Question

In a binary communication system, 1’s are sent twice as frequently as 0’s. Whichever symbol is sent, the receiver makes the correct decision as to which it was only 3/4 of the time. Errors in di↵erent symbol transmissions are independent.

(a) Suppose that the string of symbols 1001 is transmitted. What is the probability that all symbols in the string are received correctly?

(b) Find the probability of an error being incurred as a result of the receiver making the wrong decision.

(c) Find the conditional probability that a 0 was sent given that the receiver decided that a 1 was sent

Answer 1

a) The probability that the receiver makes the correct decision:

the transmitted symbol 1001 has 4 bits.

hence, the probability that all symbols in the string are received correctly=

b) The probability that 1 was sent

The probability that 0 was sent

the probability of an error being incurred as a result of the receiver making the wrong decision= The probability that 1 was sent and receiver made wrong decision + The probability that 0 was sent and receiver made the wrong decision =

c) the conditional probability that a 0 was sent given that the receiver decided that a 1 was sent =