IS-GPS-800A - US Coast Guard Navigation Center

3.2.3.3 Cyclic Redundancy CheckTwenty-four bits of CRC will provide protection against burst as well as random errors with a probability ofundetected error 2 -24 = 5.9610 -8 for all channel bit error probabilities 0.5. The CRC word is calculated in theforward direction on a given message using a seed of 0. The sequence of 24 bits (p 1 ,p 2 ,...,p 24 ) is generated from thesequence of information bits (m 1 ,m 2 ,...,m k ) (MSB to LSB sequence) in a given message. This is done by means of acode that is generated by the polynomialg24Xi0g i Xiwhereg i 1 0for i 0,1,3,4,5,6,7,10,11,14,17,18,23,24otherwiseThis code is called CRC-24Q. The generator polynomial of this code is in the following form (using binarypolynomial algebra):gX1 XpXwhere p(X) is the primitive and irreducible polynomialp23 17 13 12 11 9 8 7 5 3X X X X X X X X X X X 1 .When, by the application of binary polynomial algebra, the above g(X) is divided into m(X)X 24 , where theinformation sequence m(X) is expressed as2k 1 m m X m X m Xm X .kk 1k21The result is a quotient and a remainder R(X) of degree < 24. The bit sequence formed by this remainder representsthe CRC sequence. CRC bit p i , for any i from 1 to 24, is the coefficient of X 24-i in R(X).20 IS-GPS-800A8 June 2010