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Binary symmetric channel

Consider a source sending messages through a noisy channel; for example, a CD player reading from a scratched music CD, or a wireless cellphone capturing a weak signal from a relay tower which is too far away. For simplicity, assume that the message being sent is a sequence of 0's and 1's. Assume that, due to noise, when a 0 is sent, the probability that a 0 is (correctly) received is $ p$ and the probability that a 1 is (incorrectly) received is $ 1-p$. Assume also that the noise of the channel is not dependent on the symbol sent: when a 1 is sent, the probability that a 1 is (correctly) received is $ p$ and the probability that a 0 is (incorrectly) received is $ 1-p$. The following diagram summarizes this.

\begin{figure} \begin{center} \begin{picture}(200,150) \put(0,0){\vector(3,2)... ... \put(5,30){$1-p$} \put(3,70){$1-p$} \end{picture} \end{center} \end{figure}
This channel is called the binary symmetric channel.
David Joyner 2002-08-23