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I have no data to add, just to say that I would like an answer that includes data and calculations to verify Shannon's law in that case.

Concrete examples of this type of communication: http://en.wikipedia.org/wiki/Interstellar_communication
Deep Space Network

https://ieeexplore.ieee.org/document/1091955/references#references Excellent document with calculations

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  • $\begingroup$ given that we will all be long dead by the time any communication reaches another galaxy, I'm not sure the point... $\endgroup$ Sep 5 at 3:15
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    $\begingroup$ The transmit power (with some consideration of antenna gain) determines how far it can go before it attenuates below background radiation noise. Assuming no QRSSS methods are considered, the signal strength transmitted, pure geometry, and the level of the background noise are the major determining factors. (Attenuation due to dust is probably minor.) $\endgroup$
    – user10489
    Sep 5 at 4:08
  • $\begingroup$ @Phil I mean to find concrete examples of this type of communication, this is the point. en.wikipedia.org/wiki/Interstellar_communication $\endgroup$ Sep 5 at 17:34
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    $\begingroup$ I think this is a valid and very interesting question. How far away could a message such as the Arecibo message of 1974 be received, if the transmission had been aimed directly at the receiving antenna, and the receiving antenna were comparable to the Arecibo radio telescope (back when it was fully functional)? Of course the question may not be practical to those of us reading this web page in 2021, but I still think it's interesting. $\endgroup$
    – rclocher3
    Sep 7 at 17:11
  • $\begingroup$ Mauricio, I think that you should undo your acceptance of the answer by @hotpaw2. The question deserves an answer with a calculation. If you undo the acceptance, and there are no answers with calculations after a few days, then I will consider offering a bounty. $\endgroup$
    – rclocher3
    Sep 8 at 14:20
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The latest distance estimates for the Voyager spacecraft transmitters is displayed on a NASA web site, as well as the last communication date.

AFAIK, there is no, more distant, humanly accessible and calibrated transmitter-receiver pair on which to acquire RF test data. Even attempting to bounce a signal off of Pluto would be a lesser distance.

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  • $\begingroup$ those spacecraft were built in 1977 !! amazing, I would like to see the schematic circuits! only discrete components i guess .. $\endgroup$ Sep 5 at 18:02
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    $\begingroup$ @MauricioPagano see ieeexplore.ieee.org/document/1091955/references#references for a great list of sources $\endgroup$
    – tomnexus
    Sep 8 at 13:16
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    $\begingroup$ I mean no offense personally, but I think that this answer doesn't answer the question. The question is asking for a reasonable calculation, regardless of whether a calibrated receiver and antenna are available. Besides, by this logic, the Voyager spacecraft themselves couldn't have been built, because no calibrated receiver had ever been sent as far as the original designed maximum range of the mission, the orbit of Saturn. $\endgroup$
    – rclocher3
    Sep 8 at 14:12
  • $\begingroup$ Depends on whether one interprets "ascertainable" more as an engineer, or a scientist. One runs pre-production and QA tests to find (many!) differences from earlier calculated results. $\endgroup$
    – hotpaw2
    Sep 8 at 18:33
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    $\begingroup$ in the reference cited by @tomnexus are the calculations that I wanted. Thanks $\endgroup$ Sep 13 at 1:08

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