Exercise 2. Consider a transmission system in which only four payloads are allowed. The four allowed payloads are "000", "100", "010", and "001" (K = 3) . A CRC is attached to the end of each payload during transmission to create the corresponding codework. The CRC is computed using the generator polynomial g(D) = D ^ 5 + D ^ 4 + D ^ 2 + 1
A) Generate all 4 possible codewords [pt * 0.1]
B) Assume that at the receiver the received sequence of bits is affected by an error pattern described by e(D) = D ^ 7 + D ^ 6 + D ^ 5 + 1 Regardless of what codeword is affected by this error, will the error be detected at the receiver and why? [ pt . overline 10 ].
C) Compute the distance between every pair of codewords, and the minimum distance of the code d min based on the 4 allowed payloads [pt * 0.1]
D) Corroborate the d min value obtained in the previous answer using properties that you may identify in the used generator polynomial g(D) [pt. 10].
E) Produce one error pattern (using polynomial notation) that will be detected by the receiver using the chosen g(D) and explain why [pt. 10].
F) With the given g(D) what would be the maximum number of bits that one could use as payload without reducing the value of d min as computed in question C) [pt, 10]