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Triangular network coding

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In TNC, coding is performed in two stages. First redundant "0" bits are added at the head and tail of each packet such that all packets are of uniform bit length. Then the packets are
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Qureshi, Jalaluddin; Foh, Chuan Heng; Cai, Jianfei (2012). "Optimal solution for the index coding problem using network coding over GF(2)".
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alleviates the concern of high computational complexity, coding over GF(2) comes at the tradeoff cost of degrading throughput performance.
546: 36:. Previously, packet coding for network coding was done using linear network coding (LNC). The drawback of LNC over large 127:
is the total number of data packets being encoded in a coded packet) without degrading the throughput performance, with
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2012 9th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks (SECON)
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The main contribution of triangular network coding is to reduce the worst-case decoding computational complexity of
229:, bit-by-bit. The "0" bits are added in such a way that these redundant "0" bits added to each packet generate a 536: 531: 498: 455:
J. B. Fraleigh, and R. A. Beauregard, Linear Algebra. Chapter 10, Addison-Wesley Publishing Company, 1995.
372: 237: 188: 177: 478: 398: 362: 141: 388: 307: 247: 230: 176:. It has been further shown that triangular based fountain code can even outperform optimized 90: 54: 433: 380: 138:
to achieve near-optimal performance with encoding and decoding computational complexity of
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is the number of packets, can be bypassed. The receiver now only needs to perform
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In essence, the TNC decoding process, like the LNC decoding process involves
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Qureshi, Jalaluddin; Foh, Chuan Heng (August 2023).
332: 292: 272: 168: 115: 79: 40:is that it resulted in high encoding and decoding 415: 413: 192:An example of coding four packets using TNC. Bit 131:comparable to that of optimal coding schemes. 506: 33: 8: 451: 449: 217:bits. The resulting coded packet has length 213:packet. Each packet has original length of 513: 499: 134:Triangular code has also been proposed as 44:. While linear encoding and decoding over 437: 366: 321: 309: 285: 261: 249: 143: 104: 92: 68: 56: 32:based packet coding scheme introduced by 187: 349: 7: 467: 465: 304:with worst-case complexity given as 426:Digital Communications and Networks 14: 469: 327: 314: 267: 254: 163: 148: 110: 97: 74: 61: 1: 34:Qureshi, Foh & Cai (2012) 485:. You can help Knowledge by 563: 464: 439:10.1016/j.dcan.2022.12.006 385:10.1109/SECON.2012.6275780 169:{\displaystyle O(n\log n)} 22:triangular network coding 547:Telecommunications stubs 477:This article related to 333:{\displaystyle O(n^{2})} 273:{\displaystyle O(n^{3})} 116:{\displaystyle O(n^{2})} 80:{\displaystyle O(n^{3})} 42:computational complexity 340:for each bit location. 334: 294: 274: 222: 170: 117: 81: 335: 295: 275: 205:∈ {0,1} is the 191: 171: 118: 82: 361:. pp. 134–142. 308: 284: 248: 238:Gaussian elimination 142: 91: 55: 377:2012arXiv1209.6539Q 244:with complexity of 184:Coding and decoding 178:Luby transform code 542:Information theory 479:telecommunications 330: 302:back-substitution, 290: 270: 242:triangularization, 231:triangular pattern 223: 166: 113: 77: 28:) is a non-linear 494: 493: 394:978-1-4673-1905-8 293:{\displaystyle n} 554: 515: 508: 501: 473: 466: 456: 453: 444: 443: 441: 417: 408: 406: 370: 354: 339: 337: 336: 331: 326: 325: 299: 297: 296: 291: 279: 277: 276: 271: 266: 265: 175: 173: 172: 167: 122: 120: 119: 114: 109: 108: 86: 84: 83: 78: 73: 72: 562: 561: 557: 556: 555: 553: 552: 551: 522: 521: 520: 519: 462: 460: 459: 454: 447: 419: 418: 411: 395: 356: 355: 351: 346: 317: 306: 305: 282: 281: 257: 246: 245: 204: 186: 140: 139: 100: 89: 88: 64: 53: 52: 12: 11: 5: 560: 558: 550: 549: 544: 539: 534: 524: 523: 518: 517: 510: 503: 495: 492: 491: 474: 458: 457: 445: 432:(4): 869–878. 409: 393: 348: 347: 345: 342: 329: 324: 320: 316: 313: 289: 269: 264: 260: 256: 253: 196: 185: 182: 165: 162: 159: 156: 153: 150: 147: 112: 107: 103: 99: 96: 76: 71: 67: 63: 60: 30:network coding 13: 10: 9: 6: 4: 3: 2: 559: 548: 545: 543: 540: 538: 537:Finite fields 535: 533: 532:Coding theory 530: 529: 527: 516: 511: 509: 504: 502: 497: 496: 490: 488: 484: 480: 475: 472: 468: 463: 452: 450: 446: 440: 435: 431: 427: 423: 416: 414: 410: 404: 400: 396: 390: 386: 382: 378: 374: 369: 364: 360: 353: 350: 343: 341: 322: 318: 311: 303: 287: 262: 258: 251: 243: 239: 234: 232: 228: 220: 216: 212: 208: 203: 199: 195: 190: 183: 181: 179: 160: 157: 154: 151: 145: 137: 136:Fountain code 132: 130: 126: 105: 101: 94: 69: 65: 58: 49: 47: 43: 39: 35: 31: 27: 23: 19: 18:coding theory 487:expanding it 476: 461: 429: 425: 358: 352: 301: 241: 235: 224: 218: 214: 210: 206: 201: 197: 193: 133: 124: 50: 38:finite field 25: 21: 15: 209:bit of the 526:Categories 344:References 368:1209.6539 227:XOR coded 158:⁡ 129:code rate 280:, where 403:8977891 373:Bibcode 123:(where 401:  391:  481:is a 399:S2CID 363:arXiv 46:GF(2) 483:stub 389:ISBN 434:doi 381:doi 155:log 87:to 26:TNC 16:In 528:: 448:^ 428:. 424:. 412:^ 397:. 387:. 379:. 371:. 233:. 180:. 20:, 514:e 507:t 500:v 489:. 442:. 436:: 430:9 407:. 405:. 383:: 375:: 365:: 328:) 323:2 319:n 315:( 312:O 288:n 268:) 263:3 259:n 255:( 252:O 219:B 215:B 211:k 207:i 202:k 200:, 198:i 194:b 164:) 161:n 152:n 149:( 146:O 125:n 111:) 106:2 102:n 98:( 95:O 75:) 70:3 66:n 62:( 59:O 24:(

Index

coding theory
network coding
Qureshi, Foh & Cai (2012)
finite field
computational complexity
GF(2)
code rate
Fountain code
Luby transform code

XOR coded
triangular pattern
Gaussian elimination
arXiv
1209.6539
Bibcode
2012arXiv1209.6539Q
doi
10.1109/SECON.2012.6275780
ISBN
978-1-4673-1905-8
S2CID
8977891


"Triangular code: Near-optimal linear time fountain code"
doi
10.1016/j.dcan.2022.12.006

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