Communication under the Poisson regime

Bar-David, I.

doi:10.1109/tit.1969.1054238

Cited by 144 publications

(81 citation statements)

References 6 publications

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“…This expression appears in [1], [2], [3] and in similar forms in [6]- [10]. Note that for n = 1 this expression becomes…”

Section: B Position Of Pointsmentioning

confidence: 73%

“…Another approach consists in defining the PP by the position of its points [1], [6] - [10]. Let 0 be an arbitrary origin and X i be the RV equal to the distance between the origin and the ith point of the…”

Section: B Position Of Pointsmentioning

confidence: 99%

“…The principle of the proof of (3) appearing almost in the same form in [1], [2], [3], [6] is given in Appendix I where it is also shown that if M = m(+∞) is not finite the integral of (3) is 1, as expected for any PDF.…”

Section: B Position Of Pointsmentioning

confidence: 99%

“…This ensures that the density is integrable. The same kind of assumption is introduced in [6] and [10]. In some sense this assumption corresponds to any experimental situation with Poisson processes because any experiment has a beginning (0) and an end (T ).…”

Section: B Marginal Probability Density Functionsmentioning

confidence: 99%

“…They are defined and studied in various books corresponding to quite different approaches and among them we can cite [1], [2], [3], [4], [5]. There are also many papers discussing the use of Poisson processes in communication theory [6], [7], [8], [9], [10]. This is especially important in the context of optical communications at very low level of intensity.…”

Section: Introductionmentioning

confidence: 99%

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Poisson Processes With Integrable Density

Picinbono

Bendjaballah²

2006

IEEE Trans. Inform. Theory

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When the density of a Poisson process is integrable various expressions published in the literature are incorrect. This is especially the case of the probability distribution of the distance between an origin and the following points of the process. The first purpose of this paper is to explain why the integrability of the density changes the situation. The second is to discuss various consequences of this fact on the probability distribution of random variables extracted from the process. Computer experiments are presented and are in excellent agreement with theoretical results. Some extensions of the same problem concerning renewal processes are discussed. Index TermsDetection and estimation, integration of the density, nonhomogeneous Poisson processes, point processes, renewal processes.

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“…This expression appears in [1], [2], [3] and in similar forms in [6]- [10]. Note that for n = 1 this expression becomes…”

Section: B Position Of Pointsmentioning

confidence: 73%