Lower bounds on the capacity of discrete-time Poisson channels with dark current

Cao, Jihai; Hranilovic, Steve

doi:10.1109/bsc.2010.5472956

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…A more detailed discussion of these upper bounds and of the asymptotic behavior of the capacity can be found in Section 3. While we focus on capacity upper bounds, we mention that explicit (asymptotic and non-asymptotic) capacity lower bounds for several settings have been derived in [8,2,9,3,4,10].…”

Section: Previous Workmentioning

confidence: 99%

Improved Upper Bounds and Structural Results on the Capacity of the Discrete-Time Poisson Channel

Cheraghchi

Ribeiro

2019

IEEE Trans. Inform. Theory

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New capacity upper bounds are presented for the discrete-time Poisson channel with no dark current and an average-power constraint. These bounds are a simple consequence of techniques developed for the seemingly unrelated problem of upper bounding the capacity of binary deletion and repetition channels. Previously, the best known capacity upper bound in the regime where the average-power constraint does not approach zero was due to Martinez (JOSA B, 2007), which is re-derived as a special case of the framework developed in this paper. Furthermore, this framework is carefully instantiated in order to obtain a closed-form bound that noticeably improves the result of Martinez everywhere. Finally, capacity-achieving distributions for the discrete-time Poisson channel are studied under an average-power constraint and/or a peak-power constraint and arbitrary dark current. In particular, it is shown that the support of the capacity-achieving distribution under an average-power constraint only must be countably infinite. This settles a conjecture of Shamai (IEE Proceedings I, 1990) in the affirmative. Previously, it was only known that the support must be unbounded.

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Section: Previous Workmentioning

confidence: 99%

Improved Upper Bounds and Structural Results on the Capacity of the Discrete-Time Poisson Channel

Cheraghchi

Ribeiro

2019

IEEE Trans. Inform. Theory

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“…Note that we have ∆ λ (λ) = 0 and ∆ λ (z) → 0 exponentially fast when z → ∞ (in general, ∆ λ is always smaller than ∆). Theorem 5 and the observations above justify our choice of δ λ in (16); With this choice, we obtain a new family of modified digamma distributions Y (q) λ with KL-gap ∆ λ that is always smaller than the original KL-gap ∆ of the digamma distributions. Moreover, the KL-gap ∆ λ equals 0 at z = λ and is significantly smaller than ∆ around z = λ.…”

Section: The Modified Digamma Distributionmentioning

confidence: 90%

“…Besides the capacity upper bounds discussed above, several other aspects of the capacity of the DTP channel have been studied. Still with respect to capacity bounds, several works have derived both asymptotic and non-asymptotic lower bounds on the capacity of the DTP channel under different combinations of average-and peak-power constraints and dark current [12,13,14,15,7,8,16,9,10,17]. Moreover, when both averageand peak-power constraints are imposed on the input, some algorithms have been proposed to numerically approximate C(λ, µ, A) and the corresponding capacity-achieving input distribution [2,3].…”

Section: Previous Workmentioning

confidence: 99%

Improved Capacity Upper Bounds for the Discrete-Time Poisson Channel

Cheraghchi

Ribeiro

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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We derive improved and easily computable upper bounds on the capacity of the discrete-time Poisson channel under an average-power constraint and an arbitrary constant dark current term. This is accomplished by combining a general convex duality framework with a modified version of the digamma distribution considered in previous work of the authors (Cheraghchi, J. ACM 2019; Cheraghchi, Ribeiro, IEEE Trans. Inf. Theory 2019). For most choices of parameters, our upper bounds improve upon previous results even when an additional peak-power constraint is imposed on the input.

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Deterministic Identification Over Poisson Channels

Salariseddigh

Pereg

Boche

et al. 2021

2021 IEEE Globecom Workshops (GC Wkshps)

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Several applications of molecular communications (MC) feature an alarmprompt behavior for which the prevalent Shannon capacity may not be the appropriate performance metric. The identification capacity as an alternative measure for such systems has been motivated and established in the literature. In this paper, we study deterministic identification (DI) for the discrete-time Poisson channel (DTPC) with inter-symbol interference (ISI) where the transmitter is restricted to an average and a peak molecule release rate constraint. Such a channel serves as a model for diffusive MC systems featuring long channel impulse responses and employing molecule counting receivers. We derive lower and upper bounds on the DI capacity of the DTPC with ISI when the number of ISI channel taps K may grow with the codeword length (e.g., due to increasing symbol rate). As a key finding, we establish that for deterministic encoding, the codebook size scales as 2 ( log )R assuming that the number of ISI channel taps scales as K = 2 κ log , where R is the coding rate and κ is the ISI rate. Moreover, we show that optimizing κ leads to an effective identification rate [bits/s] that scales linearly with , which is in contrast to the typical transmission rate [bits/s] that is independent of .

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Lower bounds on the capacity of discrete-time Poisson channels with dark current

Cited by 4 publications

References 14 publications

Improved Upper Bounds and Structural Results on the Capacity of the Discrete-Time Poisson Channel

Improved Upper Bounds and Structural Results on the Capacity of the Discrete-Time Poisson Channel

Improved Capacity Upper Bounds for the Discrete-Time Poisson Channel

Deterministic Identification Over Poisson Channels

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