I'm studing Digital Communications - Fundamentals and Applications by Bernard Sklar.
About channel coding - convolutional coding, looking for a common factor is a key to check if it's catastrophic or not.
For example, question 1:
Common factor of
g1(x) = 1 + X^2
g2(x) = 1 + X^3
is 1 + X -> I could check it by hand, but still don't know how to find in a mathematical way.
For example, question 2:
Common factor of
g3(x) = 1 + X + X^2
g4(x) = 1 + X + X^3 + X^4
is 1 + X^2 -> I can't check it by hand, writing the division, but the author said it is.
Can you guys check if those two answers are right, and the way to find them?
