From a86b96fd5f330914a5e5e62c9886ebb753365382 Mon Sep 17 00:00:00 2001 From: zeefaad Date: Wed, 11 Feb 2026 16:35:01 +0100 Subject: [PATCH] ldpc notes --- Notes/notes.pdf | 8462 ++++++++++++++++++++++++++++++++++++----------- Notes/notes.typ | 256 ++ 2 files changed, 6727 insertions(+), 1991 deletions(-) diff --git a/Notes/notes.pdf b/Notes/notes.pdf index 49d6b16..9bd4571 100644 --- a/Notes/notes.pdf +++ b/Notes/notes.pdf @@ -4,8 +4,8 @@ 1 0 obj << /Type /Pages - /Count 5 - /Kids [337 0 R 340 0 R 346 0 R 351 0 R 355 0 R] + /Count 9 + /Kids [700 0 R 703 0 R 709 0 R 714 0 R 716 0 R 718 0 R 724 0 R 727 0 R 731 0 R] >> endobj @@ -13,8 +13,8 @@ endobj << /Type /Outlines /First 3 0 R - /Last 10 0 R - /Count 6 + /Last 20 0 R + /Count 8 >> endobj @@ -23,7 +23,7 @@ endobj /Parent 2 0 R /Next 4 0 R /Title - /Dest 323 0 R + /Dest 676 0 R >> endobj @@ -36,7 +36,7 @@ endobj /Last 5 0 R /Count -1 /Title - /Dest 325 0 R + /Dest 678 0 R >> endobj @@ -44,7 +44,7 @@ endobj << /Parent 4 0 R /Title - /Dest 324 0 R + /Dest 677 0 R >> endobj @@ -57,7 +57,7 @@ endobj /Last 7 0 R /Count -1 /Title - /Dest 327 0 R + /Dest 680 0 R >> endobj @@ -65,7 +65,7 @@ endobj << /Parent 6 0 R /Title - /Dest 326 0 R + /Dest 679 0 R >> endobj @@ -75,36 +75,138 @@ endobj /Next 9 0 R /Prev 6 0 R /Title (Code de Hamming) - /Dest 328 0 R + /Dest 681 0 R >> endobj 9 0 obj << /Parent 2 0 R - /Next 10 0 R + /Next 18 0 R /Prev 8 0 R + /First 10 0 R + /Last 17 0 R + /Count -5 /Title (Low-density parity-check codes (LDPC) ) - /Dest 329 0 R + /Dest 690 0 R >> endobj 10 0 obj << - /Parent 2 0 R - /Prev 9 0 R - /Title (Bibliographie) - /Dest 330 0 R + /Parent 9 0 R + /Next 11 0 R + /Title + /Dest 682 0 R >> endobj 11 0 obj << - /Nums [0 280 0 R 1 281 0 R 2 282 0 R 3 283 0 R 4 284 0 R] + /Parent 9 0 R + /Next 15 0 R + /Prev 10 0 R + /First 12 0 R + /Last 14 0 R + /Count -3 + /Title (LDPC constructions) + /Dest 686 0 R >> endobj 12 0 obj +<< + /Parent 11 0 R + /Next 13 0 R + /Title (Gallager) + /Dest 683 0 R +>> +endobj + +13 0 obj +<< + /Parent 11 0 R + /Next 14 0 R + /Prev 12 0 R + /Title (MacKay et Neal) + /Dest 684 0 R +>> +endobj + +14 0 obj +<< + /Parent 11 0 R + /Prev 13 0 R + /Title (Codes Repeat-Accumulate (RA)) + /Dest 685 0 R +>> +endobj + +15 0 obj +<< + /Parent 9 0 R + /Next 16 0 R + /Prev 11 0 R + /Title (Graphe de Tanner) + /Dest 687 0 R +>> +endobj + +16 0 obj +<< + /Parent 9 0 R + /Next 17 0 R + /Prev 15 0 R + /Title (Encodage) + /Dest 688 0 R +>> +endobj + +17 0 obj +<< + /Parent 9 0 R + /Prev 16 0 R + /Title + /Dest 689 0 R +>> +endobj + +18 0 obj +<< + /Parent 2 0 R + /Next 19 0 R + /Prev 9 0 R + /Title (QC-LDPC) + /Dest 691 0 R +>> +endobj + +19 0 obj +<< + /Parent 2 0 R + /Next 20 0 R + /Prev 18 0 R + /Title (Code Rust) + /Dest 692 0 R +>> +endobj + +20 0 obj +<< + /Parent 2 0 R + /Prev 19 0 R + /Title (Bibliographie) + /Dest 693 0 R +>> +endobj + +21 0 obj +<< + /Nums [0 621 0 R 1 622 0 R 2 623 0 R 3 624 0 R 4 625 0 R 5 626 0 R 6 627 0 R 7 628 0 R 8 629 0 R] +>> +endobj + +22 0 obj << /Type /StructTreeRoot /RoleMap << @@ -114,277 +216,137 @@ endobj /Strong /Span /Em /Span >> - /K [18 0 R] + /K [32 0 R] /ParentTree << - /Nums [0 265 0 R 1 238 0 R 2 13 0 R 3 168 0 R 4 14 0 R 5 148 0 R 6 148 0 R 7 125 0 R 8 119 0 R 9 15 0 R 10 36 0 R 11 35 0 R 12 33 0 R 13 16 0 R 14 30 0 R 15 24 0 R 16 17 0 R] + /Nums [0 606 0 R 1 579 0 R 2 23 0 R 3 509 0 R 4 24 0 R 5 489 0 R 6 489 0 R 7 466 0 R 8 460 0 R 9 25 0 R 10 377 0 R 11 376 0 R 12 374 0 R 13 26 0 R 14 27 0 R 15 28 0 R 16 104 0 R 17 90 0 R 18 85 0 R 19 80 0 R 20 29 0 R 21 56 0 R 22 30 0 R 23 44 0 R 24 38 0 R 25 31 0 R] >> - /ParentTreeNextKey 17 ->> -endobj - -13 0 obj -[279 0 R 278 0 R 277 0 R 274 0 R 274 0 R 274 0 R 276 0 R 274 0 R 275 0 R 274 0 R 273 0 R 270 0 R 270 0 R 272 0 R 270 0 R 271 0 R 269 0 R 268 0 R 267 0 R 266 0 R 266 0 R 264 0 R 265 0 R 262 0 R 262 0 R 262 0 R 262 0 R 263 0 R 262 0 R 261 0 R 260 0 R 248 0 R 259 0 R 248 0 R 257 0 R 248 0 R 255 0 R 248 0 R 248 0 R 253 0 R 248 0 R 251 0 R 248 0 R 250 0 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186 0 R 189 0 R 186 0 R 188 0 R 188 0 R 186 0 R 186 0 R 187 0 R 186 0 R 184 0 R 185 0 R 184 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 181 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 181 0 R 180 0 R 180 0 R 180 0 R 180 0 R 180 0 R 180 0 R 180 0 R 180 0 R 180 0 R 177 0 R 179 0 R 177 0 R 178 0 R 177 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 175 0 R 173 0 R 174 0 R 173 0 R 170 0 R 172 0 R 170 0 R 171 0 R 171 0 R 171 0 R 170 0 R 170 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 167 0 R 168 0 R 166 0 R 163 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 163 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 164 0 R 163 0 R] -endobj - -15 0 obj -[162 0 R 162 0 R 162 0 R 162 0 R 162 0 R 162 0 R 162 0 R 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79 0 R 79 0 R 79 0 R 79 0 R 78 0 R] -endobj - -16 0 obj -[75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 71 0 R 74 0 R 71 0 R 73 0 R 71 0 R 70 0 R 68 0 R 69 0 R 68 0 R 66 0 R 64 0 R 65 0 R 64 0 R 58 0 R 58 0 R 61 0 R 58 0 R 59 0 R 58 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 54 0 R 56 0 R 54 0 R 52 0 R 52 0 R 53 0 R 52 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 44 0 R 50 0 R 50 0 R 50 0 R 50 0 R 44 0 R 49 0 R 44 0 R 48 0 R 44 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 44 0 R 46 0 R 44 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 44 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 37 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 37 0 R 41 0 R 37 0 R 39 0 R 39 0 R 39 0 R 39 0 R 37 0 R 38 0 R 38 0 R 37 0 R 34 0 R 36 0 R 34 0 R 35 0 R 32 0 R 33 0 R] -endobj - -17 0 obj -[31 0 R 30 0 R 27 0 R 28 0 R 27 0 R 27 0 R 24 0 R 22 0 R] -endobj - -18 0 obj -<< - /Type /StructElem - /S /Document - /P 12 0 R - /K [279 0 R 278 0 R 277 0 R 274 0 R 273 0 R 272 0 R 271 0 R 270 0 R 269 0 R 268 0 R 267 0 R 266 0 R 264 0 R 262 0 R 261 0 R 260 0 R 248 0 R 247 0 R 246 0 R 245 0 R 244 0 R 236 0 R 234 0 R 231 0 R 230 0 R 227 0 R 226 0 R 223 0 R 222 0 R 221 0 R 215 0 R 214 0 R 213 0 R 211 0 R 210 0 R 207 0 R 202 0 R 201 0 R 196 0 R 193 0 R 186 0 R 184 0 R 183 0 R 181 0 R 180 0 R 177 0 R 176 0 R 173 0 R 170 0 R 169 0 R 167 0 R 166 0 R 163 0 R 162 0 R 156 0 R 153 0 R 147 0 R 131 0 R 128 0 R 127 0 R 118 0 R 116 0 R 111 0 R 110 0 R 107 0 R 105 0 R 92 0 R 87 0 R 86 0 R 76 0 R 75 0 R 71 0 R 62 0 R 58 0 R 57 0 R 54 0 R 52 0 R 51 0 R 44 0 R 43 0 R 37 0 R 34 0 R 32 0 R 31 0 R 19 0 R] ->> -endobj - -19 0 obj -<< - /Type /StructElem - /S /L - /P 18 0 R - /A [<< - /O /List - /ListNumbering /Decimal - >>] - /K [25 0 R 20 0 R] ->> -endobj - -20 0 obj -<< - /Type /StructElem - /S /LI - /P 19 0 R - /K [23 0 R 21 0 R] ->> -endobj - -21 0 obj -<< - /Type /StructElem - /S /LBody - /P 20 0 R - /K [22 0 R] ->> -endobj - -22 0 obj -<< - /Type /StructElem - /S /BibEntry - /P 21 0 R - /K [7] - /Pg 355 0 R + /ParentTreeNextKey 26 >> endobj 23 0 obj -<< - /Type /StructElem - /S /Lbl - /P 20 0 R - /K [24 0 R] ->> +[620 0 R 619 0 R 618 0 R 615 0 R 615 0 R 615 0 R 617 0 R 615 0 R 616 0 R 615 0 R 614 0 R 611 0 R 611 0 R 613 0 R 611 0 R 612 0 R 610 0 R 609 0 R 608 0 R 607 0 R 607 0 R 605 0 R 606 0 R 603 0 R 603 0 R 603 0 R 603 0 R 604 0 R 603 0 R 602 0 R 601 0 R 589 0 R 600 0 R 589 0 R 598 0 R 589 0 R 596 0 R 589 0 R 589 0 R 594 0 R 589 0 R 592 0 R 589 0 R 591 0 R 591 0 R 591 0 R 591 0 R 591 0 R 589 0 R 588 0 R 588 0 R 588 0 R 588 0 R 588 0 R 588 0 R 588 0 R 588 0 R 588 0 R 588 0 R 588 0 R 587 0 R 587 0 R 587 0 R 587 0 R 587 0 R 587 0 R 587 0 R 587 0 R 587 0 R 587 0 R 587 0 R 586 0 R 586 0 R 586 0 R 586 0 R 586 0 R 586 0 R 586 0 R 586 0 R 586 0 R 586 0 R 586 0 R 585 0 R 585 0 R 585 0 R 585 0 R 585 0 R 585 0 R 585 0 R 585 0 R 585 0 R 585 0 R 585 0 R 577 0 R 577 0 R 584 0 R 577 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 583 0 R 577 0 R 582 0 R 582 0 R 582 0 R 582 0 R 582 0 R 577 0 R 581 0 R 581 0 R 581 0 R 581 0 R 581 0 R 577 0 R 580 0 R 580 0 R 580 0 R 580 0 R 580 0 R 580 0 R 577 0 R 577 0 R 579 0 R 577 0 R 578 0 R 577 0 R 576 0 R 575 0 R 572 0 R 572 0 R 574 0 R 572 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 571 0 R 568 0 R 570 0 R 570 0 R 570 0 R 570 0 R 570 0 R 570 0 R 570 0 R 570 0 R 568 0 R 569 0 R 568 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 567 0 R 566 0 R 564 0 R 564 0 R 565 0 R 564 0 R 564 0 R 563 0 R] endobj 24 0 obj -<< - /Type /StructElem - /S /Link - /P 23 0 R - /K [6 << - /Type /OBJR - /Pg 355 0 R - /Obj 354 0 R - >>] - /Pg 355 0 R ->> +[562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 562 0 R 556 0 R 561 0 R 556 0 R 560 0 R 556 0 R 559 0 R 556 0 R 556 0 R 558 0 R 556 0 R 557 0 R 556 0 R 555 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 554 0 R 552 0 R 553 0 R 553 0 R 553 0 R 553 0 R 553 0 R 553 0 R 553 0 R 553 0 R 552 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 551 0 R 548 0 R 550 0 R 548 0 R 543 0 R 547 0 R 547 0 R 547 0 R 547 0 R 547 0 R 547 0 R 547 0 R 547 0 R 547 0 R 547 0 R 547 0 R 543 0 R 546 0 R 543 0 R 545 0 R 543 0 R 544 0 R 544 0 R 544 0 R 544 0 R 544 0 R 544 0 R 544 0 R 544 0 R 544 0 R 544 0 R 544 0 R 544 0 R 542 0 R 542 0 R 542 0 R 542 0 R 537 0 R 541 0 R 537 0 R 540 0 R 537 0 R 539 0 R 537 0 R 538 0 R 538 0 R 538 0 R 538 0 R 538 0 R 538 0 R 538 0 R 538 0 R 538 0 R 538 0 R 538 0 R 538 0 R 537 0 R 534 0 R 536 0 R 536 0 R 534 0 R 535 0 R 534 0 R 527 0 R 533 0 R 527 0 R 532 0 R 532 0 R 527 0 R 531 0 R 527 0 R 530 0 R 527 0 R 529 0 R 529 0 R 527 0 R 527 0 R 528 0 R 527 0 R 525 0 R 526 0 R 525 0 R 524 0 R 524 0 R 524 0 R 524 0 R 524 0 R 524 0 R 524 0 R 524 0 R 524 0 R 524 0 R 522 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 523 0 R 522 0 R 521 0 R 521 0 R 521 0 R 521 0 R 521 0 R 521 0 R 521 0 R 521 0 R 521 0 R 518 0 R 520 0 R 518 0 R 519 0 R 518 0 R 517 0 R 517 0 R 517 0 R 517 0 R 517 0 R 516 0 R 514 0 R 515 0 R 514 0 R 511 0 R 513 0 R 511 0 R 512 0 R 512 0 R 512 0 R 511 0 R 511 0 R 510 0 R 510 0 R 510 0 R 510 0 R 510 0 R 510 0 R 510 0 R 510 0 R 508 0 R 509 0 R 507 0 R 504 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 506 0 R 504 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 505 0 R 504 0 R] endobj 25 0 obj -<< - /Type /StructElem - /S /LI - /P 19 0 R - /K [29 0 R 26 0 