Since Shannon's paper Mathematical theory of communications, probability theory has played an important role on communications (digital and analog).
I've been checking some course descriptions on my college and noted that for almost every course related with communications an important prerequisite is probability.
Why is that? What is the role of probability in communications? Is it a practical approach or just theoretical?
In analog communications, you are trying to recover a message signal from a received signal containing noise. Noise is a random fluctuation of the signal variable. So with out some theory of what random means, we can't even understand what noise is.
Furthermore when we talk about recovering the message signal, we're basically talking about estimating the original signal from the received signal (corrupted by noise). Again, estimation is a fundamental of probability theory.
In digital communications, at the most basic level, we talk about receiving bits of a message after they pass through a channel with some probability of error. Again, this description doesn't even have meaning until we have a theory of probability.
From what I understand, probability theory matters since it is used to model phenomena (e.g. noise, interference, fading etc...), which follow known statistical distributions., in communication systems - specially when we're considering complex systems (e.g. cellphones/wireless networks in a large city).
E.g. the effects of propagation upon a radio signal can be modeled as Rayleigh fading.
