35 732 basic 81767156 ldpc code used in construction

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Unformatted text preview: formed by using a 2 × 16 array of 511 × 511 square circulants. CCSDS 131.0-B-2 Page 7-2 August 2011 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING NOTE – This creates a parity check matrix of size 1022 × 8176 and rank 1020. 7.3.2.2 ⎡ A1,1 ⎢A ⎣ 2,1 The structure of the parity check base matrix shall be as shown in figure 7-1. A1, 2 A2, 2 A1,3 A2,3 A1, 4 A2, 4 A1,5 A2,5 A1,6 A2,6 A1,7 A2, 7 A1,8 A2,8 A1,9 A2,9 A1,10 A2,10 A1,11 A2,11 A1,12 A2,12 A1,13 A2,13 A1,14 A2,14 A1,15 A2,15 A1,16 ⎤ A2,16 ⎥ ⎦ Figure 7-1: Base Parity Check Matrix of the Basic (8176,7156) LDPC Code 7.3.3 DISCUSSION Each 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 is 2 × 16 = 32. The position of the ‘1’s in the first row of each circulant is defined in the second column of table 7-1; each subsequent row is given by a one-bit right cyclic shift of the preceding 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 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING Table 7-1: Specification of Circulants Circulant A1,1 A1,2 A1,3 A1,4 A1,5 A1,6 A1,7 A1,8 A1,9 A1,10 A1,11 A1,12 A1,13 A1,14 A1,15 A1,16 A2,1 A2,2 A2,3 A2,4 A2,5 A2,6 A2,7 A2,8 A2,9 A2,10 A2,11 A2,12 A2,13 A2,14 A2,15 A2,16 CCSDS 131.0-B-2 ‘1’s position in 1st row of circulant 0, 176 12, 239 0, 352 24, 431 0, 392 151, 409 0, 351 9, 359 0, 307 53, 329 0, 207 18, 281 0, 399 202, 457 0, 247 36, 261 99, 471 130, 473 198, 435 260, 478 215, 420 282, 481 48, 396 193, 445 273, 430 302, 451 96, 379 191, 386 244, 467 364, 470 51, 382 192, 414 Page 7-4 Absolute ‘1’s position in 1st row of Parity Check Matrix 0, 176 523, 750 1022, 1374 1557, 1964 2044, 2436 2706, 2964 3066, 3417 3586, 3936 4088, 4395 4652, 4928 5110, 5317 5639, 5902 6132, 6531 6845, 7100 7154, 7401 7701, 7926 99, 471 641, 984 1220, 1457 1793, 2011 2259, 2464 2837, 3036 3114, 3462 3770, 4022 4361, 4518 4901, 5050 5206, 5489 5812, 6007 6376, 6599 7007, 7113 7205, 7536 7857, 8079 August 2011 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING 7.3.4 ENCODING NOTE – Two bits of information lie outside the struct...
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This document was uploaded on 03/06/2014.

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