R] ->> +[503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 503 0 R 497 0 R 502 0 R 502 0 R 502 0 R 502 0 R 502 0 R 497 0 R 501 0 R 497 0 R 500 0 R 497 0 R 499 0 R 497 0 R 497 0 R 498 0 R 497 0 R 494 0 R 496 0 R 496 0 R 496 0 R 496 0 R 496 0 R 496 0 R 496 0 R 494 0 R 495 0 R 495 0 R 495 0 R 495 0 R 495 0 R 495 0 R 495 0 R 495 0 R 494 0 R 488 0 R 493 0 R 488 0 R 492 0 R 488 0 R 488 0 R 491 0 R 488 0 R 489 0 R 490 0 R 488 0 R 487 0 R 481 0 R 486 0 R 481 0 R 481 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 485 0 R 481 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 484 0 R 481 0 R 483 0 R 481 0 R 482 0 R 481 0 R 478 0 R 475 0 R 477 0 R 477 0 R 475 0 R 475 0 R 476 0 R 475 0 R 469 0 R 471 0 R 471 0 R 469 0 R 470 0 R 469 0 R 468 0 R 468 0 R 468 0 R 468 0 R 459 0 R 459 0 R 467 0 R 459 0 R 466 0 R 459 0 R 465 0 R 465 0 R 465 0 R 465 0 R 459 0 R 464 0 R 459 0 R 463 0 R 463 0 R 463 0 R 459 0 R 462 0 R 459 0 R 461 0 R 459 0 R 459 0 R 460 0 R 459 0 R 457 0 R 458 0 R 457 0 R 452 0 R 456 0 R 452 0 R 455 0 R 452 0 R 454 0 R 452 0 R 452 0 R 453 0 R 452 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 451 0 R 448 0 R 450 0 R 448 0 R 449 0 R 448 0 R 446 0 R 447 0 R 433 0 R 445 0 R 433 0 R 444 0 R 433 0 R 442 0 R 433 0 R 441 0 R 433 0 R 439 0 R 433 0 R 433 0 R 438 0 R 433 0 R 437 0 R 437 0 R 437 0 R 433 0 R 433 0 R 436 0 R 436 0 R 436 0 R 433 0 R 435 0 R 433 0 R 433 0 R 434 0 R 433 0 R 432 0 R 431 0 R 430 0 R 427 0 R 427 0 R 426 0 R 423 0 R 425 0 R 425 0 R 425 0 R 425 0 R 425 0 R 425 0 R 425 0 R 425 0 R 425 0 R 425 0 R 425 0 R 423 0 R 424 0 R 424 0 R 424 0 R 424 0 R 424 0 R 424 0 R 423 0 R 421 0 R 419 0 R 420 0 R 420 0 R 420 0 R 420 0 R 420 0 R 420 0 R 420 0 R 420 0 R 419 0 R] endobj 26 0 obj -<< - /Type /StructElem - /S /LBody - /P 25 0 R - /K [27 0 R] ->> +[416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 416 0 R 412 0 R 415 0 R 412 0 R 414 0 R 412 0 R 411 0 R 409 0 R 410 0 R 409 0 R 407 0 R 405 0 R 406 0 R 405 0 R 399 0 R 399 0 R 402 0 R 399 0 R 400 0 R 399 0 R 398 0 R 398 0 R 398 0 R 398 0 R 398 0 R 395 0 R 397 0 R 395 0 R 393 0 R 393 0 R 394 0 R 393 0 R 392 0 R 392 0 R 392 0 R 392 0 R 392 0 R 392 0 R 392 0 R 392 0 R 385 0 R 391 0 R 391 0 R 391 0 R 391 0 R 385 0 R 390 0 R 385 0 R 389 0 R 385 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 388 0 R 385 0 R 387 0 R 385 0 R 386 0 R 386 0 R 386 0 R 386 0 R 386 0 R 385 0 R 384 0 R 384 0 R 384 0 R 384 0 R 384 0 R 384 0 R 384 0 R 384 0 R 378 0 R 383 0 R 383 0 R 383 0 R 383 0 R 383 0 R 383 0 R 383 0 R 378 0 R 382 0 R 378 0 R 380 0 R 380 0 R 380 0 R 380 0 R 378 0 R 379 0 R 379 0 R 378 0 R 375 0 R 377 0 R 375 0 R 376 0 R 373 0 R 374 0 R 372 0 R 365 0 R 371 0 R 365 0 R 370 0 R 365 0 R 368 0 R 365 0 R 367 0 R 365 0 R 366 0 R 366 0 R 366 0 R 366 0 R 364 0 R 363 0 R 358 0 R 362 0 R 358 0 R 360 0 R 358 0 R 358 0 R 357 0 R 354 0 R 356 0 R 354 0 R 354 0 R 353 0 R 351 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 351 0 R 350 0 R 348 0 R 349 0 R 349 0 R 348 0 R 346 0 R 344 0 R 345 0 R 345 0 R 344 0 R 341 0 R 335 0 R 340 0 R 335 0 R 339 0 R 335 0 R 335 0 R 337 0 R 335 0 R 336 0 R 336 0 R 336 0 R 336 0 R 336 0 R 335 0 R 334 0 R 333 0 R 333 0 R 330 0 R 331 0 R 330 0 R 328 0 R 327 0 R 327 0 R 324 0 R 325 0 R 324 0 R 321 0 R 320 0 R 318 0 R 317 0 R 315 0 R 312 0 R 314 0 R 312 0 R 313 0 R 312 0 R 311 0 R 309 0 R 310 0 R 310 0 R 310 0 R 310 0 R 310 0 R 310 0 R 310 0 R 310 0 R 310 0 R] endobj 27 0 obj -<< - /Type /StructElem - /S /BibEntry - /P 26 0 R - /K [2 28 0 R 4 5] - /Pg 355 0 R ->> +[307 0 R 305 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 306 0 R 302 0 R 301 0 R 299 0 R 300 0 R 299 0 R 299 0 R 298 0 R 289 0 R 297 0 R 289 0 R 295 0 R 289 0 R 293 0 R 293 0 R 289 0 R 289 0 R 291 0 R 291 0 R 291 0 R 289 0 R 288 0 R 287 0 R 282 0 R 286 0 R 286 0 R 282 0 R 284 0 R 282 0 R 282 0 R 283 0 R 282 0 R 279 0 R 278 0 R 277 0 R 277 0 R 274 0 R 273 0 R 265 0 R 272 0 R 272 0 R 265 0 R 270 0 R 265 0 R 265 0 R 269 0 R 265 0 R 267 0 R 267 0 R 265 0 R 262 0 R 261 0 R 254 0 R 257 0 R 257 0 R 257 0 R 257 0 R 254 0 R 256 0 R 256 0 R 256 0 R 256 0 R 254 0 R 255 0 R 255 0 R 255 0 R 255 0 R 254 0 R 253 0 R 250 0 R 251 0 R 251 0 R 251 0 R 251 0 R 251 0 R 251 0 R 251 0 R 251 0 R 251 0 R 250 0 R 248 0 R 249 0 R 249 0 R 249 0 R 249 0 R 248 0 R 247 0 R 246 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 244 0 R 243 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 242 0 R 241 0 R 240 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 239 0 R 238 0 R 237 0 R 237 0 R 237 0 R 237 0 R 237 0 R 237 0 R 237 0 R 237 0 R 237 0 R 237 0 R 235 0 R 236 0 R 235 0 R 234 0 R 233 0 R 230 0 R 232 0 R 230 0 R 227 0 R 225 0 R 226 0 R 225 0 R] endobj 28 0 obj -<< - /Type /StructElem - /S /Em - /P 27 0 R - /K [3] - /Pg 355 0 R ->> +[222 0 R 221 0 R 221 0 R 221 0 R 218 0 R 217 0 R 205 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 205 0 R 212 0 R 212 0 R 205 0 R 205 0 R 211 0 R 211 0 R 205 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 205 0 R 209 0 R 205 0 R 205 0 R 208 0 R 205 0 R 207 0 R 207 0 R 207 0 R 205 0 R 206 0 R 205 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 203 0 R 202 0 R 196 0 R 201 0 R 196 0 R 199 0 R 196 0 R 197 0 R 196 0 R 196 0 R 193 0 R 192 0 R 189 0 R 188 0 R 182 0 R 184 0 R 184 0 R 182 0 R 183 0 R 183 0 R 182 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 175 0 R 180 0 R 175 0 R 175 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 175 0 R 175 0 R 175 0 R 174 0 R 173 0 R 172 0 R 171 0 R 171 0 R 171 0 R 171 0 R 171 0 R 171 0 R 171 0 R 171 0 R 171 0 R 170 0 R 168 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 165 0 R 166 0 R 166 0 R 166 0 R 166 0 R 166 0 R 163 0 R 162 0 R 162 0 R 162 0 R 162 0 R 162 0 R 159 0 R 161 0 R 159 0 R 160 0 R 160 0 R 160 0 R 160 0 R 160 0 R] endobj 29 0 obj -<< - /Type /StructElem - /S /Lbl - /P 25 0 R - /K [30 0 R] ->> +[157 0 R 154 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 154 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 154 0 R 154 0 R 152 0 R 151 0 R 151 0 R 151 0 R 151 0 R 149 0 R 150 0 R 149 0 R 146 0 R 142 0 R 145 0 R 142 0 R 144 0 R 144 0 R 144 0 R 144 0 R 142 0 R 143 0 R 143 0 R 143 0 R 143 0 R 142 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 141 0 R 140 0 R 139 0 R 138 0 R 137 0 R 137 0 R 135 0 R 136 0 R 135 0 R 134 0 R 134 0 R 133 0 R 132 0 R 132 0 R 131 0 R 131 0 R 130 0 R 130 0 R 129 0 R 129 0 R 128 0 R 128 0 R 127 0 R 127 0 R 126 0 R 126 0 R 125 0 R 125 0 R 124 0 R 124 0 R 123 0 R 123 0 R 122 0 R 121 0 R 117 0 R 119 0 R 117 0 R 117 0 R 118 0 R 117 0 R 114 0 R 113 0 R 106 0 R 108 0 R 106 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 106 0 R 103 0 R 105 0 R 103 0 R 103 0 R 104 0 R 103 0 R 102 0 R 100 0 R 101 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 95 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 95 0 R 97 0 R 95 0 R 96 0 R 95 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 93 0 R 89 0 R 92 0 R 89 0 R 89 0 R 91 0 R 89 0 R 90 0 R 89 0 R 89 0 R 87 0 R 84 0 R 86 0 R 84 0 R 85 0 R 84 0 R 81 0 R 79 0 R 80 0 R 79 0 R] endobj 30 0 obj -<< - /Type /StructElem - /S /Link - /P 29 0 R - /K [1 << - /Type /OBJR - /Pg 355 0 R - /Obj 353 0 R - >>] - /Pg 355 0 R ->> +[78 0 R 77 0 R 76 0 R 75 0 R 73 0 R 72 0 R 69 0 R 66 0 R 68 0 R 66 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 66 0 R 64 0 R 63 0 R 60 0 R 59 0 R 59 0 R 57 0 R 55 0 R 56 0 R 55 0 R 53 0 R 51 0 R 52 0 R 51 0 R 49 0 R 48 0 R] endobj 31 0 obj -<< - /Type /StructElem - /S /H1 - /P 18 0 R - /T (Bibliographie) - /K [0] - /Pg 355 0 R ->> +[45 0 R 44 0 R 41 0 R 42 0 R 41 0 R 41 0 R 38 0 R 36 0 R] endobj 32 0 obj << /Type /StructElem - /S /H1 - /P 18 0 R - /T (Low-density parity-check codes (LDPC) ) - /K [143 33 0 R] - /Pg 351 0 R + /S /Document + /P 22 0 R + /K [620 0 R 619 0 R 618 0 R 615 0 R 614 0 R 613 0 R 612 0 R 611 0 R 610 0 R 609 0 R 608 0 R 607 0 R 605 0 R 603 0 R 602 0 R 601 0 R 589 0 R 588 0 R 587 0 R 586 0 R 585 0 R 577 0 R 575 0 R 572 0 R 571 0 R 568 0 R 567 0 R 564 0 R 563 0 R 562 0 R 556 0 R 555 0 R 554 0 R 552 0 R 551 0 R 548 0 R 543 0 R 542 0 R 537 0 R 534 0 R 527 0 R 525 0 R 524 0 R 522 0 R 521 0 R 518 0 R 517 0 R 514 0 R 511 0 R 510 0 R 508 0 R 507 0 R 504 0 R 503 0 R 497 0 R 494 0 R 488 0 R 472 0 R 469 0 R 468 0 R 459 0 R 457 0 R 452 0 R 451 0 R 448 0 R 446 0 R 433 0 R 428 0 R 427 0 R 417 0 R 416 0 R 412 0 R 403 0 R 399 0 R 398 0 R 395 0 R 393 0 R 392 0 R 385 0 R 384 0 R 378 0 R 375 0 R 373 0 R 365 0 R 364 0 R 358 0 R 354 0 R 351 0 R 342 0 R 335 0 R 322 0 R 312 0 R 303 0 R 302 0 R 299 0 R 298 0 R 289 0 R 258 0 R 254 0 R 250 0 R 248 0 R 246 0 R 245 0 R 243 0 R 242 0 R 240 0 R 239 0 R 238 0 R 237 0 R 235 0 R 234 0 R 214 0 R 205 0 R 204 0 R 203 0 R 185 0 R 182 0 R 181 0 R 175 0 R 174 0 R 173 0 R 147 0 R 142 0 R 141 0 R 140 0 R 139 0 R 138 0 R 137 0 R 136 0 R 135 0 R 134 0 R 133 0 R 132 0 R 131 0 R 130 0 R 129 0 R 128 0 R 127 0 R 126 0 R 125 0 R 124 0 R 123 0 R 109 0 R 106 0 R 103 0 R 102 0 R 100 0 R 99 0 R 95 0 R 94 0 R 82 0 R 81 0 R 79 0 R 78 0 R 77 0 R 46 0 R 45 0 R 33 0 R] >> endobj 33 0 obj << /Type /StructElem - /S /Link + /S /L /P 32 0 R - /K [144 << - /Type /OBJR - /Pg 351 0 R - /Obj 350 0 R + /A [<< + /O /List + /ListNumbering /Decimal >>] - /Pg 351 0 R + /K [39 0 R 34 0 R] >> endobj 34 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [139 36 0 R 141 35 0 R] - /Pg 351 0 R + /S /LI + /P 33 0 R + /K [37 0 R 35 0 R] >> endobj 35 0 obj << /Type /StructElem - /S /Link + /S /LBody /P 34 0 R - /K [142 << - /Type /OBJR - /Pg 351 0 R - /Obj 349 0 R - >>] - /Pg 351 0 R + /K [36 0 R] >> endobj 36 0 obj << /Type /StructElem - /S /Link - /P 34 0 R - /K [140 << - /Type /OBJR - /Pg 351 0 R - /Obj 348 0 R - >>] - /Pg 351 0 R + /S /BibEntry + /P 35 0 R + /K [7] + /Pg 731 0 R >> endobj 37 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [120 42 0 R 128 40 0 R 130 39 0 R 135 38 0 R 138] - /Pg 351 0 R + /S /Lbl + /P 34 0 R + /K [38 0 R] >> endobj 38 0 obj << /Type /StructElem - /S /Em + /S /Link /P 37 0 R - /K [136 137] - /Pg 351 0 R + /K [6 << + /Type /OBJR + /Pg 731 0 R + /Obj 730 0 R + >>] + /Pg 731 0 R >> endobj 39 0 obj << /Type /StructElem - /S /Formula - /P 37 0 R - /K [131 132 133 134] - /Pg 351 0 R + /S /LI + /P 33 0 R + /K [43 0 R 40 0 R] >> endobj 40 0 obj << /Type /StructElem - /S /Formula - /P 37 0 R + /S /LBody + /P 39 0 R /K [41 0 R] >> endobj @@ -392,488 +354,489 @@ endobj 41 0 obj << /Type /StructElem - /S /Strong + /S /BibEntry /P 40 0 R - /K [129] - /Pg 351 0 R + /K [2 42 0 R 4 5] + /Pg 731 0 R >> endobj 42 0 obj << /Type /StructElem - /S /Formula - /P 37 0 R - /K [121 122 123 124 125 126 127] - /Pg 351 0 R + /S /Em + /P 41 0 R + /K [3] + /Pg 731 0 R >> endobj 43 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [112 113 114 115 116 117 118 119] - /Pg 351 0 R + /S /Lbl + /P 39 0 R + /K [44 0 R] >> endobj 44 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [75 50 0 R 80 49 0 R 82 48 0 R 84 47 0 R 103 46 0 R 105 45 0 R 111] - /Pg 351 0 R + /S /Link + /P 43 0 R + /K [1 << + /Type /OBJR + /Pg 731 0 R + /Obj 729 0 R + >>] + /Pg 731 0 R >> endobj 45 0 obj << /Type /StructElem - /S /Formula - /P 44 0 R - /K [106 107 108 109 110] - /Pg 351 0 R + /S /H1 + /P 32 0 R + /T (Bibliographie) + /K [0] + /Pg 731 0 R >> endobj 46 0 obj << /Type /StructElem - /S /Em - /P 44 0 R - /K [104] - /Pg 351 0 R + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [74 0 R 70 0 R 61 0 R 58 0 R 54 0 R 50 0 R 47 0 R] >> endobj 47 0 obj << /Type /StructElem - /S /Formula - /P 44 0 R - /K [85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102] - /Pg 351 0 R + /S /LI + /P 46 0 R + /K [49 0 R 48 0 R] >> endobj 48 0 obj << /Type /StructElem - /S /Em - /P 44 0 R - /K [83] - /Pg 351 0 R + /S /LBody + /P 47 0 R + /K [30] + /Pg 727 0 R >> endobj 49 0 obj << /Type /StructElem - /S /Formula - /P 44 0 R - /K [81] - /Pg 351 0 R + /S /Lbl + /P 47 0 R + /K [29] + /Pg 727 0 R >> endobj 50 0 obj << /Type /StructElem - /S /Formula - /P 44 0 R - /K [76 77 78 79] - /Pg 351 0 R + /S /LI + /P 46 0 R + /K [53 0 R 51 0 R] >> endobj 51 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [67 68 69 70 71 72 73 74] - /Pg 351 0 R + /S /LBody + /P 50 0 R + /K [26 52 0 R 28] + /Pg 727 0 R >> endobj 52 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [63 64 53 0 R 66] - /Pg 351 0 R + /S /Code + /P 51 0 R + /Lang (en) + /K [27] + /Pg 727 0 R >> endobj 53 0 obj << /Type /StructElem - /S /Formula - /P 52 0 R - /K [65] - /Pg 351 0 R + /S /Lbl + /P 50 0 R + /K [25] + /Pg 727 0 R >> endobj 54 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [60 55 0 R 62] - /Pg 351 0 R + /S /LI + /P 46 0 R + /K [57 0 R 55 0 R] >> endobj 55 0 obj << /Type /StructElem - /S /Formula + /S /LBody /P 54 0 R - /K [56 0 R] + /K [22 56 0 R 24] + /Pg 727 0 R >> endobj 56 0 obj << /Type /StructElem - /S /Strong + /S /Link /P 55 0 R - /K [61] - /Pg 351 0 R + /K [23 << + /Type /OBJR + /Pg 727 0 R + /Obj 726 0 R + >>] + /Pg 727 0 R >> endobj 57 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [55 56 57 58 59] - /Pg 351 0 R + /S /Lbl + /P 54 0 R + /K [21] + /Pg 727 0 R >> endobj 58 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [49 50 60 0 R 52 59 0 R 54] - /Pg 351 0 R + /S /LI + /P 46 0 R + /K [60 0 R 59 0 R] >> endobj 59 0 obj << /Type /StructElem - /S /Em + /S /LBody /P 58 0 R - /K [53] - /Pg 351 0 R + /K [19 20] + /Pg 727 0 R >> endobj 60 0 obj << /Type /StructElem - /S /Formula + /S /Lbl /P 58 0 R - /K [61 0 R] + /K [18] + /Pg 727 0 R >> endobj 61 0 obj << /Type /StructElem - /S /Strong - /P 60 0 R - /K [51] - /Pg 351 0 R + /S /L + /P 46 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [65 0 R 62 0 R] >> endobj 62 0 obj << /Type /StructElem - /S /L - /P 18 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [67 0 R 63 0 R] + /S /LI + /P 61 0 R + /K [64 0 R 63 0 R] >> endobj 63 0 obj << /Type /StructElem - /S /LI + /S /LBody /P 62 0 R - /K [66 0 R 64 0 R] + /K [17] + /Pg 727 0 R >> endobj 64 0 obj << /Type /StructElem - /S /LBody - /P 63 0 R - /K [46 65 0 R 48] - /Pg 351 0 R + /S /Lbl + /P 62 0 R + /K [16] + /Pg 727 0 R >> endobj 65 0 obj << /Type /StructElem - /S /Formula - /P 64 0 R - /K [47] - /Pg 351 0 R + /S /LI + /P 61 0 R + /K [69 0 R 66 0 R] >> endobj 66 0 obj << /Type /StructElem - /S /Lbl - /P 63 0 R - /K [45] - /Pg 351 0 R + /S /LBody + /P 65 0 R + /K [7 68 0 R 9 67 0 R 15] + /Pg 727 0 R >> endobj 67 0 obj << /Type /StructElem - /S /LI - /P 62 0 R - /K [70 0 R 68 0 R] + /S /Formula + /P 66 0 R + /K [10 11 12 13 14] + /Pg 727 0 R >> endobj 68 0 obj << /Type /StructElem - /S /LBody - /P 67 0 R - /K [42 69 0 R 44] - /Pg 351 0 R + /S /Formula + /P 66 0 R + /K [8] + /Pg 727 0 R >> endobj 69 0 obj << /Type /StructElem - /S /Formula - /P 68 0 R - /K [43] - /Pg 351 0 R + /S /Lbl + /P 65 0 R + /K [6] + /Pg 727 0 R >> endobj 70 0 obj << /Type /StructElem - /S /Lbl - /P 67 0 R - /K [41] - /Pg 351 0 R + /S /LI + /P 46 0 R + /K [73 0 R 71 0 R] >> endobj 71 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [36 74 0 R 38 72 0 R 40] - /Pg 351 0 R + /S /LBody + /P 70 0 R + /K [72 0 R] >> endobj 72 0 obj << /Type /StructElem - /S /Formula + /S /P /P 71 0 R - /K [73 0 R] + /K [5] + /Pg 727 0 R >> endobj 73 0 obj << /Type /StructElem - /S /Strong - /P 72 0 R - /K [39] - /Pg 351 0 R + /S /Lbl + /P 70 0 R + /K [4] + /Pg 727 0 R >> endobj 74 0 obj << /Type /StructElem - /S /Strong - /P 71 0 R - /K [37] - /Pg 351 0 R + /S /LI + /P 46 0 R + /K [76 0 R 75 0 R] >> endobj 75 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 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 27 28 29 30 31 32 33 34 35] - /Pg 351 0 R + /S /LBody + /P 74 0 R + /K [3] + /Pg 727 0 R >> endobj 76 0 obj << /Type /StructElem - /S /L - /P 18 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [81 0 R 77 0 R] + /S /Lbl + /P 74 0 R + /K [2] + /Pg 727 0 R >> endobj 77 0 obj << /Type /StructElem - /S /LI - /P 76 0 R - /K [80 0 R 78 0 R] + /S /H1 + /P 32 0 R + /T (Code Rust) + /K [1] + /Pg 727 0 R >> endobj 78 0 obj << /Type /StructElem - /S /LBody - /P 77 0 R - /K [259 79 0 R 268] - /Pg 346 0 R + /S /H1 + /P 32 0 R + /T (QC-LDPC) + /K [0] + /Pg 727 0 R >> endobj 79 0 obj << /Type /StructElem - /S /Formula - /P 78 0 R - /K [260 261 262 263 264 265 266 267] - /Pg 346 0 R + /S /P + /P 32 0 R + /K [203 80 0 R 205] + /Pg 724 0 R >> endobj 80 0 obj << /Type /StructElem - /S /Lbl - /P 77 0 R - /K [258] - /Pg 346 0 R + /S /Link + /P 79 0 R + /K [204 << + /Type /OBJR + /Pg 724 0 R + /Obj 723 0 R + >>] + /Pg 724 0 R >> endobj 81 0 obj << /Type /StructElem - /S /LI - /P 76 0 R - /K [85 0 R 82 0 R] + /S /H2 + /P 32 0 R + /T + /K [202] + /Pg 724 0 R >> endobj 82 0 obj << /Type /StructElem - /S /LBody - /P 81 0 R - /K [238 84 0 R 250 83 0 R 257] - /Pg 346 0 R + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Decimal + >>] + /K [88 0 R 83 0 R] >> endobj 83 0 obj << /Type /StructElem - /S /Formula + /S /LI /P 82 0 R - /K [251 252 253 254 255 256] - /Pg 346 0 R + /K [87 0 R 84 0 R] >> endobj 84 0 obj << /Type /StructElem - /S /Formula - /P 82 0 R - /K [239 240 241 242 243 244 245 246 247 248 249] - /Pg 346 0 R + /S /LBody + /P 83 0 R + /K [197 86 0 R 199 85 0 R 201] + /Pg 724 0 R >> endobj 85 0 obj << /Type /StructElem - /S /Lbl - /P 81 0 R - /K [237] - /Pg 346 0 R + /S /Link + /P 84 0 R + /K [200 << + /Type /OBJR + /Pg 724 0 R + /Obj 722 0 R + >>] + /Pg 724 0 R >> endobj 86 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [235 236] - /Pg 346 0 R + /S /Formula + /P 84 0 R + /K [198] + /Pg 724 0 R >> endobj 87 0 obj << /Type /StructElem - /S /L - /P 18 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [88 0 R] + /S /Lbl + /P 83 0 R + /K [196] + /Pg 724 0 R >> endobj @@ -881,8 +844,8 @@ endobj << /Type /StructElem /S /LI - /P 87 0 R - /K [91 0 R 89 0 R] + /P 82 0 R + /K [93 0 R 89 0 R] >> endobj @@ -891,48 +854,52 @@ endobj /Type /StructElem /S /LBody /P 88 0 R - /K [90 0 R 234] - /Pg 346 0 R + /K [187 92 0 R 189 190 91 0 R 192 90 0 R 194 195] + /Pg 724 0 R >> endobj 90 0 obj << /Type /StructElem - /S /Em + /S /Link /P 89 0 R - /K [233] - /Pg 346 0 R + /K [193 << + /Type /OBJR + /Pg 724 0 R + /Obj 721 0 R + >>] + /Pg 724 0 R >> endobj 91 0 obj << /Type /StructElem - /S /Lbl - /P 88 0 R - /K [232] - /Pg 346 0 R + /S /Formula + /P 89 0 R + /K [191] + /Pg 724 0 R >> endobj 92 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [204 104 0 R 206 102 0 R 208 101 0 R 210 99 0 R 212 98 0 R 214 215 97 0 R 217 96 0 R 221 222 95 0 R 226 94 0 R 228 229 93 0 R 231] - /Pg 346 0 R + /S /Formula + /P 89 0 R + /K [188] + /Pg 724 0 R >> endobj 93 0 obj << /Type /StructElem - /S /Em - /P 92 0 R - /K [230] - /Pg 346 0 R + /S /Lbl + /P 88 0 R + /K [186] + /Pg 724 0 R >> endobj @@ -940,19 +907,23 @@ endobj << /Type /StructElem /S /Formula - /P 92 0 R - /K [227] - /Pg 346 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [177 178 179 180 181 182 183 184 185] + /Pg 724 0 R >> endobj 95 0 obj << /Type /StructElem - /S /Formula - /P 92 0 R - /K [223 224 225] - /Pg 346 0 R + /S /P + /P 32 0 R + /K [155 98 0 R 172 97 0 R 174 96 0 R 176] + /Pg 724 0 R >> endobj @@ -960,9 +931,9 @@ endobj << /Type /StructElem /S /Formula - /P 92 0 R - /K [218 219 220] - /Pg 346 0 R + /P 95 0 R + /K [175] + /Pg 724 0 R >> endobj @@ -970,9 +941,9 @@ endobj << /Type /StructElem /S /Formula - /P 92 0 R - /K [216] - /Pg 346 0 R + /P 95 0 R + /K [173] + /Pg 724 0 R >> endobj @@ -980,9 +951,9 @@ endobj << /Type /StructElem /S /Formula - /P 92 0 R - /K [213] - /Pg 346 0 R + /P 95 0 R + /K [156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171] + /Pg 724 0 R >> endobj @@ -990,216 +961,216 @@ endobj << /Type /StructElem /S /Formula - /P 92 0 R - /K [100 0 R] + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [145 146 147 148 149 150 151 152 153 154] + /Pg 724 0 R >> endobj 100 0 obj << /Type /StructElem - /S /Strong - /P 99 0 R - /K [211] - /Pg 346 0 R + /S /P + /P 32 0 R + /K [143 101 0 R] + /Pg 724 0 R >> endobj 101 0 obj << /Type /StructElem - /S /Formula - /P 92 0 R - /K [209] - /Pg 346 0 R + /S /Em + /P 100 0 R + /K [144] + /Pg 724 0 R >> endobj 102 0 obj << /Type /StructElem - /S /Formula - /P 92 0 R - /K [103 0 R] + /S /H2 + /P 32 0 R + /T (Encodage) + /K [142] + /Pg 724 0 R >> endobj 103 0 obj << /Type /StructElem - /S /Strong - /P 102 0 R - /K [207] - /Pg 346 0 R + /S /P + /P 32 0 R + /K [136 105 0 R 138 139 104 0 R 141] + /Pg 724 0 R >> endobj 104 0 obj << /Type /StructElem - /S /Em - /P 92 0 R - /K [205] - /Pg 346 0 R + /S /Link + /P 103 0 R + /K [140 << + /Type /OBJR + /Pg 724 0 R + /Obj 720 0 R + >>] + /Pg 724 0 R >> endobj 105 0 obj << /Type /StructElem - /S /H1 - /P 18 0 R - /T (Code de Hamming) - /K [202 106 0 R] - /Pg 346 0 R + /S /Formula + /P 103 0 R + /K [137] + /Pg 724 0 R >> endobj 106 0 obj << /Type /StructElem - /S /Em - /P 105 0 R - /K [203] - /Pg 346 0 R + /S /P + /P 32 0 R + /K [110 108 0 R 112 107 0 R 135] + /Pg 724 0 R >> endobj 107 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [197 109 0 R 199 108 0 R 201] - /Pg 346 0 R + /S /Formula + /P 106 0 R + /K [113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134] + /Pg 724 0 R >> endobj 108 0 obj << /Type /StructElem - /S /Em - /P 107 0 R - /K [200] - /Pg 346 0 R + /S /Formula + /P 106 0 R + /K [111] + /Pg 724 0 R >> endobj 109 0 obj << /Type /StructElem - /S /Formula - /P 107 0 R - /K [198] - /Pg 346 0 R + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [115 0 R 110 0 R] >> endobj 110 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [183 184 185 186 187 188 189 190 191 192 193 194 195 196] - /Pg 346 0 R + /S /LI + /P 109 0 R + /K [114 0 R 111 0 R] >> endobj 111 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [173 115 0 R 175 114 0 R 177 113 0 R 179 180 112 0 R 182] - /Pg 346 0 R + /S /LBody + /P 110 0 R + /K [112 0 R] >> endobj 112 0 obj << /Type /StructElem - /S /Formula + /S /P /P 111 0 R - /K [181] - /Pg 346 0 R + /K [113 0 R] >> endobj 113 0 obj << /Type /StructElem - /S /Formula - /P 111 0 R - /K [178] - /Pg 346 0 R + /S /Strong + /P 112 0 R + /K [109] + /Pg 724 0 R >> endobj 114 0 obj << /Type /StructElem - /S /Em - /P 111 0 R - /K [176] - /Pg 346 0 R + /S /Lbl + /P 110 0 R + /K [108] + /Pg 724 0 R >> endobj 115 0 obj << /Type /StructElem - /S /Em - /P 111 0 R - /K [174] - /Pg 346 0 R + /S /LI + /P 109 0 R + /K [122 0 R 116 0 R] >> endobj 116 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [170 117 0 R 172] - /Pg 346 0 R + /S /LBody + /P 115 0 R + /K [117 0 R] >> endobj 117 0 obj << /Type /StructElem - /S /Em + /S /P /P 116 0 R - /K [171] - /Pg 346 0 R + /K [120 0 R 102 119 0 R 104 105 118 0 R 107] + /Pg 724 0 R >> endobj 118 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [146 147 126 0 R 149 125 0 R 151 124 0 R 156 123 0 R 158 122 0 R 162 121 0 R 164 120 0 R 166 167 119 0 R 169] - /Pg 346 0 R + /S /Formula + /P 117 0 R + /K [106] + /Pg 724 0 R >> endobj 119 0 obj << /Type /StructElem - /S /Link - /P 118 0 R - /K [168 << - /Type /OBJR - /Pg 346 0 R - /Obj 345 0 R - >>] - /Pg 346 0 R + /S /Formula + /P 117 0 R + /K [103] + /Pg 724 0 R >> endobj @@ -1207,29 +1178,28 @@ endobj << /Type /StructElem /S /Em - /P 118 0 R - /K [165] - /Pg 346 0 R + /P 117 0 R + /K [121 0 R] >> endobj 121 0 obj << /Type /StructElem - /S /Formula - /P 118 0 R - /K [163] - /Pg 346 0 R + /S /Strong + /P 120 0 R + /K [101] + /Pg 724 0 R >> endobj 122 0 obj << /Type /StructElem - /S /Formula - /P 118 0 R - /K [159 160 161] - /Pg 346 0 R + /S /Lbl + /P 115 0 R + /K [100] + /Pg 724 0 R >> endobj @@ -1237,9 +1207,13 @@ endobj << /Type /StructElem /S /Formula - /P 118 0 R - /K [157] - /Pg 346 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [98 99] + /Pg 724 0 R >> endobj @@ -1247,33 +1221,41 @@ endobj << /Type /StructElem /S /Formula - /P 118 0 R - /K [152 153 154 155] - /Pg 346 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [96 97] + /Pg 724 0 R >> endobj 125 0 obj << /Type /StructElem - /S /Link - /P 118 0 R - /K [150 << - /Type /OBJR - /Pg 346 0 R - /Obj 344 0 R + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block >>] - /Pg 346 0 R + /K [94 95] + /Pg 724 0 R >> endobj 126 0 obj << /Type /StructElem - /S /Em - /P 118 0 R - /K [148] - /Pg 346 0 R + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [92 93] + /Pg 724 0 R >> endobj @@ -1281,23 +1263,27 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R + /P 32 0 R /A [<< /O /Layout /Placement /Block >>] - /K [142 143 144 145] - /Pg 346 0 R + /K [90 91] + /Pg 724 0 R >> endobj 128 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [136 130 0 R 139 129 0 R 141] - /Pg 346 0 R + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [88 89] + /Pg 724 0 R >> endobj @@ -1305,9 +1291,13 @@ endobj << /Type /StructElem /S /Formula - /P 128 0 R - /K [140] - /Pg 346 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [86 87] + /Pg 724 0 R >> endobj @@ -1315,98 +1305,139 @@ endobj << /Type /StructElem /S /Formula - /P 128 0 R - /K [137 138] - /Pg 346 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [84 85] + /Pg 724 0 R >> endobj 131 0 obj << /Type /StructElem - /S /L - /P 18 0 R + /S /Formula + /P 32 0 R /A [<< - /O /List - /ListNumbering /Circle + /O /Layout + /Placement /Block >>] - /K [138 0 R 132 0 R] + /K [82 83] + /Pg 724 0 R >> endobj 132 0 obj << /Type /StructElem - /S /LI - /P 131 0 R - /K [137 0 R 133 0 R] + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [80 81] + /Pg 724 0 R >> endobj 133 0 obj << /Type /StructElem - /S /LBody - /P 132 0 R - /K [134 0 R] + /S /Span + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [79] + /Pg 724 0 R >> endobj 134 0 obj << /Type /StructElem - /S /P - /P 133 0 R - /K [129 136 0 R 132 133 135 0 R 135] - /Pg 346 0 R + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [77 78] + /Pg 724 0 R >> endobj 135 0 obj << /Type /StructElem - /S /Em - /P 134 0 R - /K [134] - /Pg 346 0 R + /S /Span + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [74 76] + /Pg 724 0 R >> endobj 136 0 obj << /Type /StructElem - /S /Formula - /P 134 0 R - /K [130 131] - /Pg 346 0 R + /S /Strong + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [75] + /Pg 724 0 R >> endobj 137 0 obj << /Type /StructElem - /S /Lbl - /P 132 0 R - /K [128] - /Pg 346 0 R + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [72 73] + /Pg 724 0 R >> endobj 138 0 obj << /Type /StructElem - /S /LI - /P 131 0 R - /K [146 0 R 139 0 R] + /S /Span + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [71] + /Pg 724 0 R >> endobj 139 0 obj << /Type /StructElem - /S /LBody - /P 138 0 R - /K [140 0 R] + /S /Strong + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [70] + /Pg 724 0 R >> endobj @@ -1414,9 +1445,9 @@ endobj << /Type /StructElem /S /P - /P 139 0 R - /K [84 145 0 R 86 87 144 0 R 105 143 0 R 123 142 0 R 125 141 0 R 127] - /Pg 346 0 R + /P 32 0 R + /K [69] + /Pg 724 0 R >> endobj @@ -1424,19 +1455,23 @@ endobj << /Type /StructElem /S /Formula - /P 140 0 R - /K [126] - /Pg 346 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68] + /Pg 724 0 R >> endobj 142 0 obj << /Type /StructElem - /S /Formula - /P 140 0 R - /K [124] - /Pg 346 0 R + /S /P + /P 32 0 R + /K [146 0 R 28 145 0 R 30 144 0 R 35 143 0 R 40] + /Pg 724 0 R >> endobj @@ -1444,9 +1479,9 @@ endobj << /Type /StructElem /S /Formula - /P 140 0 R - /K [106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122] - /Pg 346 0 R + /P 142 0 R + /K [36 37 38 39] + /Pg 724 0 R >> endobj @@ -1454,9 +1489,9 @@ endobj << /Type /StructElem /S /Formula - /P 140 0 R - /K [88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104] - /Pg 346 0 R + /P 142 0 R + /K [31 32 33 34] + /Pg 724 0 R >> endobj @@ -1464,107 +1499,100 @@ endobj << /Type /StructElem /S /Em - /P 140 0 R - /K [85] - /Pg 346 0 R + /P 142 0 R + /K [29] + /Pg 724 0 R >> endobj 146 0 obj << /Type /StructElem - /S /Lbl - /P 138 0 R - /K [83] - /Pg 346 0 R + /S /Strong + /P 142 0 R + /K [27] + /Pg 724 0 R >> endobj 147 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [72 152 0 R 74 151 0 R 76 77 150 0 R 79 148 0 R 82] - /Pg 346 0 R + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [169 0 R 164 0 R 158 0 R 153 0 R 148 0 R] >> endobj 148 0 obj << /Type /StructElem - /S /Link + /S /LI /P 147 0 R - /K [80 << - /Type /OBJR - /Pg 346 0 R - /Obj 342 0 R - >> << - /Type /OBJR - /Pg 346 0 R - /Obj 343 0 R - >> 149 0 R] - /Pg 346 0 R + /K [152 0 R 149 0 R] >> endobj 149 0 obj << /Type /StructElem - /S /Em + /S /LBody /P 148 0 R - /K [81] - /Pg 346 0 R + /K [151 0 R 24 150 0 R 26] + /Pg 724 0 R >> endobj 150 0 obj << /Type /StructElem - /S /Em - /P 147 0 R - /K [78] - /Pg 346 0 R + /S /Formula + /P 149 0 R + /K [25] + /Pg 724 0 R >> endobj 151 0 obj << /Type /StructElem - /S /Em - /P 147 0 R - /K [75] - /Pg 346 0 R + /S /Formula + /P 149 0 R + /K [20 21 22 23] + /Pg 724 0 R >> endobj 152 0 obj << /Type /StructElem - /S /Em - /P 147 0 R - /K [73] - /Pg 346 0 R + /S /Lbl + /P 148 0 R + /K [19] + /Pg 724 0 R >> endobj 153 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [54 155 0 R 62 154 0 R 71] - /Pg 346 0 R + /S /LI + /P 147 0 R + /K [157 0 R 154 0 R] >> endobj 154 0 obj << /Type /StructElem - /S /Formula + /S /LBody /P 153 0 R - /K [63 64 65 66 67 68 69 70] - /Pg 346 0 R + /K [1 156 0 R 9 155 0 R 17 18] + /Pg 724 0 R >> endobj @@ -1572,69 +1600,68 @@ endobj << /Type /StructElem /S /Formula - /P 153 0 R - /K [55 56 57 58 59 60 61] - /Pg 346 0 R + /P 154 0 R + /K [10 11 12 13 14 15 16] + /Pg 724 0 R >> endobj 156 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [38 161 0 R 44 160 0 R 46 159 0 R 48 158 0 R 50 51 157 0 R 53] - /Pg 346 0 R + /S /Formula + /P 154 0 R + /K [2 3 4 5 6 7 8] + /Pg 724 0 R >> endobj 157 0 obj << /Type /StructElem - /S /Formula - /P 156 0 R - /K [52] - /Pg 346 0 R + /S /Lbl + /P 153 0 R + /K [0] + /Pg 724 0 R >> endobj 158 0 obj << /Type /StructElem - /S /Em - /P 156 0 R - /K [49] - /Pg 346 0 R + /S /LI + /P 147 0 R + /K [163 0 R 159 0 R] >> endobj 159 0 obj << /Type /StructElem - /S /Formula - /P 156 0 R - /K [47] - /Pg 346 0 R + /S /LBody + /P 158 0 R + /K [162 0 R 343 161 0 R 345 160 0 R] + /Pg 718 0 R >> endobj 160 0 obj << /Type /StructElem - /S /Strong - /P 156 0 R - /K [45] - /Pg 346 0 R + /S /Formula + /P 159 0 R + /K [346 347 348 349 350] + /Pg 718 0 R >> endobj 161 0 obj << /Type /StructElem - /S /Formula - /P 156 0 R - /K [39 40 41 42 43] - /Pg 346 0 R + /S /Em + /P 159 0 R + /K [344] + /Pg 718 0 R >> endobj @@ -1642,102 +1669,87 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 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 27 28 29 30 31 32 33 34 35 36 37] - /Pg 346 0 R + /P 159 0 R + /K [338 339 340 341 342] + /Pg 718 0 R >> endobj 163 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [294 165 0 R 310 164 0 R 326] - /Pg 340 0 R + /S /Lbl + /P 158 0 R + /K [337] + /Pg 718 0 R >> endobj 164 0 obj << /Type /StructElem - /S /Formula - /P 163 0 R - /K [311 312 313 314 315 316 317 318 319 320 321 322 323 324 325] - /Pg 340 