Question

Consider a CRC code with a generator polynomial of g(x) -xSx21 a. (15 points) Show step by step (using the longhand division) how to find the codeword that corresponds to information bits of 10011 b. (15 points) Show the shift-register circuit that implements this CRC code. C. Suppose the codeword length is 10. Answer the following questions, with proper justifications i. (10 points) Give an example of undetectable error burst of length 9 ii. (10 points) Give an example of undetectable error burst of length 6; ii 5 points) Give an example of undetectable 4-bit error; iv. (5 points) Give an example of undetectable 3-bit error

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Answer 1

Cyclic Redundancy Check (CRC) q(x) = x^5 + x^2 + 1 1.x^5 + 0.x^4 + 0.x^3 + 1/x^2 + 0.x' + 1. x^0 m + 5R 5 rightarrow Redundancy bit (highest degree of polynomial) Redundancy bits = divisor bits - 1 message becomes = m + R = 10011110000 combination of m & R is called code word sent to the receiver.