- Consider the communication of binary messages in a transmission medium. Any message sent is selected from two possible symbols, 0 or 1. Each symbol occurs with equal probability. It is also known that any numerical value sent on that channel is subjected to distortion. If a value x is transmitted, the y value is received at its destination, described by y = x + n, where n represents a random variable that additive noise is independent of x. The noise has a normal distribution with parameters σ2 = 4 and m = 0.

(a) Suppose the transmitter encodes the symbol 0 with the value x = -2 and 1 with the symbol value x = 2. At the destination, the received message is decoded according to the

following rules:

• If y ≥ 0, one concludes that the symbol was sent.

• If y <0, complete the symbol 0 was sent.

Determine the probability of error for this schema encoding / decoding.

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Bit error probability P(x0|y1) e P(x1|y0)

The probabilities of transmitting each signal (0,1) are equal = 1/2

y(t) = x(t) + n(t) where x(t) is a free signal of noise.

Assuming that the noise has a gaussian distribution .