10.3.4 Cyclic Code Analysis - CRC Performance (summary) Dataword: d(x) Codeword: c(x) Generator: g(x) Syndrome: s(x) Error: e(x) Received codeword =c(x)+e(x) g(x)Receivedcodeword=g(x)c(x)+g(x)e(x) if e(x) is divisible by g(x), errors are not detected Considerations for selection of g(x), the predetermined divisor or generator polynomial: 1. If the generator has more than one term and the coefficient of x0 is 1 , all single-bit errors can be detected 2. If the generator cannot divide xt+1 (for 0r+1 will be detected with probability 1(1/2)r 2. Consider the CRC-8 polynomial: x8+x2+x+1 a. Does it detect a single error? Defend your answer. b. Does it detect a burst error of size 6? Defend your answer. c. Will it detect all odd numbers of errors? d. What is the probability of detecting a burst error of size 9 ? e. What is the probability of detecting a burst error of size 15