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class="body-wrapper"><div id="l_main" class=""><article itemscope="" itemtype="http://schema.org/Article" class="article post white-box reveal md shadow floatable blur article-type-docs" id="docs" itemprop="blogPost"><link itemprop="mainEntityOfPage" href="https://blog.mhuig.top/notes/datacom/4"><span hidden="" itemprop="publisher" itemscope="" itemtype="http://schema.org/Organization"><meta itemprop="name" content="Magicland"></span><span hidden="" itemprop="post" itemscope="" itemtype="http://schema.org/CreativeWork"><meta itemprop="name" content="以太网帧结构"><meta itemprop="description" content="本文解析以太网技术核心要素，涵盖Ethernet_II与IEEE 802.3帧格式（含目的/源MAC地址、类型字段及帧校验序列），MAC地址三类通信模式（单播一对一、组播分组内、广播全网）。详解透明传输机制（零比特填充防控制信息误解）、CRC循环冗余码检错技术及流量控制协议（停止等待/滑动窗口），附后退N帧与选择重传协议的可靠传输实现方式。"></span><span hidden=""><meta itemprop="image" content="/lib/favicon/android-chrome-192x192.png"></span><div class="article-meta" id="top"><span hidden="" itemprop="name headline"></span></div><div id="layoutHelper-page-plugins"></div><div id="post-body" itemprop="articleBody"><p> <span class="p logo center large">以太网帧结构</span></p><br><h1 hidden="">以太网帧结构</h1><div class="story post-story"><h2 id="协议"><a href="#协议" class="headerlink" title="协议"></a>协议</h2><p>一套约定俗成的特殊形式, 是设备与设备之间的语言, 固定格式化信息, 所有的设备根据协议的字段来理解报文的作用.</p><p>以太网协议分类：</p><ul><li><code>IEEE 802.3</code>：一般应用于以太网的控制协议信息. 例如 STP 协议使用的是 802.3 的数据帧.</li><li><code>Eternet_II</code>：是目前以太网数据使用最多的帧格式.</li></ul><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1701856225388/image-20231206174618481.png" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1701856225388/image-20231206174618481.png" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="帧格式"></p></div><div class="story post-story"><h2 id="以太网MAC地址"><a href="#以太网MAC地址" class="headerlink" title="以太网MAC地址"></a>以太网 MAC 地址</h2><p>F0-03-8C-XX-XX-XX</p><p>MAC 地址: 一台物理设备唯一且不可更改的标识信息, 以十六进制表示的.</p><p>OUI (厂商标识符): 前 24bit, 由 IEEE 管理和分配. <a target="_blank" rel="external nofollow noopener noreferrer" href="/go.html?u=aHR0cHM6Ly93d3cucmZjLWVkaXRvci5vcmcvcmZjL3JmYzcwNDIudHh0">RFC 7042</a></p><p>厂商自定义标识: 后 24bit, 由厂商自己分配.</p><p>单播 MAC 地址: 当第 8bit 为 <code>0</code> 时, 该地址为单播 MAC 地址.</p><blockquote><p>当十六进制第二位为偶数时第八 bit 一定为 0.</p></blockquote><p>组播 MAC 地址: 当第 8bit 为 <code>1</code> 时, 该地址为组播 MAC 地址.</p><blockquote><p>组播 MAC 地址不能用作 源 MAC 地址, 不能给设备使用.</p></blockquote><p>广播 MAC 地址: 当 48bit 全为 <code>1</code> 时, 该地址为广播 MAC 地址.