ccsds 131.0-b-2

CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODINGFigure 7-3: Shortened Codeword7.4 LOW-DENSITY PARITY-CHECK CODE FAMILY WITH RATES 1/2, 2/3,AND 4/57.4.1 OVERVIEWNine punctured LDPC codes are specified, with information block lengths k=1024 bits, 4096bits, and 16384 bits, and code rates r=1/2, 2/3, and 4/5. These parameters and thecorresponding codeword lengths, n=k/r, are shown in table 7-5.7.4.2 PARITY CHECK MATRICES7.4.2.1 The parity check matrices shall be constructed from M×M submatrices, where thesubmatrix size is listed in table 7-2.Table 7-2: Values of Submatrix Size M for Supported CodesInformationblock length kSubmatrix size Mrate 1/2 rate 2/3 rate 4/51024 512 256 1284096 2048 1024 51216384 8192 4096 20487.4.2.2 The parity check matrices for the rate-1/2 codes shall satisfy the followingequation:⎡0M 0M IM 0M IM⊕Π1⎤H1/2 =⎢IM IM 0M I⎥⎢MΠ2 ⊕Π3 ⊕Π4⎥⎢⎣IM Π5⊕Π6 0M Π7 ⊕Π8I ⎥M ⎦where I Mand 0 Mare the M×M identity and zero matrices, respectively, and Π 1through Π 8arepermutation matrices.CCSDS 131.0-B-2 Page 7-7 August 2011