Suppose that a binary message – either 0 or 1 – must be transmitted by wire from location A to location B. However, the data sent over the wire are subject to a channel noise disturbance, so to reduce the possibility of error, the value 2 is sent over the wire when the message is 1, and the value −2 is sent when the message is 0. If X, X = {−2,2}, is the value sent at location A, the value received at location B, denoted as R, is given by R = X + N , where N is the channel noise disturbance, which is independent of X. When the message is received at location B, the receiver decodes it according to the following rule: if R ≥.5, then conclude that message 1 was sent if R < .5, then conclude that message 0 was sent Assuming that the channel noise, N, is a unit normal random variable and that the message 0 or 1 is sent with equal probability, what is the probability that we conclude that the wrong message was sent? This is the probability of error for this communication channel
Suppose that a binary message – either 0 or 1 – must be transmitted by wire from location A
to location B. However, the data sent over the wire are subject to a channel noise disturbance,
so to reduce the possibility of error, the value 2 is sent over the wire when the message is
1, and the value −2 is sent when the message is 0. If X, X = {−2,2}, is the value sent at
location A, the value received at location B, denoted as R, is given by
R = X + N ,
where N is the channel noise disturbance, which is independent of X. When the message is
received at location B, the receiver decodes it according to the following rule:
if R ≥.5, then conclude that message 1 was sent
if R < .5, then conclude that message 0 was sent
Assuming that the channel noise, N, is a unit normal random variable and that the message
0 or 1 is sent with equal probability, what is the probability that we conclude that the wrong
message was sent? This is the probability of error for this communication channel
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