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

This code has the following characteristics:It detects all single bit errors per code word.It detects all double bit error combinations in a codeword because the generator polynomial g(X) has afactor of at least three terms.It detects any odd number of errors because g(X) contains a factor 1+X.It detects any burst error for which the length of the burst is 24 bits.It detects most large error bursts with length greater than the CRC length r = 24 bits. The fraction of errorbursts of length b > 24 that are undetected is:2 -24 = 5.96 10 -8 , if b > 25 bits2 -23 = 1.19 10 -7 , if b = 25 bits3.2.3.4 Low Density Parity Check (LDPC) CodeSubframe 2 and subframe 3 are separately encoded using rate ½ LDPC codes. Subframe 2 has a total of 600 bitsconsisting of 576 bits for Clock and Ephemeris and 24 bits for CRC. Subframe 3 has a total of 274 bits consisting of250 bits for Variable Data and 24 bits for CRC. As a result of rate ½ LDPC encoding, there are 1200 symbols (codedbits) for Subframe 2 and 548 symbols for Subframe 3 as described in Figure 3.2-3.The LDPC encoder structure is based on a parity-check matrix H(m, n) of m rows and n columns. For Subframe 2,m=600, n=1200 and for Subframe 3, m=274, n=548. H(m, n) is further decomposed into 6 submatrices A, B, T, C, D,and E as shown in Figure 3.2-5 (see reference document [1]). Each element of matrix H(m, n) is either a value of “0”or “1”.21 IS-GPS-800A8 June 2010