ccsds 131.0-b-2

CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODINGNOTE – This creates a parity check matrix of size 1022 × 8176 and rank 1020.7.3.2.2 The structure of the parity check base matrix shall be as shown in figure 7-1.⎡ A⎢⎣A1,12,1AA1,22,2AA1,32,3AA1,42,4AA1,52,5AA1,62,6AA1,72,7AA1,82,8AA1,92,9AA1,102,10AA1,112,11AA1,122,12AA1,132,13AA1,142,14AA1,152,15AA1,162,16⎤⎥⎦Figure 7-1: Base Parity Check Matrix of the Basic (8176,7156) LDPC Code7.3.3 DISCUSSIONEach A i,j is a 511 × 511 circulant. The row weight of each of the 32 circulants is two; i.e.,there are two ‘1’s in each row. The total row weight of each row in the parity check matrix is2 × 16 = 32. The position of the ‘1’s in the first row of each circulant is defined in the secondcolumn of table 7-1; each subsequent row is given by a one-bit right cyclic shift of thepreceding row. There are 511 possible positions, with position numbers between 0 and 510.The third column represents the absolute position of the ‘1’s in the parity check matrix.There are 8176 possible positions; therefore these numbers are between 0 and 8175.CCSDS 131.0-B-2 Page 7-3 August 2011