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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

594.0. "The AUTODIN-II CRC polynomial" by EAGLE1::DANTOWITZ (David .. DTN: 226-6957) Wed Oct 08 1986 12:12

	Does anyone know the properties of the AUTODIN-II CRC
	polynomial?  (Or the name of a paper that discusses it?)


	AUTODIN-II is  EDB88320 in compressed bits and in polynomial
	form is:

        x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x+1

	David
T.RTitleUserPersonal
Name		DateLines
594.1CLT::GILBERTeager like a childWed Oct 08 1986 15:504
    It's an irreducible polynomial modulo x^32 (as I recall the terminology).
    Thus, the CRC provides a one-to-one mapping for the number range 0..2^32-1.

    In what properties are you interested?
594.2EAGLE1::DANTOWITZDavid .. DTN: 226-6957Wed Oct 08 1986 16:5916
	Knowing it's irreducable helps.

	Specifically, the VAX description for CRC lists
	three sample polynomials, and things like
	initial value and to get the CRC take the
	one's complement of the result etc.

	I'm curious where this information comes from.
	As far as I know as long as you start with
	the same initial value for all CRC computations
	the actual value shouldn't matter.  Also, why
	take the one's complement of the residual?

	David
594.3CLT::GILBERTeager like a childWed Oct 08 1986 18:3518
    The comments about the initial value and complenting the result
    are primarily concerned with describing how the CRC instruction
    can be used to implement some commonly used CRC polynomials.

    There is not much difference between an initial value of 0 or -1,
    except that an an initial value of 0 will allow an arbitrary number
    of zero bytes to be prepended to the string without affecting the
    result.

    There is no advantage in complementing the result, it's just that
    that's what the creator or first user of AUTODIN-II did.

    BTW, The 'error pattern' that AUTODIN-II misses is 1DB710641 (hex).
    That is, if you take the AUTODIN-II CRC of a string, then XOR that
    (33-bit!) error pattern into the string and calculate the CRC again,
    you'll get the same result.
    
					- Gilbert