Question

Consider a binary communication channel, where 0 or 1 is sent independently over time with probability po=0.6 and p₁=0.4, respectively, and the noisy channel introduces errors independently over time with probabilities po1=P(1 is received | 0 is sent)=0.2 and p10=P(0 is received | 1 is sent)=0.1.

(a) Calculate the probability that "01" is sent.

(b) Calculate the probability that “01” is received.

(c) Calculate the probability that "01" is sent given that "01" is received.

(d) Is the event that "01" is sent independent of that "01" is received? Justify your answer.

(e) Suppose that "00000" is sent. Calculate the probability that no error occurs over this transmission.

(f) Suppose that "00000" is sent. Calculate the probability that exactly 2 errors occur over this transmission.

(g) Calculate the bit error probability of this channel (i.e., the probability of any bit in error).

(h) Calculate the probability that the first error occurs over the 6-th bit sent.

(i) Suppose that 10 bits are sent and there are 3 errors. Conditioned on this, calculate the probability that the 3 errors are continuous over time.

Fig: 1