🚀 go-pugleaf

A couple of errors appeared in recent postings about CRC-16 error
checking.

    Date: Fri, 25 Jul 86 15:04:27 PDT
    From: Marc Kaufman <kaufman@shasta.stanford.edu>
    Subject: RF modem problem / CRC

    CRC-16 is extremely susceptible to even-number-of-bit errors.  For
    example, the following error pattern will not change the CRC:
	10000100000010001 (binary), where '1' indicates a bit error....

The example applies to the CCITT V41 polynomial.  The CRC-16 polynomial
is different, so the example should be
	10100000000000011 (binary), where '1' indicates a bit error.
or, if you are a big-endian,
	11000000000000101 (binary), where '1' indicates a bit error.

    Subject: Re: Interview with MNP protocol author
    Date: 05 Aug 86 17:09:30 EDT (Tue)
    From: John Robinson <jr@cc5.bbn.com>

    ...>>> Using the 16-bit redundancy check, it will detect every 
    >> error which is 16 bits or smaller, with 100% probability.

    No!  No!  No!  Any error in an odd number of bits, and all one-, two-,
    and three- bit errors will be detected.  16 bits in a row which are
    inverted are detected, yes (I think!), but a sequence of 16 bits in
    which some bits are in error is NOT necessarily detected.  CRCs aren't
    that good....

The original statement is correct.  Both CRC-16 and CCITT V41 will
detect any error that is a subset of sixteen consecutive bits.  (Not to
say that's all that good, as we have seen.)  This can be seen by
noticing that nonzero multiples of a degree sixteen polynomial must
have degree at least sixteen.  The only undetected pattern that spans
seventeen bits is the polynomial itself, as shown above.

Dan Hoey