Fiber optics in the AT&T Information Systems Network

Adding RLL Properties to Four CCSDS LDPC Codes without Increasing Their Redundancy

“…The idea to use a coset code of a linear ECCs is not new. In [36] Lee and Heegard demonstrated that it is possible to limit the run length of zeros by adding a periodic fixed binary sequence to each convolutional code's codeword. The purpose was to improve clock synchronization.…”

“…, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 83, 85, 87, 89, 91, 93, 95, 96, 98, 100, 102, 104, 106, 108, 110, 113, 115, 117, 119, 121, 123, 125, 127}.8.2 Appendix IIIndexes of subsets in which the modifier can invert an uneven number of symbols in a codeword of the CCSDS LDPC code defined by(19):S 1 = {0,31, 47, 89, 96, 180, 205, 224}, S 2 = {1, 2, 49, 91, 98, 182, 207, 226}, S 3 = {3, 4, 51, 93, 100, 184, 209, 228}, S 4 = {5, 6, 53, 95, 102, 186, 211, 230}, S 5 = {7, 8, 55, 65, 104, 188, 213, 232}, S 6 = {9, 10, 57, 67, 106, 190, 215, 234}, S 7 = {11, 12, 59, 69, 108, 160, 217, 236}, S 8 = {13, 14, 61, 71, 110, 162, 219, 238}, S 9 = {15, 16, 63, 73, 112, 164, 221, 240}, S 10 = {17, 18, 33, 75, 114, 166, 223, 242}, S 11 = {19, 20, 35, 77, 116, 168, 193, 244}, S 12 = {21, 22, 37, 79, 118, 170, 195, 246}, S 13 = {23, 24, 39, 81, 120, 172, 197, 248}, S 14 = {25, 26, 41, 83, 122, 174, 199, 250}, S 15 = {27, 28, 43, 85, 124, 176, 201, 252}, S 16 = {29, 30, 45, 87, 126, 178, 203, 254}.The set of the remaining column indexes in H 128×256 is the following:S R = {32,34,36,38,40,42,44,46,48,50,52,54,56,58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155,…”

“…63, 94, 178, 217, 363, 446, 448}, S 2 = {1, 2, 96, 180, 219, 365, 384, 450}, S 3 = {3, 4, 98, 182, 221, 367, 386, 452}, S 4 = {5, 6, 100, 184, 223, 369, 388, 454}, S 5 = {7, 8, 102, 186, 225, 371, 390, 456}, S 6 = {9, 10, 104, 188, 227, 373, 392, 458}, S 7 = {11, 12, 106, 190, 229, 375, 394, 460}, S 8 = {13, 14, 108, 128, 231, 377, 396, 462}, S 9 = {15, 16, 110, 130, 233, 379, 398, 464}, S 10 = {17, 18, 112, 132, 235, 381, 400, 466}, S 11 = {19, 20, 114, 134, 237, 383, 402, 468}, S 12 = {21, 22, 116, 136, 239, 321, 404, 470}, S 13 = {23, 24, 118, 138, 241, 323, 406, 472}, S 14 = {25, 26, 120, 140, 243, 325, 408, 474}, S 15 = {27, 28, 122, 142, 245, 327, 410, 476}, S 16 = {29, 30, 124, 144, 247, 329, 412, 478}, S 17 = {31, 32, 126, 146, 249, 331, 414, 480}, S 18 = {33, 34, 64, 148, 251, 333, 416, 482}, S 19 = {35, 36, 66, 150, 253, 335, 418, 484}, S 20 = {37, 38, 68, 152, 255, 337, 420, 486}, S 21 = {39, 40, 70, 154, 193, 339, 422, 488},beginning with 0 and starting from left in the final word it is necessary to subtract 18 from all numbers listed in Appendix VI(8.6).Example of possible order of symbols in the RLL ECC obtained from the CCSDS LDPC code defined by matrix(23):18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 80, 256, 603, 830, 1 102, 1 454, 1 533, 1 637, 2 124, 2 516, 2 786, 3 044, 3 146, 3 497, 3 666, 4 016, 4 168, 4 271, 4 475, 4 732, 5 008, 5 190, 5 397, 5 719, 5 982, 6 212, 6 669, 6 925, 7 234, 7 481, 7 781, 8 006,…”