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In my opinion, the effect of noise is that we can not transmit information over any channel with an unbounded rate, that is every channel has a capacity, just as Shannon's celebrated channel coding theorem states.
imagine you are a teacher and you start speaking to everyone in class. If everybody is quiet you can speak at some volume level. Everybody can listen to you with no problem.
Now imagine everybody starts speaking at the same time you are. You are still speaking at the same level you were before. But now people can't hear you right, because there is not just your voice, there are others' voices too. There is noise.
Now imagine the same thing in a communications channel. You send your information through a channel, at some frequency at some power level. But in the path to the receiver there are many external (and internal) noise sources that add up to your signal. The receiver will detect your signal plus some other signals that are added up to yours, thus not being able to understand the original message.
This is where the signal-to-noise ratio (SNR) enters the scene, a ratio given by the division between the signal received and the noise received. For a communications system it doesn't matter just the power level of the signal received but the level of the noise received too.
The higher the noise level, the lower the SNR, so there would be necessary to increase the signal level.
Often receiver systems are characterized by their SNR sensibility, which means, the minimum signal they need to receive over the noise the receive.
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