In many cases, you can model a binary communication system as follows. A 0 or 1

Question

In many cases, you can model a binary communication system as follows. A 0 or 1 is chosen as the message, and the transmitter sends a signal over a medium to indicate that choice. The receiver receives a corrupted version of that signal and makes the best decision it can about whether a 0 or 1 was intended. Suppose that the message is a 1 with probability p. Also, suppose that no matter what the transmitted message was, there is a probability of belongsto that the receiver decodes it as the wrong bit. Let A be the event that the intended message was a 1, and B be the event that the receiver decision was a 1. There are four possible outcomes for this experiment. List them along with their associated probabilities. Find a value for belongsto for which the intended message and received message are independent. Comment on the value of this as a practical communication system.

Explanation / Answer

a) The four possibilities are AB - 00 , AB - 01 , AB - 10 , AB-11

the p(AB) = 1/4 , p(AB) = 1/2 , p(AB) = 1/4

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