Интерфейсный документ GPS (1015430), страница 25

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Twenty-four bits of CRC parity will provide protection against burst as well as randomerrors with a probability of undetected error ≤ 2-24 = 5.96×10-8 for all channel bit error probabilities ≤ 0.5. TheCRC word is calculated in the forward direction on a given message using a seed of 0. The sequence of 24 bits(p1,p2,...,p24) is generated from the sequence of information bits (m1,m2,...,m276) in a given message. This is done bymeans of a code that is generated by the polynomial24g(X ) = ∑ g i X ii=0whereg i = 1 for i = 0,1,3, 4,5,6,7,10,11,14,17,18, 23, 24= 0 otherwiseThis code is called CRC-24Q. The generator polynomial of this code is in the following form (using binarypolynomial algebra):g(X ) = (1 + X )p(X )where p(X) is the primitive and irreducible polynomialp(X ) = X 23 + X17 + X13 + X12 + X11 + X 9 + X 8 + X 7 + X 5 + X 3 + 1When, by the application of binary polynomial algebra, the above g(X) is divided into m(X)X24, where theinformation sequence m(X) is expressed asm(X ) = m k + m k −1X + m k − 2 X 2 + ⋅ ⋅ ⋅ + m1X k −1IS-GPS-200D7 Dec 2004191The result is a quotient and a remainder R(X) of degree < 24.

The bit sequence formed by this remainder representsthe parity check sequence. Parity bit pi, for any i from 1 to 24, is the coefficient of X24-i in R(X).This code has the following characteristics:1) It detects all single bit errors per code word.2) It detects all double bit error combinations in a codeword because the generator polynomial g(X) has afactor of at least three terms.3) It detects any odd number of errors because g(X) contains a factor 1+X.4) It detects any burst error for which the length of the burst is ≤ 24 bits.5) It detects most large error bursts with length greater than the parity length r = 24 bits.

The fraction oferror bursts of length b > 24 that are undetected is:a) 2-24 = 5.96 × 10-8, if b > 25 bits.b) 2-23 = 1.19 × 10-7, if b = 25 bits.IS-GPS-200D7 Dec 2004192(This page intentionally left blank.)IS-GPS-200D7 Dec 2004193.

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