A Lightweight Modulation Classification Network Resisting White Box Gradient Attacks

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left" colspan="3">Multiplication of 1-bit weight</td><td class="align_center" colspan="3">Equivalent computer operation</td></tr><tr class="thead"><td class="align_left"><span style="width: 21.0725ptpx;"><svg height="11.6151pt" id="M21" style="vertical-align:-3.18146pt" version="1.1" viewbox="-0.0498162 -8.43364 21.0725 11.6151" width="21.0725pt" 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="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.775,3.132)"><path d="M823 0V32C771 40 767 43 767 100V293C767 395 719 454 632 454C603 454 576 441 554 426C530 409 507 394 482 376C464 421 424 454 368 454C339 454 312 442 281 422C259 409 240 395 218 379V456C157 439 89 425 42 418V389C89 382 93 373 93 315V105C93 42 88 39 30 32V0H265V32C227 38 220 43 220 100V344C248 366 273 376 297 376C334 376 366 354 366 282V100C366 41 362 38 315 32V0H546V32C501 38 494 43 494 100V302C494 317 493 331 492 342C524 369 549 376 569 376C601 376 639 359 639 277V105C639 42 632 38 588 32V0H823Z"></path></g></svg></span></td><td class="align_center"><span style="width: 18.5424ptpx;"><svg height="11.6151pt" id="M22" style="vertical-align:-3.18146pt" version="1.1" viewbox="-0.0498162 -8.43364 18.5424 11.6151" width="18.5424pt" 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="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.775,3.132)"><path d="M549 0V32C497 40 491 42 491 105V294C491 394 441 454 360 454C331 454 312 445 282 426C260 412 240 396 220 383V456C161 439 95 425 39 418V390C87 380 92 377 92 317V109C92 42 88 41 26 32V0H267V32C225 38 220 42 220 104V346C246 366 268 377 294 377C330 377 363 355 363 283V113C363 42 358 38 316 32V0H549Z"></path></g></svg></span></td><td class="align_center"><span style="width: 52.9859ptpx;"><svg height="11.6151pt" id="M23" style="vertical-align:-3.18146pt" version="1.1" viewbox="-0.0498162 -8.43364 52.9859 11.6151" width="52.9859pt" 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="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.775,3.132)"><path d="M823 0V32C771 40 767 43 767 100V293C767 395 719 454 632 454C603 454 576 441 554 426C530 409 507 394 482 376C464 421 424 454 368 454C339 454 312 442 281 422C259 409 240 395 218 379V456C157 439 89 425 42 418V389C89 382 93 373 93 315V105C93 42 88 39 30 32V0H265V32C227 38 220 43 220 100V344C248 366 273 376 297 376C334 376 366 354 366 282V100C366 41 362 38 315 32V0H546V32C501 38 494 43 494 100V302C494 317 493 331 492 342C524 369 549 376 569 376C601 376 639 359 639 277V105C639 42 632 38 588 32V0H823Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.878,0)"><path d="M528 54L331 254L528 455L492 493L294 291L96 493L60 455L257 254L60 54L96 16L294 217L492 16L528 54Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.415,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,47.19,3.132)"><path d="M549 0V32C497 40 491 42 491 105V294C491 394 441 454 360 454C331 454 312 445 282 426C260 412 240 396 220 383V456C161 439 95 425 39 418V390C87 380 92 377 92 317V109C92 42 88 41 26 32V0H267V32C225 38 220 42 220 104V346C246 366 268 377 294 377C330 377 363 355 363 283V113C363 42 358 38 316 32V0H549Z"></path></g></svg></span></td><td class="align_center"><span style="width: 15.3102ptpx;"><svg height="11.927pt" id="M24" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 15.3102 11.927" width="15.3102pt" 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="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"></path></g></svg></span></td><td class="align_center"><span style="width: 12.6339ptpx;"><svg height="11.927pt" id="M25" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 12.6339 11.927" width="12.6339pt" 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="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g></svg></span></td><td class="align_center"><span style="width: 41.3151ptpx;"><svg height="11.927pt" id="M26" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 41.3151 11.927" width="41.3151pt" 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="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.089,0)"><path d="M573 255C573 407 448 530 294 530S15 407 15 255S140 -20 294 -20S573 103 573 255ZM521 255C521 127 419 24 294 24S67 127 67 255S169 486 294 486S521 383 521 255ZM350 255C350 288 326 313 294 313S238 288 238 255C238 220 262 197 294 197S350 220 350 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.625,0)"><path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.957,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center">1</td><td class="align_center">1</td><td class="align_center">1</td><td class="align_center">1</td><td class="align_center">1</td></tr><tr><td class="align_left">1</td><td class="align_center">−1</td><td class="align_center">−1</td><td class="align_center">1</td><td class="align_center">0</td><td class="align_center">0</td></tr><tr><td class="align_left">−1</td><td class="align_center">1</td><td class="align_center">−1</td><td class="align_center">0</td><td class="align_center">1</td><td class="align_center">0</td></tr><tr><td class="align_left">−1</td><td class="align_center">−1</td><td class="align_center">1</td><td class="align_center">0</td><td class="align_center">0</td><td class="align_center">1</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The truth value table of the multiplication of 1-bit weight and the computer variable operation.</div>

Security and Communication Networks

tab1

Table 1

Table 1: A Lightweight Modulation Classification Network Resisting White Box Gradient Attacks 