Ccsds 1310 b 2 page 7 7 august 2011 ccsds recommended

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Unformatted text preview: ⎥ IM ⎦ where IM and 0M are the M×M identity and zero matrices, respectively, and Π1 through Π8 are permutation matrices. CCSDS 131.0-B-2 Page 7-7 August 2011 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING 7.4.2.3 The parity check matrices for the rate-2/3 and rate-4/5 codes are specified with additional columns and permutation matrices and shall satisfy the following equations: H 2/3 H 4 /5 ⎡ 0M ⎢ = ⎢Π 9 ⊕ Π10 ⊕ Π11 ⎢ IM ⎣ ⎡ 0M ⎢ = ⎢ Π 21 ⊕ Π 22 ⊕ Π 23 ⎢ IM ⎣ 7.4.2.4 0M IM Π12 ⊕ Π13 Π14 ⎤ ⎥ H1/2 ⎥ ⎥ ⎦ 0M 0M 0M IM Π15 ⊕ Π16 ⊕ Π17 IM IM Π 24 ⊕ Π 25 ⊕ Π 26 Π18 ⊕ Π19 ⊕ Π 20 ⎤ ⎥ H 2/3 ⎥ ⎥ ⎦ The permutation matrix ΠK shall have non-zero entries in row i and column πK(i) for i ∈ {0,..., M-1} and π k (i) = M 4 ( (θ k )( ) + ⎢ 4i / M ⎥ ) mod 4 + φk ( ⎢ 4i / M ⎥ , M ) + i mod ⎣ ⎦ ⎣ ⎦ M 4 where the functions θk and φk(j,M) are defined in table 7-3 and table 7-4. NOTE – Values defined in tables 7-3 and 7-4 describe φk(j,M)s using 7-tuples where consecutive positions in a tuple correspond to submatrix sizes from the set M={128, 256, 512, 1024, 2048, 4096, 8192}. 7.4.2.5 For each of the parity check matrices, the code symbols corresponding to the last M columns shall be punctured (not transmitted). CCSDS 131.0-B-2 Page 7-8 August 2011 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING Table 7-3: Description of φk(0,M) and φk(1,M) φk(0,M) k 3 0 1 2 2 3 0 1 0 1 2 0 2 3 0 1 2 0 1 2 0 1 2 1 2 3 φk(1,M) 13 M = 27 … 213 M=2 …2 θk 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 7 1 22 0 26 0 10 5 18 3 22 3 8 25 25 2 27 7 7 15 10 4 19 7 9 26 17 59 18 52 23 11 7 22 25 27 30 43 14 46 62 44 12 38 47 1 52 61 10 55 7 12 2 CCSDS 131.0-B-2 16 103 105 0 50 29 115 30 92 78 70 66 39 84 79 70 29 32 45 113 86 1 42 118 33 126 160 241 185 251 209 103 90 184 248 12 111 66 173 42 157 174 104 144 43 181 250 202 68 177 170 89 108 126 238 481 96 28 59 225 323 28 386 305 34 510...
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This document was uploaded on 03/06/2014.

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