Achievable Rates of Gaussian Interference Channel with Multi-Layer Rate-Splitting and Successive Simple Decoding

<div>Illustrations of the increasing/decreasing property of <svg height="19.2968pt" id="M242" style="vertical-align:-5.2601pt" version="1.1" viewbox="-0.0498162 -14.0367 36.0599 19.2968" width="36.0599pt" 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="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.488,-7.52)"><path d="M713 650H37V617C122 611 130 604 130 523V127C130 48 121 39 41 33V0H305V33C226 39 217 47 217 127V577C217 605 221 609 251 609H500C528 609 534 607 534 579V127C534 49 526 39 439 33V0H711V33C629 39 621 47 621 127V523C621 602 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95 2 122 6L160 166C192 225 325 384 381 384C403 384 405 375 390 295C371 194 348 91 323 -6L327 -12C347 -6 379 3 407 6C417 61 432 125 445 170C479 232 607 384 659 384C679 384 690 370 677 322L616 88C600 26 608 -12 640 -12C667 -12 736 23 798 93Z" id="g176-110"></path></g><g transform="matrix(.0091,0,0,-0.0091,21.589,-7.52)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.746,-7.52)"><path d="M297 -163V-131C189 -122 187 -119 187 -41V582C187 660 190 663 297 672V704H122V-163H297Z" id="g50-92"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.004,-7.52)"><path d="M567 167L534 181C505 122 482 94 454 70C428 46 385 42 330 42C288 42 248 44 235 55C216 70 213 91 220 130L295 528C310 609 314 611 401 618L409 650H140L131 618C222 611 224 609 209 528L133 126C118 47 108 41 25 33L18 0H497C514 33 554 126 567 167Z" id="g50-77"></path></g><g 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For example, if <span class="nowrap"><svg height="8.8423pt" id="M244" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 24.8487 8.8423" width="24.8487pt" 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="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z" id="g113-106"></path></g><g transform="matrix(.013,0,0,-0.013,7.181,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,18.444,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g></svg>,</span> the decoding orders of the four cases are <span class="nowrap"><svg height="12.9866pt" id="M245" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 21.2891 12.9866" width="21.2891pt" 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="M703 650H36V622C118 616 126 607 126 526V124C126 45 117 34 40 28V0H297V28C219 34 211 44 211 124V581C211 609 214 613 245 613H494C521 613 527 610 527 583V124C527 45 519 34 434 28V0H700V28C620 34 612 44 612 124V526C612 605 620 616 703 622V650Z" id="g113-145"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.594,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.026,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 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131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg>,</span> and <span class="nowrap"><svg height="12.9866pt" id="M248" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 21.2891 12.9866" width="21.2891pt" 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="M703 650H36V622C118 616 126 607 126 526V124C126 45 117 34 40 28V0H297V28C219 34 211 44 211 124V581C211 609 214 613 245 613H494C521 613 527 610 527 583V124C527 45 519 34 434 28V0H700V28C620 34 612 44 612 124V526C612 605 620 616 703 622V650Z" id="g113-145"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.594,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 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Wireless Communications and Mobile Computing

fig4

Figure 4

Figure 4: Achievable Rates of Gaussian Interference Channel with Multi-Layer Rate-Splitting and Successive Simple Decoding 