Cyclic Redundancy Code

cyclic redundancy check
CRC
cyclic redundancy code

   <algorithm> (CRC or "cyclic redundancy code") A number derived
   from, and stored or transmitted with, a block of data in order
   to detect corruption.  By recalculating the CRC and comparing
   it to the value originally transmitted, the receiver can
   detect some types of transmission errors.

   A CRC is more complicated than a {checksum}.  It is calculated
   using division either using {shifts} and {exclusive ORs} or
   {table lookup} ({modulo} 256 or 65536).

   The CRC is "redundant" in that it adds no information.  A
   single corrupted {bit} in the data will result in a one bit
   change in the calculated CRC but multiple corrupted bits may
   cancel each other out.

   CRCs treat blocks of input bits as coefficient-sets for
   {polynomials}.  E.g., binary 10100000 implies the polynomial:
   1*x^7 + 0*x^6 + 1*x^5 + 0*x^4 + 0*x^3 + 0*x^2 + 0*x^1 + 0*x^0.
   This is the "message polynomial".  A second polynomial, with
   constant coefficients, is called the "generator polynomial".
   This is divided into the message polynomial, giving a quotient
   and remainder.  The coefficients of the remainder form the
   bits of the final CRC.  So, an order-33 generator polynomial
   is necessary to generate a 32-bit CRC.  The exact bit-set used
   for the generator polynomial will naturally affect the CRC
   that is computed.

   Most CRC implementations seem to operate 8 bits at a time by
   building a table of 256 entries, representing all 256 possible
   8-bit byte combinations, and determining the effect that each
   byte will have.  CRCs are then computed using an input byte to
   select a 16- or 32-bit value from the table.  This value is
   then used to update the CRC.

   {Ethernet} {packets} have a 32-bit CRC.  Many disk formats
   include a CRC at some level.

   (1997-08-02)