A variant of the binary symmetric communication channel is called a binary erasure channel. The transmitter sends a ‘0' or ‘1,' but at the receiver there are three possibilities: a ‘0' or ‘1' or ‘undecided bit (called erasure)' received. If the receiver cannot decide, it will ask the transmitter to resend that bit. Define the event T1 = {1 is sent}, T0 = {0 is sent} and assume that they are equally probable. At the receiver we have three events: R1 = {1 is received}, R0 = {0 is received}, and Ru = {cannot decide if the received bit is a 0 or 1}. Given the following probabilities: P{R0|T0} = P{R1|T1} = 0.9 and P{Ru|T0} = P{Ru|T1} = 0.09.
(a) Find the probability that a transmitted bit is received as "undecided."
(b) Find the probability that a bit is received in error.
(c) Given that we received a ‘0,' what is the conditional probability that a ‘0' was sent? What is the conditional probability that a ‘1' was sent?