0 R + /S /LI + /P 147 0 R + /K [168 0 R 165 0 R] >> endobj 165 0 obj << /Type /StructElem - /S /Formula - /P 163 0 R - /K [295 296 297 298 299 300 301 302 303 304 305 306 307 308 309] - /Pg 340 0 R + /S /LBody + /P 164 0 R + /K [167 0 R 331 166 0 R] + /Pg 718 0 R >> endobj 166 0 obj << /Type /StructElem - /S /H2 - /P 18 0 R - /T - /K [293] - /Pg 340 0 R + /S /Formula + /P 165 0 R + /K [332 333 334 335 336] + /Pg 718 0 R >> endobj 167 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [291 168 0 R] - /Pg 340 0 R + /S /Formula + /P 165 0 R + /K [326 327 328 329 330] + /Pg 718 0 R >> endobj 168 0 obj << /Type /StructElem - /S /Link - /P 167 0 R - /K [292 << - /Type /OBJR - /Pg 340 0 R - /Obj 339 0 R - >>] - /Pg 340 0 R + /S /Lbl + /P 164 0 R + /K [325] + /Pg 718 0 R >> endobj 169 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [283 284 285 286 287 288 289 290] - /Pg 340 0 R + /S /LI + /P 147 0 R + /K [172 0 R 170 0 R] >> endobj 170 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [275 172 0 R 277 171 0 R 281 282] - /Pg 340 0 R + /S /LBody + /P 169 0 R + /K [171 0 R 324] + /Pg 718 0 R >> endobj @@ -1746,18 +1758,18 @@ endobj /Type /StructElem /S /Formula /P 170 0 R - /K [278 279 280] - /Pg 340 0 R + /K [315 316 317 318 319 320 321 322 323] + /Pg 718 0 R >> endobj 172 0 obj << /Type /StructElem - /S /Em - /P 170 0 R - /K [276] - /Pg 340 0 R + /S /Lbl + /P 169 0 R + /K [314] + /Pg 718 0 R >> endobj @@ -1765,29 +1777,30 @@ endobj << /Type /StructElem /S /P - /P 18 0 R - /K [175 0 R 272 174 0 R 274] - /Pg 340 0 R + /P 32 0 R + /K [313] + /Pg 718 0 R >> endobj 174 0 obj << /Type /StructElem - /S /Formula - /P 173 0 R - /K [273] - /Pg 340 0 R + /S /H2 + /P 32 0 R + /T (Graphe de Tanner) + /K [312] + /Pg 718 0 R >> endobj 175 0 obj << /Type /StructElem - /S /Formula - /P 173 0 R - /K [271] - /Pg 340 0 R + /S /P + /P 32 0 R + /K [284 179 0 R 286 287 178 0 R 177 0 R 176 0 R 309 310 311] + /Pg 718 0 R >> endobj @@ -1795,23 +1808,19 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [266 267 268 269 270] - /Pg 340 0 R + /P 175 0 R + /K [301 302 303 304 305 306 307 308] + /Pg 718 0 R >> endobj 177 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [261 179 0 R 263 178 0 R 265] - /Pg 340 0 R + /S /Formula + /P 175 0 R + /K [293 294 295 296 297 298 299 300] + /Pg 718 0 R >> endobj @@ -1819,9 +1828,9 @@ endobj << /Type /StructElem /S /Formula - /P 177 0 R - /K [264] - /Pg 340 0 R + /P 175 0 R + /K [288 289 290 291 292] + /Pg 718 0 R >> endobj @@ -1829,43 +1838,42 @@ endobj << /Type /StructElem /S /Formula - /P 177 0 R - /K [262] - /Pg 340 0 R + /P 175 0 R + /K [180 0 R] >> endobj 180 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [252 253 254 255 256 257 258 259 260] - /Pg 340 0 R + /S /Strong + /P 179 0 R + /K [285] + /Pg 718 0 R >> endobj 181 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [234 182 0 R 251] - /Pg 340 0 R + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283] + /Pg 718 0 R >> endobj 182 0 obj << /Type /StructElem - /S /Formula - /P 181 0 R - /K [235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250] - /Pg 340 0 R + /S /P + /P 32 0 R + /K [165 184 0 R 168 183 0 R 171] + /Pg 718 0 R >> endobj @@ -1873,133 +1881,126 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [224 225 226 227 228 229 230 231 232 233] - /Pg 340 0 R + /P 182 0 R + /K [169 170] + /Pg 718 0 R >> endobj 184 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [221 185 0 R 223] - /Pg 340 0 R + /S /Formula + /P 182 0 R + /K [166 167] + /Pg 718 0 R >> endobj 185 0 obj << /Type /StructElem - /S /Formula - /P 184 0 R - /K [222] - /Pg 340 0 R + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [194 0 R 190 0 R 186 0 R] >> endobj 186 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [205 192 0 R 207 191 0 R 210 190 0 R 212 189 0 R 214 188 0 R 217 218 187 0 R 220] - /Pg 340 0 R + /S /LI + /P 185 0 R + /K [189 0 R 187 0 R] >> endobj 187 0 obj << /Type /StructElem - /S /Formula + /S /LBody /P 186 0 R - /K [219] - /Pg 340 0 R + /K [188 0 R] >> endobj 188 0 obj << /Type /StructElem - /S /Formula - /P 186 0 R - /K [215 216] - /Pg 340 0 R + /S /P + /P 187 0 R + /K [164] + /Pg 718 0 R >> endobj 189 0 obj << /Type /StructElem - /S /Em + /S /Lbl /P 186 0 R - /K [213] - /Pg 340 0 R + /K [163] + /Pg 718 0 R >> endobj 190 0 obj << /Type /StructElem - /S /Em - /P 186 0 R - /K [211] - /Pg 340 0 R + /S /LI + /P 185 0 R + /K [193 0 R 191 0 R] >> endobj 191 0 obj << /Type /StructElem - /S /Formula - /P 186 0 R - /K [208 209] - /Pg 340 0 R + /S /LBody + /P 190 0 R + /K [192 0 R] >> endobj 192 0 obj << /Type /StructElem - /S /Formula - /P 186 0 R - /K [206] - /Pg 340 0 R + /S /P + /P 191 0 R + /K [162] + /Pg 718 0 R >> endobj 193 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [199 195 0 R 202 194 0 R 204] - /Pg 340 0 R + /S /Lbl + /P 190 0 R + /K [161] + /Pg 718 0 R >> endobj 194 0 obj << /Type /StructElem - /S /Em - /P 193 0 R - /K [203] - /Pg 340 0 R + /S /LI + /P 185 0 R + /K [202 0 R 195 0 R] >> endobj 195 0 obj << /Type /StructElem - /S /Formula - /P 193 0 R - /K [200 201] - /Pg 340 0 R + /S /LBody + /P 194 0 R + /K [196 0 R] >> endobj @@ -2007,9 +2008,9 @@ endobj << /Type /StructElem /S /P - /P 18 0 R - /K [179 200 0 R 181 199 0 R 183 198 0 R 185 197 0 R 198] - /Pg 340 0 R + /P 195 0 R + /K [153 200 0 R 155 198 0 R 157 197 0 R 159 160] + /Pg 718 0 R >> endobj @@ -2018,28 +2019,27 @@ endobj /Type /StructElem /S /Formula /P 196 0 R - /K [186 187 188 189 190 191 192 193 194 195 196 197] - /Pg 340 0 R + /K [158] + /Pg 718 0 R >> endobj 198 0 obj << /Type /StructElem - /S /Em + /S /Formula /P 196 0 R - /K [184] - /Pg 340 0 R + /K [199 0 R] >> endobj 199 0 obj << /Type /StructElem - /S /Formula - /P 196 0 R - /K [182] - /Pg 340 0 R + /S /Strong + /P 198 0 R + /K [156] + /Pg 718 0 R >> endobj @@ -2048,42 +2048,38 @@ endobj /Type /StructElem /S /Formula /P 196 0 R - /K [180] - /Pg 340 0 R + /K [201 0 R] >> endobj 201 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [175 176 177 178] - /Pg 340 0 R + /S /Strong + /P 200 0 R + /K [154] + /Pg 718 0 R >> endobj 202 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [146 206 0 R 158 205 0 R 160 204 0 R 162 203 0 R] - /Pg 340 0 R + /S /Lbl + /P 194 0 R + /K [152] + /Pg 718 0 R >> endobj 203 0 obj << /Type /StructElem - /S /Formula - /P 202 0 R - /K [163 164 165 166 167 168 169 170 171 172 173 174] - /Pg 340 0 R + /S /H3 + /P 32 0 R + /T (Codes Repeat-Accumulate (RA)) + /K [151] + /Pg 718 0 R >> endobj @@ -2091,19 +2087,23 @@ endobj << /Type /StructElem /S /Formula - /P 202 0 R - /K [161] - /Pg 340 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150] + /Pg 718 0 R >> endobj 205 0 obj << /Type /StructElem - /S /Formula - /P 202 0 R - /K [159] - /Pg 340 0 R + /S /P + /P 32 0 R + /K [6 213 0 R 12 212 0 R 15 16 211 0 R 19 210 0 R 27 209 0 R 29 30 208 0 R 32 207 0 R 36 206 0 R 38] + /Pg 718 0 R >> endobj @@ -2111,19 +2111,19 @@ endobj << /Type /StructElem /S /Formula - /P 202 0 R - /K [147 148 149 150 151 152 153 154 155 156 157] - /Pg 340 0 R + /P 205 0 R + /K [37] + /Pg 718 0 R >> endobj 207 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [143 208 0 R 145] - /Pg 340 0 R + /S /Formula + /P 205 0 R + /K [33 34 35] + /Pg 718 0 R >> endobj @@ -2131,18 +2131,19 @@ endobj << /Type /StructElem /S /Formula - /P 207 0 R - /K [209 0 R] + /P 205 0 R + /K [31] + /Pg 718 0 R >> endobj 209 0 obj << /Type /StructElem - /S /Strong - /P 208 0 R - /K [144] - /Pg 340 0 R + /S /Formula + /P 205 0 R + /K [28] + /Pg 718 0 R >> endobj @@ -2150,23 +2151,19 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142] - /Pg 340 0 R + /P 205 0 R + /K [20 21 22 23 24 25 26] + /Pg 718 0 R >> endobj 211 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [84 212 0 R 93] - /Pg 340 0 R + /S /Formula + /P 205 0 R + /K [17 18] + /Pg 718 0 R >> endobj @@ -2174,9 +2171,9 @@ endobj << /Type /StructElem /S /Formula - /P 211 0 R - /K [85 86 87 88 89 90 91 92] - /Pg 340 0 R + /P 205 0 R + /K [13 14] + /Pg 718 0 R >> endobj @@ -2184,137 +2181,126 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83] - /Pg 340 0 R + /P 205 0 R + /K [7 8 9 10 11] + /Pg 718 0 R >> endobj 214 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [56] - /Pg 340 0 R + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [228 0 R 223 0 R 219 0 R 215 0 R] >> endobj 215 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [44 220 0 R 46 219 0 R 48 218 0 R 50 51 217 0 R 53 216 0 R 55] - /Pg 340 0 R + /S /LI + /P 214 0 R + /K [218 0 R 216 0 R] >> endobj 216 0 obj << /Type /StructElem - /S /Em + /S /LBody /P 215 0 R - /K [54] - /Pg 340 0 R + /K [217 0 R] >> endobj 217 0 obj << /Type /StructElem - /S /Formula - /P 215 0 R - /K [52] - /Pg 340 0 R + /S /P + /P 216 0 R + /K [5] + /Pg 718 0 R >> endobj 218 0 obj << /Type /StructElem - /S /Formula + /S /Lbl /P 215 0 R - /K [49] - /Pg 340 0 R + /K [4] + /Pg 718 0 R >> endobj 219 0 obj << /Type /StructElem - /S /Em - /P 215 0 R - /K [47] - /Pg 340 0 R + /S /LI + /P 214 0 R + /K [222 0 R 220 0 R] >> endobj 220 0 obj << /Type /StructElem - /S /Formula - /P 215 0 R - /K [45] - /Pg 340 0 R + /S /LBody + /P 219 0 R + /K [221 0 R] >> endobj 221 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 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 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43] - /Pg 340 0 R + /S /P + /P 220 0 R + /K [1 2 3] + /Pg 718 0 R >> endobj 222 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [203] - /Pg 337 0 R + /S /Lbl + /P 219 0 R + /K [0] + /Pg 718 0 R >> endobj 223 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [225 0 R 198 199 224 0 R 201 202] - /Pg 337 0 R + /S /LI + /P 214 0 R + /K [227 0 R 224 0 R] >> endobj 224 0 obj << /Type /StructElem - /S /Formula + /S /LBody /P 223 0 R - /K [200] - /Pg 337 0 R + /K [225 0 R] >> endobj 225 0 obj << /Type /StructElem - /S /Em - /P 223 0 R - /K [197] - /Pg 337 0 R + /S /P + /P 224 0 R + /K [255 226 0 R 257] + /Pg 716 0 R >> endobj @@ -2322,141 +2308,131 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196] - /Pg 337 0 R + /P 225 0 R + /K [256] + /Pg 716 0 R >> endobj 227 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [165 229 0 R 174 228 0 R 176] - /Pg 337 0 R + /S /Lbl + /P 223 0 R + /K [254] + /Pg 716 0 R >> endobj 228 0 obj << /Type /StructElem - /S /Em - /P 227 0 R - /K [175] - /Pg 337 0 R + /S /LI + /P 214 0 R + /K [233 0 R 229 0 R] >> endobj 229 0 obj << /Type /StructElem - /S /Formula - /P 227 0 R - /K [166 167 168 169 170 171 172 173] - /Pg 337 0 R + /S /LBody + /P 228 0 R + /K [230 0 R] >> endobj 230 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164] - /Pg 337 0 R + /S /P + /P 229 0 R + /K [251 231 0 R 253] + /Pg 716 0 R >> endobj 231 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [140 141 232 0 R 143] - /Pg 337 0 R + /S /Formula + /P 230 0 R + /K [232 0 R] >> endobj 232 0 obj << /Type /StructElem - /S /Formula + /S /Strong /P 231 0 R - /K [233 0 R] + /K [252] + /Pg 716 0 R >> endobj 233 0 obj << /Type /StructElem - /S /Strong - /P 232 0 R - /K [142] - /Pg 337 0 R + /S /Lbl + /P 228 0 R + /K [250] + /Pg 716 0 R >> endobj 234 0 obj << /Type /StructElem - /S /H1 - /P 18 0 R - /T - /K [235 0 R 139] - /Pg 337 0 R + /S /H3 + /P 32 0 R + /T (MacKay et Neal) + /K [249] + /Pg 716 0 R >> endobj 235 0 obj << /Type /StructElem - /S /Em - /P 234 0 R - /K [138] - /Pg 337 0 R + /S /P + /P 32 0 R + /K [246 236 0 R 248] + /Pg 716 0 R >> endobj 236 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [93 94 243 0 R 96 242 0 R 113 241 0 R 119 240 0 R 125 239 0 R 132 133 238 0 R 135 237 0 R 137] - /Pg 337 0 R + /S /Formula + /P 235 0 R + /K [247] + /Pg 716 0 R >> endobj 237 0 obj << /Type /StructElem - /S /Strong - /P 236 0 R - /K [136] - /Pg 337 0 R + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [236 237 238 239 240 241 242 243 244 245] + /Pg 716 0 R >> endobj 238 0 obj << /Type /StructElem - /S /Link - /P 236 0 R - /K [134 << - /Type /OBJR - /Pg 337 0 R - /Obj 336 0 R - >>] - /Pg 337 0 R + /S /P + /P 32 0 R + /K [235] + /Pg 716 0 R >> endobj @@ -2464,29 +2440,33 @@ endobj << /Type /StructElem /S /Formula - /P 236 0 R - /K [126 127 128 129 130 131] - /Pg 337 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234] + /Pg 716 0 R >> endobj 240 0 obj << /Type /StructElem - /S /Formula - /P 236 0 R - /K [120 121 122 123 124] - /Pg 337 0 R + /S /P + /P 32 0 R + /K [241 0 R 193] + /Pg 716 0 R >> endobj 241 0 obj << /Type /StructElem - /S /Formula - /P 236 0 R - /K [114 115 116 117 118] - /Pg 337 0 R + /S /Strong + /P 240 0 R + /K [192] + /Pg 716 0 R >> endobj @@ -2494,33 +2474,33 @@ endobj << /Type /StructElem /S /Formula - /P 236 0 R - /K [97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112] - /Pg 337 0 R + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191] + /Pg 716 0 R >> endobj 243 0 obj << /Type /StructElem - /S /Em - /P 236 0 R - /K [95] - /Pg 337 0 R + /S /P + /P 32 0 R + /K [244 0 R 150] + /Pg 716 0 R >> endobj 244 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [82 83 84 85 86 87 88 89 90 91 92] - /Pg 337 0 R + /S /Strong + /P 243 0 R + /K [149] + /Pg 716 0 R >> endobj @@ -2528,41 +2508,33 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R + /P 32 0 R /A [<< /O /Layout /Placement /Block >>] - /K [71 72 73 74 75 76 77 78 79 80 81] - /Pg 337 0 R + /K [108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148] + /Pg 716 0 R >> endobj 246 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [60 61 62 63 64 65 66 67 68 69 70] - /Pg 337 0 R + /S /P + /P 32 0 R + /K [247 0 R 107] + /Pg 716 0 R >> endobj 247 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [49 50 51 52 53 54 55 56 57 58 59] - /Pg 337 0 R + /S /Strong + /P 246 0 R + /K [106] + /Pg 716 0 R >> endobj @@ -2570,9 +2542,9 @@ endobj << /Type /StructElem /S /P - /P 18 0 R - /K [31 258 0 R 33 256 0 R 35 254 0 R 37 38 252 0 R 40 251 0 R 42 249 0 R 48] - /Pg 337 0 R + /P 32 0 R + /K [100 249 0 R 105] + /Pg 716 0 R >> endobj @@ -2581,17 +2553,18 @@ endobj /Type /StructElem /S /Formula /P 248 0 R - /K [250 0 R] + /K [101 102 103 104] + /Pg 716 0 R >> endobj 250 0 obj << /Type /StructElem - /S /Strong - /P 249 0 R - /K [43 44 45 46 47] - /Pg 337 0 R + /S /P + /P 32 0 R + /K [252 0 R 89 251 0 R 99] + /Pg 716 0 R >> endobj @@ -2599,9 +2572,9 @@ endobj << /Type /StructElem /S /Formula - /P 248 0 R - /K [41] - /Pg 337 0 R + /P 250 0 R + /K [90 91 92 93 94 95 96 97 98] + /Pg 716 0 R >> endobj @@ -2609,7 +2582,7 @@ endobj << /Type /StructElem /S /Formula - /P 248 0 R + /P 250 0 R /K [253 0 R] >> endobj @@ -2619,27 +2592,28 @@ endobj /Type /StructElem /S /Strong /P 252 0 R - /K [39] - /Pg 337 0 R + /K [88] + /Pg 716 0 R >> endobj 254 0 obj << /Type /StructElem - /S /Formula - /P 248 0 R - /K [255 0 R] + /S /P + /P 32 0 R + /K [72 257 0 R 77 256 0 R 82 255 0 R 87] + /Pg 716 0 R >> endobj 255 0 obj << /Type /StructElem - /S /Strong + /S /Formula /P 254 0 R - /K [36] - /Pg 337 0 R + /K [83 84 85 86] + /Pg 716 0 R >> endobj @@ -2647,103 +2621,98 @@ endobj << /Type /StructElem /S /Formula - /P 248 0 R - /K [257 0 R] + /P 254 0 R + /K [78 79 80 81] + /Pg 716 0 R >> endobj 257 0 obj << /Type /StructElem - /S /Strong - /P 256 0 R - /K [34] - /Pg 337 0 R + /S /Formula + /P 254 0 R + /K [73 74 75 76] + /Pg 716 0 R >> endobj 258 0 obj << /Type /StructElem - /S /Formula - /P 248 0 R - /K [259 0 R] + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [280 0 R 275 0 R 263 0 R 259 0 R] >> endobj 259 0 obj << /Type /StructElem - /S /Strong + /S /LI /P 258 0 R - /K [32] - /Pg 337 0 R + /K [262 0 R 260 0 R] >> endobj 260 0 obj << /Type /StructElem - /S /H2 - /P 18 0 R - /T - /K [30] - /Pg 337 0 R + /S /LBody + /P 259 0 R + /K [261 0 R] >> endobj 261 0 obj << /Type /StructElem - /S /H1 - /P 18 0 R - /T - /K [29] - /Pg 337 0 R + /S /P + /P 260 0 R + /K [71] + /Pg 716 0 R >> endobj 262 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [23 24 25 26 263 0 R 28] - /Pg 337 0 R + /S /Lbl + /P 259 0 R + /K [70] + /Pg 716 0 R >> endobj 263 0 obj << /Type /StructElem - /S /Em - /P 262 0 R - /K [27] - /Pg 337 0 R + /S /LI + /P 258 0 R + /K [274 0 R 264 0 R] >> endobj 264 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [21 265 0 R] - /Pg 337 0 R + /S /LBody + /P 263 0 R + /K [265 0 R] >> endobj 265 0 obj << /Type /StructElem - /S /Link + /S /P /P 264 0 R - /K [22 << - /Type /OBJR - /Pg 337 0 R - /Obj 335 0 R - >>] - /Pg 337 0 R + /K [273 0 R 58 271 0 R 61 270 0 R 63 64 268 0 R 66 266 0 R 69] + /Pg 716 0 R >> endobj @@ -2751,27 +2720,18 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [19 20] - /Pg 337 0 R + /P 265 0 R + /K [267 0 R] >> endobj 267 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [18] - /Pg 337 0 R + /S /Strong + /P 266 0 R + /K [67 68] + /Pg 716 0 R >> endobj @@ -2779,69 +2739,47 @@ endobj << /Type /StructElem /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [17] - /Pg 337 0 R + /P 265 0 R + /K [269 0 R] >> endobj 269 0 obj << /Type /StructElem - /S /Formula - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [16] - /Pg 337 0 R + /S /Strong + /P 268 0 R + /K [65] + /Pg 716 0 R >> endobj 270 0 obj << /Type /StructElem - /S /Span - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [11 12 14] - /Pg 337 0 R + /S /Formula + /P 265 0 R + /K [62] + /Pg 716 0 R >> endobj 271 0 obj << /Type /StructElem - /S /Strong - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [15] - /Pg 337 0 R + /S /Formula + /P 265 0 R + /K [272 0 R] >> endobj 272 0 obj << /Type /StructElem - /S /Em - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [13] - /Pg 337 0 R + /S /Strong + /P 271 0 R + /K [59 60] + /Pg 716 0 R >> endobj @@ -2849,78 +2787,3624 @@ endobj << /Type /StructElem /S /Strong - /P 18 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [10] - /Pg 337 0 R + /P 265 0 R + /K [57] + /Pg 716 0 R >> endobj 274 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [3 4 5 276 0 R 7 275 0 R 9] - /Pg 337 0 R + /S /Lbl + /P 263 0 R + /K [56] + /Pg 716 0 R >> endobj 275 0 obj << /Type /StructElem - /S /Strong - /P 274 0 R - /K [8] - /Pg 337 0 R + /S /LI + /P 258 0 R + /K [279 0 R 276 0 R] >> endobj 276 0 obj << /Type /StructElem - /S /Strong - /P 274 0 R - /K [6] - /Pg 337 0 R + /S /LBody + /P 275 0 R + /K [277 0 R] >> endobj 277 0 obj << /Type /StructElem - /S /H1 - /P 18 0 R - /T - /K [2] - /Pg 337 0 R + /S /P + /P 276 0 R + /K [278 0 R 54 55] + /Pg 716 0 R >> endobj 278 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [1] - /Pg 337 0 R + /S /Strong + /P 277 0 R + /K [53] + /Pg 716 0 R >> endobj 279 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [0] - /Pg 337 0 R + /S /Lbl + /P 275 0 R + /K [52] + /Pg 716 0 R >> endobj 280 0 obj +<< + /Type /StructElem + /S /LI + /P 258 0 R + /K [288 0 R 281 0 R] +>> +endobj + +281 0 obj +<< + /Type /StructElem + /S /LBody + /P 280 0 R + /K [282 0 R] +>> +endobj + +282 0 obj +<< + /Type /StructElem + /S /P + /P 281 0 R + /K [287 0 R 43 285 0 R 46 284 0 R 48 49 283 0 R 51] + /Pg 716 0 R +>> +endobj + +283 0 obj +<< + /Type /StructElem + /S /Formula + /P 282 0 R + /K [50] + /Pg 716 0 R +>> +endobj + +284 0 obj +<< + /Type /StructElem + /S /Formula + /P 282 0 R + /K [47] + /Pg 716 0 R +>> +endobj + +285 0 obj +<< + /Type /StructElem + /S /Formula + /P 282 0 R + /K [286 0 R] +>> +endobj + +286 0 obj +<< + /Type /StructElem + /S /Strong + /P 285 0 R + /K [44 45] + /Pg 716 0 R +>> +endobj + +287 0 obj +<< + /Type /StructElem + /S /Strong + /P 282 0 R + /K [42] + /Pg 716 0 R +>> +endobj + +288 0 obj +<< + /Type /StructElem + /S /Lbl + /P 280 0 R + /K [41] + /Pg 716 0 R +>> +endobj + +289 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [28 296 0 R 30 294 0 R 32 292 0 R 35 36 290 0 R 40] + /Pg 716 0 R +>> +endobj + +290 0 obj +<< + /Type /StructElem + /S /Formula + /P 289 0 R + /K [291 0 R] +>> +endobj + +291 0 obj +<< + /Type /StructElem + /S /Strong + /P 290 0 R + /K [37 38 39] + /Pg 716 0 R +>> +endobj + +292 0 obj +<< + /Type /StructElem + /S /Formula + /P 289 0 R + /K [293 0 R] +>> +endobj + +293 0 obj +<< + /Type /StructElem + /S /Strong + /P 292 0 R + /K [33 34] + /Pg 716 0 R +>> +endobj + +294 0 obj +<< + /Type /StructElem + /S /Formula + /P 289 0 R + /K [295 0 R] +>> +endobj + +295 0 obj +<< + /Type /StructElem + /S /Strong + /P 294 0 R + /K [31] + /Pg 716 0 R +>> +endobj + +296 0 obj +<< + /Type /StructElem + /S /Formula + /P 289 0 R + /K [297 0 R] +>> +endobj + +297 0 obj +<< + /Type /StructElem + /S /Strong + /P 296 0 R + /K [29] + /Pg 716 0 R +>> +endobj + +298 0 obj +<< + /Type /StructElem + /S /H3 + /P 32 0 R + /T (Gallager) + /K [27] + /Pg 716 0 R +>> +endobj + +299 