter would result in a non-homogeneous Poisson process of rate λ(t) = |S(t)| 2 . The mean number of photons,T 0 |S(t)| 2 dt, expended in the transmitted pulse, is the natural metric quantifying communication cost. A photon counter with sub-unity detection efficiency η ∈ (0, 1] can be modeled as a lossy channel of transmissivity η followed by ideal photon counting. Further, a coherent state at the input of a lossy channel appears as a coherent state at the output of the channel with its amplitude scaled by the channel's transmissivity η ∈ (0, 1]. Therefore, without loss of generality, in this paper we will assume a lossless channel and unity-efficiency photodetection, with an implicit scaling of any constraint imposed on the t...

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Section: Coded Transmissions and Capacity Resultsmentioning

confidence: 99%

Section: Conjecturementioning

confidence: 93%

Section: Conjecturementioning

confidence: 99%

See 1 more Smart Citation

Capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control

2017

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“…It is clear that conditions (7) and (8) are equivalent to (4) and (5). Hence, if these conditions are satisfied, the capacity region of the Poisson interference channel is the same as that of the compound MAC.…”

Section: Capacity Region For the Strong Interference Channelmentioning

confidence: 95%

“…However, in the short-noise-limited regime, the Poisson channel is a suitable model [3]. The point-to-point Poisson channel has been intensively studied both in continuous time [4]- [7] and discrete time [8]- [10]. However, the study of multiuser Poisson channels is limited, with few exceptions on the multiple-access channel (MAC) [11], on the broadcast channel [12] and on the Poisson channel with side information at the transmitter [13].…”

Section: Introductionmentioning

confidence: 99%

On the Capacity Bounds for Poisson Interference Channels

Lai

Liang

Shamai

2015

IEEE Trans. Inform. Theory

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The Poisson interference channel, which models optical communication systems with multiple transceivers in the short-noise-limited regime, is investigated. Conditions for the strong interference regime are characterized and the corresponding capacity region is derived, which is the same as that of the compound Poisson multiple access channel with each receiver decoding both messages. For the cases when the strong interference conditions are not satisfied, inner and outer bounds on the capacity region are derived. The inner bound is derived via approximating the Poisson interference channel by a binary interference channel and then evaluating the corresponding HanKobayashi region. The outer bounds are obtained via various techniques including noise reduction, genie-aided scheme and channel transformation. The Poisson Z-interference channel is then studied. The sum rate capacity is obtained when the cross link coefficient is either sufficiently small or sufficiently large.

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Upper bounds on the capacity for optical intensity channels with AWGN

Zhang

et al. 2016

Sci. China Inf. Sci.

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The Discrete-Time Poisson Channel at Low Input Powers

Cited by 56 publications

References 6 publications

Capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control

Capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control

On the Capacity Bounds for Poisson Interference Channels

Upper bounds on the capacity for optical intensity channels with AWGN

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