Polynomials
o CRC generator ( the divisor) is most
often represented not as a string of 1's and 0's
but
as an algebraic polynomial
o The polynomial format is useful for two
reasons:
-It is short
-Can be used to
prove the concept mathematically
Selection
of a Polynomial
o A polynomial should have the following
properties:
-It should not
be divisible by 'x'
-It should be
divisible by 'x+1'
The first
condition guarantees that all burst errors of a length equal to the degree of
the
polynomial
are detected
The 2 nd guarantees that all burst errors affecting
an odd number of bits are detected
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ƒ Performance of CRC
o CRC can detect all burst errors that
affect an odd number of errors
o CRC can detect all burst errors of length
less than or equal to the degree of the
polynomial
o CRC can detect with a very high
probability burst errors of length greater than
the
degree of the polynomial
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