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [301 0 R 23 300 0 R 25 26] + /Pg 716 0 R +>> +endobj + +300 0 obj +<< + /Type /StructElem + /S /Formula + /P 299 0 R + /K [24] + /Pg 716 0 R +>> +endobj + +301 0 obj +<< + /Type /StructElem + /S /Strong + /P 299 0 R + /K [22] + /Pg 716 0 R +>> +endobj + +302 0 obj +<< + /Type /StructElem + /S /H2 + /P 32 0 R + /T (LDPC constructions) + /K [21] + /Pg 716 0 R +>> +endobj + +303 0 obj +<< + /Type /StructElem + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [308 0 R 304 0 R] +>> +endobj + +304 0 obj +<< + /Type /StructElem + /S /LI + /P 303 0 R + /K [307 0 R 305 0 R] +>> +endobj + +305 0 obj +<< + /Type /StructElem + /S /LBody + /P 304 0 R + /K [1 306 0 R] + /Pg 716 0 R +>> +endobj + +306 0 obj +<< + /Type /StructElem + /S /Formula + /P 305 0 R + /K [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20] + /Pg 716 0 R +>> +endobj + +307 0 obj +<< + /Type /StructElem + /S /Lbl + /P 304 0 R + /K [0] + /Pg 716 0 R +>> +endobj + +308 0 obj +<< + /Type /StructElem + /S /LI + /P 303 0 R + /K [311 0 R 309 0 R] +>> +endobj + +309 0 obj +<< + /Type /StructElem + /S /LBody + /P 308 0 R + /K [230 310 0 R] + /Pg 714 0 R +>> +endobj + +310 0 obj +<< + /Type /StructElem + /S /Formula + /P 309 0 R + /K [231 232 233 234 235 236 237 238 239] + /Pg 714 0 R +>> +endobj + +311 0 obj +<< + /Type /StructElem + /S /Lbl + /P 308 0 R + /K [229] + /Pg 714 0 R +>> +endobj + +312 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [321 0 R 319 0 R 318 0 R 316 0 R 315 0 R 224 314 0 R 226 313 0 R 228] + /Pg 714 0 R +>> +endobj + +313 0 obj +<< + /Type /StructElem + /S /Formula + /P 312 0 R + /K [227] + /Pg 714 0 R +>> +endobj + +314 0 obj +<< + /Type /StructElem + /S /Formula + /P 312 0 R + /K [225] + /Pg 714 0 R +>> +endobj + +315 0 obj +<< + /Type /StructElem + /S /Strong + /P 312 0 R + /K [223] + /Pg 714 0 R +>> +endobj + +316 0 obj +<< + /Type /StructElem + /S /Formula + /P 312 0 R + /K [317 0 R] +>> +endobj + +317 0 obj +<< + /Type /StructElem + /S /Strong + /P 316 0 R + /K [222] + /Pg 714 0 R +>> +endobj + +318 0 obj +<< + /Type /StructElem + /S /Strong + /P 312 0 R + /K [221] + /Pg 714 0 R +>> +endobj + +319 0 obj +<< + /Type /StructElem + /S /Formula + /P 312 0 R + /K [320 0 R] +>> +endobj + +320 0 obj +<< + /Type /StructElem + /S /Strong + /P 319 0 R + /K [220] + /Pg 714 0 R +>> +endobj + +321 0 obj +<< + /Type /StructElem + /S /Strong + /P 312 0 R + /K [219] + /Pg 714 0 R +>> +endobj + +322 0 obj +<< + /Type /StructElem + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [329 0 R 323 0 R] +>> +endobj + +323 0 obj +<< + /Type /StructElem + /S /LI + /P 322 0 R + /K [328 0 R 324 0 R] +>> +endobj + +324 0 obj +<< + /Type /StructElem + /S /LBody + /P 323 0 R + /K [326 0 R 216 325 0 R 218] + /Pg 714 0 R +>> +endobj + +325 0 obj +<< + /Type /StructElem + /S /Formula + /P 324 0 R + /K [217] + /Pg 714 0 R +>> +endobj + +326 0 obj +<< + /Type /StructElem + /S /Formula + /P 324 0 R + /K [327 0 R] +>> +endobj + +327 0 obj +<< + /Type /StructElem + /S /Strong + /P 326 0 R + /K [214 215] + /Pg 714 0 R +>> +endobj + +328 0 obj +<< + /Type /StructElem + /S /Lbl + /P 323 0 R + /K [213] + /Pg 714 0 R +>> +endobj + +329 0 obj +<< + /Type /StructElem + /S /LI + /P 322 0 R + /K [334 0 R 330 0 R] +>> +endobj + +330 0 obj +<< + /Type /StructElem + /S /LBody + /P 329 0 R + /K [332 0 R 210 331 0 R 212] + /Pg 714 0 R +>> +endobj + +331 0 obj +<< + /Type /StructElem + /S /Formula + /P 330 0 R + /K [211] + /Pg 714 0 R +>> +endobj + +332 0 obj +<< + /Type /StructElem + /S /Formula + /P 330 0 R + /K [333 0 R] +>> +endobj + +333 0 obj +<< + /Type /StructElem + /S /Strong + /P 332 0 R + /K [208 209] + /Pg 714 0 R +>> +endobj + +334 0 obj +<< + /Type /StructElem + /S /Lbl + /P 329 0 R + /K [207] + /Pg 714 0 R +>> +endobj + +335 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [341 0 R 193 340 0 R 195 338 0 R 197 198 337 0 R 200 336 0 R 206] + /Pg 714 0 R +>> +endobj + +336 0 obj +<< + /Type /StructElem + /S /Formula + /P 335 0 R + /K [201 202 203 204 205] + /Pg 714 0 R +>> +endobj + +337 0 obj +<< + /Type /StructElem + /S /Strong + /P 335 0 R + /K [199] + /Pg 714 0 R +>> +endobj + +338 0 obj +<< + /Type /StructElem + /S /Formula + /P 335 0 R + /K [339 0 R] +>> +endobj + +339 0 obj +<< + /Type /StructElem + /S /Strong + /P 338 0 R + /K [196] + /Pg 714 0 R +>> +endobj + +340 0 obj +<< + /Type /StructElem + /S /Formula + /P 335 0 R + /K [194] + /Pg 714 0 R +>> +endobj + +341 0 obj +<< + /Type /StructElem + /S /Strong + /P 335 0 R + /K [192] + /Pg 714 0 R +>> +endobj + +342 0 obj +<< + /Type /StructElem + /S /L + /P 32 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [347 0 R 343 0 R] +>> +endobj + +343 0 obj +<< + /Type /StructElem + /S /LI + /P 342 0 R + /K [346 0 R 344 0 R] +>> +endobj + +344 0 obj +<< + /Type /StructElem + /S /LBody + /P 343 0 R + /K [188 345 0 R 191] + /Pg 714 0 R +>> +endobj + +345 0 obj +<< + /Type /StructElem + /S /Formula + /P 344 0 R + /K [189 190] + /Pg 714 0 R +>> +endobj + +346 0 obj +<< + /Type /StructElem + /S /Lbl + /P 343 0 R + /K [187] + /Pg 714 0 R +>> +endobj + +347 0 obj +<< + /Type /StructElem + /S /LI + /P 342 0 R + /K [350 0 R 348 0 R] +>> +endobj + +348 0 obj +<< + /Type /StructElem + /S /LBody + /P 347 0 R + /K [183 349 0 R 186] + /Pg 714 0 R +>> +endobj + +349 0 obj +<< + /Type /StructElem + /S /Formula + /P 348 0 R + /K [184 185] + /Pg 714 0 R +>> +endobj + +350 0 obj +<< + /Type /StructElem + /S /Lbl + /P 347 0 R + /K [182] + /Pg 714 0 R +>> +endobj + +351 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [353 0 R 173 352 0 R 181] + /Pg 714 0 R +>> +endobj + +352 0 obj +<< + /Type /StructElem + /S /Formula + /P 351 0 R + /K [174 175 176 177 178 179 180] + /Pg 714 0 R +>> +endobj + +353 0 obj +<< + /Type /StructElem + /S /Strong + /P 351 0 R + /K [172] + /Pg 714 0 R +>> +endobj + +354 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [357 0 R 168 355 0 R 170 171] + /Pg 714 0 R +>> +endobj + +355 0 obj +<< + /Type /StructElem + /S /Formula + /P 354 0 R + /K [356 0 R] +>> +endobj + +356 0 obj +<< + /Type /StructElem + /S /Strong + /P 355 0 R + /K [169] + /Pg 714 0 R +>> +endobj + +357 0 obj +<< + /Type /StructElem + /S /Strong + /P 354 0 R + /K [167] + /Pg 714 0 R +>> +endobj + +358 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [363 0 R 161 361 0 R 163 359 0 R 165 166] + /Pg 714 0 R +>> +endobj + +359 0 obj +<< + /Type /StructElem + /S /Formula + /P 358 0 R + /K [360 0 R] +>> +endobj + +360 0 obj +<< + /Type /StructElem + /S /Strong + /P 359 0 R + /K [164] + /Pg 714 0 R +>> +endobj + +361 0 obj +<< + /Type /StructElem + /S /Formula + /P 358 0 R + /K [362 0 R] +>> +endobj + +362 0 obj +<< + /Type /StructElem + /S /Strong + /P 361 0 R + /K [162] + /Pg 714 0 R +>> +endobj + +363 0 obj +<< + /Type /StructElem + /S /Strong + /P 358 0 R + /K [160] + /Pg 714 0 R +>> +endobj + +364 0 obj +<< + /Type /StructElem + /S /H2 + /P 32 0 R + /T + /K [159] + /Pg 714 0 R +>> +endobj + +365 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [372 0 R 146 371 0 R 148 369 0 R 150 368 0 R 152 367 0 R 154 366 0 R] + /Pg 714 0 R +>> +endobj + +366 0 obj +<< + /Type /StructElem + /S /Formula + /P 365 0 R + /K [155 156 157 158] + /Pg 714 0 R +>> +endobj + +367 0 obj +<< + /Type /StructElem + /S /Formula + /P 365 0 R + /K [153] + /Pg 714 0 R +>> +endobj + +368 0 obj +<< + /Type /StructElem + /S /Strong + /P 365 0 R + /K [151] + /Pg 714 0 R +>> +endobj + +369 0 obj +<< + /Type /StructElem + /S /Formula + /P 365 0 R + /K [370 0 R] +>> +endobj + +370 0 obj +<< + /Type /StructElem + /S /Strong + /P 369 0 R + /K [149] + /Pg 714 0 R +>> +endobj + +371 0 obj +<< + /Type /StructElem + /S /Em + /P 365 0 R + /K [147] + /Pg 714 0 R +>> +endobj + +372 0 obj +<< + /Type /StructElem + /S /Em + /P 365 0 R + /K [145] + /Pg 714 0 R +>> +endobj + +373 0 obj +<< + /Type /StructElem + /S /H1 + /P 32 0 R + /T (Low-density parity-check codes (LDPC) ) + /K [143 374 0 R] + /Pg 714 0 R +>> +endobj + +374 0 obj +<< + /Type /StructElem + /S /Link + /P 373 0 R + /K [144 << + /Type /OBJR + /Pg 714 0 R + /Obj 713 0 R + >>] + /Pg 714 0 R +>> +endobj + +375 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [139 377 0 R 141 376 0 R] + /Pg 714 0 R +>> +endobj + +376 0 obj +<< + /Type /StructElem + /S /Link + /P 375 0 R + /K [142 << + /Type /OBJR + /Pg 714 0 R + /Obj 712 0 R + >>] + /Pg 714 0 R +>> +endobj + +377 0 obj +<< + /Type /StructElem + /S /Link + /P 375 0 R + /K [140 << + /Type /OBJR + /Pg 714 0 R + /Obj 711 0 R + >>] + /Pg 714 0 R +>> +endobj + +378 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [120 383 0 R 128 381 0 R 130 380 0 R 135 379 0 R 138] + /Pg 714 0 R +>> +endobj + +379 0 obj +<< + /Type /StructElem + /S /Em + /P 378 0 R + /K [136 137] + /Pg 714 0 R +>> +endobj + +380 0 obj +<< + /Type /StructElem + /S /Formula + /P 378 0 R + /K [131 132 133 134] + /Pg 714 0 R +>> +endobj + +381 0 obj +<< + /Type /StructElem + /S /Formula + /P 378 0 R + /K [382 0 R] +>> +endobj + +382 0 obj +<< + /Type /StructElem + /S /Strong + /P 381 0 R + /K [129] + /Pg 714 0 R +>> +endobj + +383 0 obj +<< + /Type /StructElem + /S /Formula + /P 378 0 R + /K [121 122 123 124 125 126 127] + /Pg 714 0 R +>> +endobj + +384 0 obj +<< + /Type /StructElem + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [112 113 114 115 116 117 118 119] + /Pg 714 0 R +>> +endobj + +385 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [75 391 0 R 80 390 0 R 82 389 0 R 84 388 0 R 103 387 0 R 105 386 0 R 111] + /Pg 714 0 R +>> +endobj + +386 0 obj +<< + /Type /StructElem + /S /Formula + /P 385 0 R + /K [106 107 108 109 110] + /Pg 714 0 R +>> +endobj + +387 0 obj +<< + /Type /StructElem + /S /Em + /P 385 0 R + /K [104] + /Pg 714 0 R +>> +endobj + +388 0 obj +<< + /Type /StructElem + /S /Formula + /P 385 0 R + /K [85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102] + /Pg 714 0 R +>> +endobj + +389 0 obj +<< + /Type /StructElem + /S /Em + /P 385 0 R + /K [83] + /Pg 714 0 R +>> +endobj + +390 0 obj +<< + /Type /StructElem + /S /Formula + /P 385 0 R + /K [81] + /Pg 714 0 R +>> +endobj + +391 0 obj +<< + /Type /StructElem + /S /Formula + /P 385 0 R + /K [76 77 78 79] + /Pg 714 0 R +>> +endobj + +392 0 obj +<< + /Type /StructElem + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [67 68 69 70 71 72 73 74] + /Pg 714 0 R +>> +endobj + +393 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [63 64 394 0 R 66] + /Pg 714 0 R +>> +endobj + +394 0 obj +<< + /Type /StructElem + /S /Formula + /P 393 0 R + /K [65] + /Pg 714 0 R +>> +endobj + +395 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [60 396 0 R 62] + /Pg 714 0 R +>> +endobj + +396 0 obj +<< + /Type /StructElem + /S /Formula + /P 395 0 R + /K [397 0 R] +>> +endobj + +397 0 obj +<< + /Type /StructElem + /S /Strong + /P 396 0 R + /K [61] + /Pg 714 0 R +>> +endobj + +398 0 obj +<< + /Type /StructElem + /S /Formula + /P 32 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [55 56 57 58 59] + /Pg 714 0 R +>> +endobj + +399 0 obj +<< + /Type /StructElem + /S /P + /P 32 0 R + /K [49 50 401 0 R 52 400 0 R 54] + /Pg 714 0 R +>> +endobj + +400 0 obj +<< + /Type /StructElem + /S /Em + /P 399 0 R + /K [53] + /Pg 714 0 R +>> +endobj + +401 0 obj +<< + /Type /StructElem + /S /Formula + /P 399 0 R + /K [402 0 R] +>> +endobj + 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c25649c..554f742 100644 --- a/Notes/notes.typ +++ b/Notes/notes.typ @@ -252,8 +252,264 @@ Pas de retransmissions. #pad(left: 1cm)[ + _Block codes_ définis par une matrice _parity-check_ *$H$* très *creuse* (beaucoup de 0).