Suppose a binary message is transmitted through a noisy channel. The transmitted signal S has uniform probability to be either 1 or −1, the noise N follows normal distribution N(0,4) and the received signal is R=S+N . Assume the receiver conclude the signal to be 1 when R≥0 and -1 when R<0.

1.What is error probability when one signal is transmitted?

2. What is error probability when one signal is transmitted if we triple the amplitude of the transmitted signal? It means S = 3 or -3 with equal probability.

3. What is the error probability if we send the same signal three times (with amplitude 1), and take majority for conlusion? For example, if three received signal was concluded 1, −1, 1 by receiver, we determine the transmitted signal to be 1.