Systematic circulant generator matrix 735 recommended

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Unformatted text preview: ⎥ B9,2 ⎥ ⎥ B10,2 ⎥ ⎥ B11,2 ⎥ B12,2 ⎥ ⎥ B13,2 ⎥ B14,2 ⎥ ⎦ Figure 7-2: Systematic Circulant Generator Matrix 7.3.5 RECOMMENDED (8160,7136) CODE NOTE – The generator matrix in 7.3.4 describes an (8176,7154) subcode of the (8176,7156) code defined by the parity check matrix in 7.3.2.2. The (8176,7154) subcode shall be shortened and extended as follows to form an (8160,7136) code with parameters that are multiples of 32. 1) The encoder shall accept as input a Telemetry Transfer Frame of 7136 bits (i.e. 892 octets matching the length and dimension of (255,223) I=4 Reed-Solomon), 2) 18 zeros shall be prefixed to the 7136-bit message to be encoded, yielding a 7154element row vector. 3) This vector shall be multiplied by the generator matrix of section 6.2.3, yielding an 8176-element vector consisting of 18 zeros, 7136 systematic message symbols, and 1022 parity symbols. 4) From this vector, the 18 leading zeros shall be discarded, and two zeros shall be appended, yielding a codeword of 8160 symbols. NOTE – The arrangement of these 18 virtual fill bits, information bits, parity bits, and two zero-fill bits is shown in figure 7-3. CCSDS 131.0-B-2 Page 7-6 August 2011 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING Figure 7-3: Shortened Codeword 7.4 7.4.1 LOW-DENSITY PARITY-CHECK CODE FAMILY WITH RATES 1/2, 2/3, AND 4/5 OVERVIEW Nine punctured LDPC codes are specified, with information block lengths k=1024 bits, 4096 bits, and 16384 bits, and code rates r=1/2, 2/3, and 4/5. These parameters and the corresponding codeword lengths, n=k/r, are shown in table 7-5. 7.4.2 PARITY CHECK MATRICES 7.4.2.1 The parity check matrices shall be constructed from M×M submatrices, where the submatrix size is listed in table 7-2. Table 7-2: Values of Submatrix Size M for Supported Codes Submatrix size M Information block length k rate 1/2 rate 2/3 rate 4/5 1024 512 256 128 4096 2048 1024 512 16384 8192 4096 2048 7.4.2.2 The parity check matrices for the rate-1/2 codes shall satisfy the following equation: H1/ 2 ⎡0 M = ⎢ IM ⎢ ⎢ IM ⎣ 0M IM Π5 ⊕ Π6 IM 0M 0M 0M IM Π 7 ⊕ Π8 I M ⊕ Π1 ⎤ Π2 ⊕ Π3 ⊕ Π4 ⎥ ...
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This document was uploaded on 03/06/2014.

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