Network Coding for Backhaul Offloading in D2D Cooperative Fog Data Networks

<div>A visualization of the theoretical graph model proposed for system model shown in Figure <a href="../fig1/">1</a>. The figure shows coding opportunities represented by edges, transmission conflicts represented in subgraphs <span class="nowrap"><svg height="14.5433pt" id="M93" style="vertical-align:-5.528979pt" version="1.1" viewbox="-0.0498162 -9.01432 17.6916 14.5433" width="17.6916pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M771 669C722 624 660 598 616 598C593 598 565 610 530 629C460 664 429 678 388 678C284 678 211 602 211 527C211 453 270 401 350 401C418 401 468 443 501 508L483 517C450 464 405 431 352 431C288 431 252 473 252 525S306 626 370 626C398 626 435 612 472 592C525 563 556 548 596 548C607 548 623 550 632 553L633 550C510 448 474 360 391 210C314 77 264 16 181 16C121 16 79 48 75 79H77C84 68 97 66 106 66C134 66 150 90 150 115C150 144 130 165 103 165C63 165 40 130 40 91C40 38 96 -15 183 -15C301 -15 418 42 546 321C553 310 560 306 580 306C619 306 620 284 620 275C620 211 535 149 535 70C535 21 581 -12 628 -12C689 -12 755 40 830 132L811 147C736 61 680 18 642 18C621 18 610 29 610 52C610 93 686 163 686 232C686 263 673 286 638 321V323C721 350 782 402 849 522C876 570 898 630 916 646H917C918 613 943 601 962 601C990 601 1004 621 1004 646C1004 674 981 687 953 687C900 687 834 608 741 471C684 385 650 354 609 346C596 358 582 360 567 360C627 465 677 573 784 653L771 669Z" id="g198-12"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.117,3.132)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path></g></svg>,</span> and limitation of one transmission per user represented in subgraph <span class="nowrap"><svg height="12.3054pt" id="M94" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -9.01432 17.3902 12.3054" width="17.3902pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M608 643C551 682 486 687 443 687C299 687 188 608 188 504C188 361 341 312 465 312C483 312 501 313 518 315C454 195 366 93 314 59C255 82 201 109 141 109C73 109 33 83 33 52C33 13 76 -9 159 -9C218 -9 267 -1 314 15C354 0 402 -15 478 -15C575 -15 671 36 759 141L740 155C657 63 571 16 475 16C448 16 411 26 372 39C458 74 565 199 627 333C806 381 931 499 931 587C931 634 908 669 848 669C767 669 671 582 620 506C591 462 569 411 534 347C503 343 490 342 471 342C330 342 229 399 229 500C229 603 346 657 451 657C486 657 540 657 596 624L608 643ZM890 588C890 519 822 457 747 414C712 395 678 378 643 369C683 484 760 632 841 632C873 632 890 615 890 588ZM266 35C235 24 200 21 161 21C103 21 74 32 74 54C74 75 122 79 141 79C172 79 209 69 266 36V35Z" id="g198-13"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.298,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path></g></svg>.</span></div>

Wireless Communications and Mobile Computing

fig2

Figure 2

Figure 2: Network Coding for Backhaul Offloading in D2D Cooperative Fog Data Networks 