A digital transmitter sends groups of 8 bits over a communication channel sequentially. The probability of a single bit error in the channel is p.
(a) How many different ways can two errors occur in 8 bits? (We will call each of these a 2-bit error.)
(b) Assume that a particular 2-bit error has occured: ΦxΦΦΦxΦΦ, where x indicates an error bit and Φ the correct bit (0 or 1). What is the probability of this particular event?
(c) Determine the probability of 2-bit errors in this system.
(d) Plot the probability of 2-bit errors for p = 0.1, 0.01, 0.001, 0.0001.
