For the binary communications system of Example 8.7, graph the error probability PERR as a function of p, the probability that the transmitted signal is 0. For the signal-to-noise voltage ratio, consider v/σ ∈ {0.1, 1, 10}. What values of p minimize PERR? Why are those values not practical?
Example 8.7
Find the error probability of the communications system of Example 8.6.
Example 8.6
With probability p, a digital communications system transmits a 0. It transmits a 1 with probability 1 - p. The received signal is either X = -v + N volts, if the transmitted bit is 0; or v + N volts, if the transmitted bit is 1. The voltage ±v is the information component of the received signal, and N, a Gaussian (0,σ) random variable, is the noise component. Given the received signal X, what is the minimum probability of error rule for deciding whether 0 or 1 was sent?