Rate Maximization for Suspicious Multicast Communication Networks with Full-Duplex Proactive Monitoring

<div>The maximal achievable average eavesdropping rate <svg height="17.2476pt" id="M25" style="vertical-align:-6.1814pt" version="1.1" viewbox="-0.0498162 -11.0662 18.9299 17.2476" width="18.9299pt" 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="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.282,-5.741)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.823,-5.741)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.491,-5.741)"><path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.434,3.784)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.264,3.784)"><path d="M478 437H300V411C357 404 363 393 347 345C325 280 293 190 258 107C229 178 188 284 163 354C147 397 149 405 203 411V437H-2V411C52 403 59 396 82 339C130 222 176 109 220 -11H248C304 138 356 261 390 336C417 395 425 404 478 411V437Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.478,3.784)"><path d="M463 437C426 431 375 425 327 422C297 440 264 449 231 449H230C153 449 51 396 51 283C51 215 94 168 139 149C123 129 91 103 51 88C50 78 53 60 62 46C75 25 100 2 136 -9C112 -28 73 -59 53 -79C38 -94 29 -113 29 -135C30 -192 91 -257 203 -257C336 -257 452 -160 452 -59C452 39 371 59 309 59C275 59 240 58 203 58C158 58 140 77 140 96C140 110 157 129 170 138C186 135 205 133 221 133C306 133 396 185 396 293C396 328 384 360 366 381L423 378C439 387 459 413 468 429L463 437ZM219 418C277 418 314 362 314 284C314 205 275 166 231 165C176 165 137 221 137 299C137 376 177 418 219 418ZM241 -11C285 -11 314 -14 339 -24C367 -36 384 -61 384 -95C384 -157 335 -206 240 -206C166 -206 108 -165 108 -110C108 -82 128 -54 154 -32C172 -17 195 -11 241 -11Z"></path></g></svg> at the legitimate monitor versus the RSI level <i>K</i>.</div>

Mobile Information Systems

fig2

Figure 2

Figure 2: Rate Maximization for Suspicious Multicast Communication Networks with Full-Duplex Proactive Monitoring 