\ + $=>$ Décodage en $cal(O)(n)$ + + == Défintions et Propriétés + + *Création* : On construit d'abord la matrice creuse *$H$*, puis on en déduit la matrice génératrice *$G$* (contrairement aux codes classiques).\ + + *Décodage* : Décodage itératif basé sur une représentation graphique de *$H$* (Graphe de Tanner) (au lieu du décodage ML habituel). + + *Régularité* : Un code LDPC est dit $(w_c, w_r)$-régulier si : + - Chaque bit de code appartient à $w_c$ équations de parité. + - Chaque équation de parité contient $w_r$ bits de code. + + *Irréguliers* + Le nombre de $1$ varie selon les lignes et les colonnes de *$H$*.\ + On définit la *distribution des degrés* $(v, h)$ : + - *$v_i$* : la fraction des colonnes (bits) ayant un poids de $i$. + - *$h_i$* : la fraction des lignes (équations de parité) ayant un poids de $i$. + + #pad(left: 1cm)[ + *Propriété : nombre total de $1$ dans $H$ :* \ + Pour une matrice de $m$ lignes et $n$ colonnes : + - Code régulier : $m dot w_r = n dot w_c$ + - Code irrégulier : $m sum_i (h_i dot i) = n sum_i (v_i dot i)$ + ] + + == LDPC constructions + + *Principe * : On part d'une matrice remplie de zéros et on y place un petit nombre de $1$ pour respecter la distribution de degrés. + + === Gallager + + Il faut imaginer que la matrice *$H$* (de *$m$* lignes) est découpée horizontalement en *$w_c$* "bandes" de même taille (chacune a donc *$m / w_c$* lignes). + + - *Création de la 1ère bande* : On place *$w_r$* $1$ consécutifs sur chaque ligne. À chaque fois qu'on descend d'une ligne, on décale ces $1$ vers la droite. + + - *Création des autres bandes* : On prend simplement la 1ère bande et on mélange aléatoirement l'ordre de ses colonnes. + + - *Résultat* : Comme on a superposé *$w_c$* bandes, et que dans chaque bande il y a exactement un $1$ par colonne, on est certain que chaque colonne de *$H$* aura exactement un poids de *$w_c$*. + + - Exemple : + + + #pad(left: 1cm)[ + Code régulier avec $n = 12$ colonnes, $w_c = 3$ et $w_r = 4$.\ + + *$H$* aura $m = (12 dot 3) / 4 = 9$ lignes.\ + + On divise ces 9 lignes en $w_c = 3$ blocs horizontaux de 3 lignes. + + *Bloc 1* (Escalier) : + $ + B_1 = mat( + 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0; + 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0; + 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1; + ) + $ + + *Bloc 2* (Permutation aléatoire des colonnes du Bloc 1) : + $ + B_2 = mat( + 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0; + 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1; + 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0 + ) + $ + + *Bloc 3* (Permutation aléatoire des colonnes du Bloc 1) : + $ + B_3 = mat( + 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0; + 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1; + 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0 + ) + $ + + Et donc + + $ + H = mat(B_1; B_2; B_3; row-gap: #0.75em) + $ + + Finalement dans n'importe quel bloc en regardant une colonne il n'y à qu'un $1$. + ] + + === MacKay et Neal + + - La matrice *$H$* est remplie une colonne à la fois, de gauche à droite. + - Les $1$ sont placés aléatoirement dans les lignes qui ne sont pas encore pleines. + - Si à un moment, il y a plus de lignes incomplètes que de colonnes restantes à ajouter, la distribution des lignes ne sera pas exacte. On peut alors revenir de quelques colonnes en arrière ou recommencer le processus jusqu'à obtenir le bon résultat. + + - Exemple : + + #pad(left: 1cm)[ + Code régulier $(3,4)$ de longueur $12$.\ + Quand on ajoute la $11$ème colonne, les lignes non remplies étaient les lignes $2, 4, 5, 6$ et $9$.\ + L'algorithme a choisi d'y placer un $1$ sur les lignes $2, 4$ et $6$. + + $ + H = mat( + 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0; + 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, bold(1), 0; + 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1; + 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, bold(1), 1; + 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0; + 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, bold(1), 1; + 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0; + 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0; + 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1 + ) + $ + ] + + + === Codes Repeat-Accumulate (RA) + + - Les *$m$* dernières colonnes de la matrice *$H$* ont toutes un poids de $2$ et forment un motif "en escalier". + - Encodage rapide. + + - Exemple : + + #pad(left: 1cm)[ + Code RA de longueur $12$ avec un ratio de $1/4$. + + $ + H = mat( + 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; + 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0; + 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0; + 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0; + 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0; + 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0; + 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0; + 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0; + 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1 + ) + $ + + Les trois premières colonnes de *$H$* correspondent aux bits du message initial.\ + Les bits de parité (à partir de la 4ème colonne) se calculent ensuite en cascade :\ + $c_4 = c_1$\ + $c_5 = c_4 plus.o c_1$\ + $c_6 = c_5 plus.o c_2$\ + ...\ + Chaque bit de parité peut être calculé un par un en utilisant seulement les bits du message et le bit de parité juste avant lui. + ] + + == Graphe de Tanner + + Deux ensembles de sommets : + - $G = (X union.sq Y, A)$ biparti. + - $X = {text("bits du codeword")}$ et $|X| = n$ + - $Y = {text("équations de parité")}$ (_check-nodes_) et $|Y| = m$ + - Soit $x in X, y in Y$, alors il existe $(x, y) in A$ si le bit est inclu dans l'équation de parité corerspondante. + - $|A| =$ nombre de $1$ dans la matrice de parité. + + *Exemple :* + Pour la matrice _parity-check_ suivante (régulière $w_c=2$, $w_r=3$) + $ + H = mat( + 1, 1, 0, 1, 0, 0; + 0, 1, 1, 0, 1, 0; + 1, 0, 0, 0, 1, 1; + 0, 0, 1, 1, 0, 1 + ) + $ + + Le graphe de Tanner correspondant + + #align(center)[ + #cetz.canvas(length: 1.2cm, { + import cetz.draw: * + + content((0, 6.5), [*Noeuds de bits* \ (Variables $s_i$)], anchor: "south") + content( + (4, 6.5), + [*Noeuds de parité* \ (Contraintes $f_j$)], + anchor: "south", + ) + + for i in range(1, 7) { + circle((0, 6.5 - i), radius: 0.3, name: "b" + str(i), fill: white) + content("b" + str(i), [$s_#i$]) + } + + for j in range(1, 5) { + let y = 6.5 - j * 1.2 + rect( + (4 - 0.3, y - 0.3), + (4 + 0.3, y + 0.3), + name: "f" + str(j), + fill: rgb("e0e0e0"), + ) + content("f" + str(j), [$f_#j$]) + } + + line("b1", "f1", stroke: (paint: gray, thickness: 2pt)) + line("b2", "f1", stroke: (paint: gray, thickness: 2pt)) + line("b4", "f1") + + line("b2", "f2", stroke: (paint: gray, thickness: 2pt)) + line("b3", "f2") + line("b5", "f2", stroke: (paint: gray, thickness: 2pt)) + + line("b1", "f3", stroke: (paint: gray, thickness: 2pt)) + line("b5", "f3", stroke: (paint: gray, thickness: 2pt)) + line("b6", "f3") + + line("b3", "f4") + line("b4", "f4") + line("b6", "f4") + }) + ] + + + - *_Girth_* : La taille du plus petit cycle présent dans tout le graphe. (biparti $=>$ cycle de taille pair donc plus petit cycle de taille $4$). + + - *Exemple :* + Dans notre $H$ le plus petit cycle est de taille 6 en gris. + $c = s_1 -> f_1 -> s_2 -> f_2 -> s_5 -> f_3 -> s_1$. + + On veut éviter les cycles courts, il existe un algorithme de Mackay Neal qui permet de d'éviter les $4$-cycles. algorithme @johnson p14. D'autre methode vont être vu (algébriques) pour des court codes. + + + == Encodage + + Matrice _parity-check_ + $ H = [A, I_(n-k)] $ avec $A in M_((n-k) times k)(ZZ\/2ZZ)$ on trouve alors $G$ par réducation de Gausse-Jordan sur $H$. + + $ + G = [I_k, A^T] + $ + + 1. Mettre $H$ sous forme échelonée puis sous forme ligne-cheloné réduite puis sous forme standard (avec des permutation de colonnes) puis construire $G$ voir @johnson p15. Cette méthode ne rend pas la matrice creuse donc complexité nul. + 2. Transformer $H$ en matrice triangulaire inférieur aproximative. Voir @johnson p17. + + + == Décodage + + Voir les exemple du papier @johnson p21. ] +#pagebreak() + += QC-LDPC + += Code Rust +#pad(left: 1cm)[ + - Voir la strucutre du projet en amont + - Implémentation des codes ldpc (avec un peu toutes les méthodes possible pour faire des test etc) + - Implémentation avec $H$ aléatoire (donc G assez dense et $O(n^2)$) + - Implémenter le "repeat-accumulate" (RA) + - Et faire un export pour visualiser les matrice et le graphe dans un fichier typst par exemple ou autre + - Implementation en rust https://github.com/daniestevez/ldpc-toolbox (lire le code pour voir) + - Voir SIMD (`std::simd`) pour le calcul de LLR sur plusieur bits en même temps. + - Voir le multi-threadage possible (après l'implementation) +] #pagebreak() #bibliography("sources.yml", style: "ieee")