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decreases of spectral efficiency after certain SNR shown hereIn fiber optics communication, there is the concept of nonlinear Shannon limit (see e.g. this article), implying that the communication capacity of an optical fiber decreases for high SNR. I don’t understand this concept, and specially the origin of the decrease of the spectral efficiency decrease after certain increase of SNR. I have read the post (Negative SNR and Shannon–Hartley theorem) on Shannon capacity theorem but it didn't clear up my concept.

I need these answer to explain the 1Tbps capacity limit of single mode fiber. So it will be helpful for me if anyone answer me the second part(cause of limit of single mode transmission) also

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    $\begingroup$ I don't get what you're asking. The shannon limit ($\rm B = C \log_2(1+SNR)$) is a monotonically increasing function of SNR. It doesn't fall after a certain SNR. It falls whenever you decrease the SNR. $\endgroup$
    – The Photon
    Commented Sep 11, 2018 at 17:04
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    $\begingroup$ @ThePhoton No, the non-linearity is the deviation from that equation; it's observed when you transfer over long distances with high signal power. The stronger electric field causes a change in the refractive indiex of the silica in the wires. Can't find a reference, but I'm quite sure I've read that somewhere. $\endgroup$
    – user191954
    Commented Sep 12, 2018 at 6:26
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    $\begingroup$ @Chair that is a real limit on fiber capacity, but it's not called the "nonlinear Shannon limit". $\endgroup$
    – The Photon
    Commented Sep 12, 2018 at 13:55
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    $\begingroup$ @ThePhoton : Apparently, it is called so: see e.g. ieeexplore.ieee.org/document/7537418 : “many works suggest the existence of an upper limit—usually but improperly referred to as the nonlinear Shannon limit—to the rate at which information can be reliably transmitted through the optical fiber channel, regardless of the available optical power” $\endgroup$
    – Frédéric Grosshans
    Commented Sep 12, 2018 at 14:03
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    $\begingroup$ I'm voting to reopen this question. @HasanShuvo please add a few details to the question, like perhaps some articles which indicate that the nonlinear Shannon limit is a formally observed concept. I'm quite sure that the lack of information in the question made it appear random. I don't really see the point of linking the Physics SE article about negative SNR... perhaps some excerpts from that would help make the question clearer.. $\endgroup$
    – user191954
    Commented Sep 12, 2018 at 14:38

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The capacity of a channel of bandwidth $W$ is known since the 1940‘s to be given by the Shannon limit: $$C=W \log (1+\mathit{SNR}), $$ where $\mathit{SNR}$ is the signal to noise ratio. In an optical fibre in the linear regime, the noise is essentially independent of the signal, and that means one just has to increase the signal power to increase the rate. Mathematically, an infinite rate seems possible, but the logarithmic dependence makes the increase really expensive. That is the reason why, historically, the capacity increase of fibers has been more focused on increasing the bandwidth $W$,through WDM. However this $W$ increase has some limits, and people also work at increasing the power.

The Shannon formula ensures that, to have a linear increase in capacity, one needs an exponential increase in $\mathit{SNR}$, and therefore, an exponential increas of optical of power. Which means that, at some point, nonlinear effects are noticable, and create what is sometimes named “the nonlinear Shannon limit”. The main effect is that the channel is non longer an additive channel: the signal as the output of the channel cannot be analyzed as the addition of the input signal and an independent noise, and the above formula is no longer valid. Effectively, some part of the signal acts as noise to other parts of the signal, creating an effective $SNR$ which decreases with increasing signal power past a power threshold, and therefore a decreasing capacity above a given optimal input power (at -$5\text{ dBM}\simeq300\text{ µW}$ on your graph.

As far as I understood (this is not my research topic), the concept of nonlinear Shannon limit is an active research topic: it has no clean formulation, and some researcher claim that, contrasting to the Shannon limit, this is not a universal limit but an artifact of current encoding techniques.

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  • $\begingroup$ ''some part of the signal acts as noise to other parts of the signal''--why? Is that because the signal in one channel induce more noise in other channel $\endgroup$
    – Hasan Shuvo
    Commented Sep 12, 2018 at 18:54
  • $\begingroup$ Basically,linear means that you can look at the signal as the sum of his parts, and that they do not interact with the others. Nonlinear means that this assumption is not true anymore. On your graph, the difference between the green curve (1 channel) and the red curve (WDM, that is multiple channels) shows that the dominant effect is indeed inter-channel interactions $\endgroup$
    – Frédéric Grosshans
    Commented Sep 12, 2018 at 19:11

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