A binary message m, where m is equal either to 0 or to 1, is sent over an information
Chapter 4, Problem 23(choose chapter or problem)
A binary message , where
is equal either to 0 or to 1 , is sent over an information channel. Because of noise in the channel, the message received is
, where \(X=m+E\), and
is a random variable representing the channel noise. Assume that if \(X \leq 0.5\) then the receiver concludes that \(m=0\) and that if \(X>0.5\) then the receiver concludes that \(m=1\). Assume that \(E \sim N(0,0.25)\)
a. If the true message is \(m=0\), what is the probability of an error, that is, what is the probability that the receiver concludes that \(m=1\)?
b. Let \(\sigma^{2}\) denote the variance of . What must be the value of \(\sigma^{2}\) so that the probability of error when \(m=0\) is
Equation Transcription:
Text Transcription:
X=m+E
X \leq 0.5
m=0
X>0.5
m=1
E \sim N (0, 0.25)
m=0
m=1
\sigma^2
\sigma^2
m=0
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer