9.10 Although ATM does not include any end-to-end error detection and control func tions on the user data, it is provided with a HEC field to detect and correct header errors. Let us consider the value of this feature. Suppose that the bit error rate of the transmission system is B. If errors are uniformly distributed, then the probability of an error in the header is h i and the probability of error in the data field is hi where h is the number of bits in the header and i is the number of bits in the data field. a. Suppose that errors in the header are not detected and not corrected. In that case, a header error may result in a misrouting of the cell to the wrong destination; therefore, i bits will arrive at an incorrect destination, and i bits will not arrive at the correct destination. What is the overall bit error rate B1? Find an expression for the multiplication effect on the bit error rate: M1B1/B. b. Now suppose that header errors are detected but not corrected. In that case, i bits will not arrive at the correct destination. What is the overall bit error rate B2? Find an expression for the multiplication effect on the bit error rate: M2-B2/B c. Now suppose that header errors are detected and corrected. What is the overall bit error rate B3? Find an expression for the multiplication effect on the bit error rate: M3 B3/B d. Plot M1M2, and M3 as a function of header length, for i-48 8 384 bits. Comment on the results