(Solved): A digital source of information generates octal symbols (values from 0 to 7 ) with a symbol rate e ...

A digital source of information generates octal symbols (values from 0 to 7 ) with a symbol rate equal to \( \mathrm{R}_{\mathrm{S}}=20 \mathrm{Msps} \). The generated symbols are independent from each other, and the probability that the source generates a specific symbol at each iteration is \[ p(0)=p(1)=1 / 4 \quad p(2)=p(3)=1 / 8 \quad p(4)=p(5)=p(6)=p(7)=1 / 16 \] The symbols are then transmitted over a noisy baseband channel, with bandwidth \( \mathrm{W}=5 \mathrm{MHz} \) and AWGN noise power spectral density \( \eta / 2=4 \cdot 10^{-21} \mathrm{~W} / \mathrm{Hz} \). 1) Find the following: - the entropy and information rate of the source - the probabilities that the symbols should have had to yield maximum source entropy - the minimum, maximum, and average information associated to a message of 2 consecutive symbols generated by this source 2) Calculate the theoretical minimum signal power required for a reliable (meaning "virtually error-free" or with arbitrarily small error bit probability) transmission over the given channel of the symbols generated by this source.