Question

A pseudo-random signal (X) of 0 or 5 is transmitted over a noisy channel. X=0 is transmitted with probability of 3/4. The received signal, Y, is the sum of the sent signal and noise, where the noise is modeled as a normal Gaussian with ? = 0, ? = 2 . The received signal is decoded as 0 for Y ? 3 and 1 for Y > 3 . a. What is the probability of error in this system? b. Assume that answer to part a was 0.1 for mathematical simplicity. 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?

          A pseudo-random signal (X) of 0 or 5 is transmitted over a noisy channel. X=0 is transmitted with probability of 3/4. The received signal, Y, is the sum of the sent signal and noise, where the noise is modeled as a normal Gaussian with ? = 0, ? = 2 . The received signal is decoded as 0 for Y ? 3 and 1 for Y > 3 .
a. What is the probability of error in this system?
b. Assume that answer to part a was 0.1 for mathematical simplicity. 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?

A pseudo-random signal (X) of 0 or 5 is transmitted over a noisy channel. X=0 is transmitted with probability of 3/4. The received signal, Y, is the sum of the sent signal and noise, where the noise is modeled as a normal Gaussian with ? = 0, ? = 2 . The received signal is decoded as 0 for Y ? 3 and 1 for Y > 3 .
a. What is the probability of error in this system?
b. Assume that answer to part a was 0.1 for mathematical simplicity. 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?

Added by Jose Manuel K.

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