A pseudo-random signal (S) of -3 or 3 is transmitted over a noisy channel. S=-3 is transmitted with probability of 1/3.  The received signal, Y, is the sum of the sent signal and the noise, N. The noise is modeled as a normal Gaussian with E[N]=0,var(N)=4 . The received signal is decoded as -3 for Y≤−0.5  and 3 for Y>−0.5. a. What is the probability of error in this

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A pseudo-random signal (S) of -3 or 3 is transmitted over a noisy channel. S=-3 is transmitted with probability of 1/3.  The received signal, Y, is the sum of the sent signal and the noise, N. The noise is modeled as a normal Gaussian with E[N]=0,var(N)=4 . The received signal is decoded as -3 for Y≤−0.5  and 3 for Y>−0.5.

a. What is the probability of error in this system?

b. To improve the system, each signal is transmitted three times and output is determine by majority rule (2 or more). What is the new probability of error?

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