</p><blockquote><p>只有单播 MAC 地址可以作为设备的 MAC 地址使用, 作为源地址使用.</p></blockquote></div><div class="story post-story"><h2 id="以太网帧格式-Eternet-II"><a href="#以太网帧格式-Eternet-II" class="headerlink" title="以太网帧格式(Eternet_II)"></a>以太网帧格式 (Eternet_II)</h2><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1701856291715/image-20231206174530591.png" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1701856291715/image-20231206174530591.png" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="以太网帧格式(Eternet_II)"></p><p><code>D.MAC (destination.MAC)</code>: 目的 MAC 地址 <code>6</code> 字节.</p><p><code>S.MAC (source.MAC)</code>: 源 MAC 地址 <code>6</code> 字节.</p><p><code>TYPE</code>: 类型, 标识上层协议类型, <code>2</code> 字节.</p><ul><li><code>0x0800</code>: IP 协议</li><li><code>0x0806</code>: ARP 协议</li></ul><p><code>DATA</code>: 数据载荷 可变长度 46 字节 - 1500 字节.</p><p><code>FCS(Frame Check Sequence)</code>: 帧校验序列, 判定数据帧在传递过程中的完整性 <code>4</code> 字节.</p></div><div class="story post-story"><h2 id="通信方式"><a href="#通信方式" class="headerlink" title="通信方式"></a>通信方式</h2><p>单播: 数据从某一台设备单独发送给另一台设备其他设备并接收处理.</p><p>组播: 数据发向某一个特定的分组, 只有在组内的设备才能够监听处理, 没有监听该组的设备无法收到数据.</p><p>广播: 数据发向广播地址, 该数据会被网络中所有的设备接收处理</p></div><div class="story post-story"><h2 id="数据帧的发送和接收"><a href="#数据帧的发送和接收" class="headerlink" title="数据帧的发送和接收"></a>数据帧的发送和接收</h2><h3 id="发送端"><a href="#发送端" class="headerlink" title="发送端"></a>发送端</h3><p>数据由发送端进行封装, 在数据封装成帧时, 会在数据帧的头部添加目的 MAC 和源 MAC, 将上层的封装协议在 TYPE 字段标明, 随后对数据帧进行计算将得出的值放置在 FCS 字段中, 随后发送出去.</p><h3 id="接收端"><a href="#接收端" class="headerlink" title="接收端"></a>接收端</h3><p>接收一个数据帧时, 首先核对帧校验, 以确保数据完整性, 在 FCS 通过后, 查看目的 MAC 地址, 当目的 MAC 地址与接收方 MAC 地址一致时, 或广播地址或自身所监听的组播 MAC 地址时, 才会处理该数据帧, 否则丢弃, 确认是自身所要处理的数据帧后, 会根据 TYPE 字段来确定后续的处理协议.</p></div><div class="story post-story"><h2 id="透明传输"><a href="#透明传输" class="headerlink" title="透明传输"></a>透明传输</h2><p>指不管所传数据时什么样的比特组合, 都应当能够在链路上传送. 因此, 链路层就 "看不见" 有什么妨碍数据传输的东西.</p><p>当所传数据中的比特组合恰巧与某一个控制信息完全一样时, 就必须采取适当的措施, 使收方不会将这样的数据误认为是某种控制信息. 这样才能保证数据链路层的传输是透明的.</p><p>透明传输是指在数据通信中，传输过程对用户或应用程序是不可见的，即无需用户或应用程序的干预或感知，数据可以自动、无缝地从发送端传输到接收端。在透明传输中，用户或应用程序无需关心底层的通信细节和协议，只需使用高层的接口或 API 来发送和接收数据。</p><p>透明传输的目标是提供简化和方便的数据传输体验，使用户能够专注于数据的使用和处理，而无需了解底层的传输机制。透明传输可以在不同的通信网络和协议中实现，包括局域网、广域网、互联网等。</p><h3 id="字符计数法"><a href="#字符计数法" class="headerlink" title="字符计数法"></a>字符计数法</h3><p>帧首部使用一个计数字段 (第一个字节, 8 位) 来标明帧内字符数</p><p>由于 count 字段的脆弱性, 容易出错, 不常用.</p><h4 id="字符填充法"><a href="#字符填充法" class="headerlink" title="字符填充法"></a>字符填充法</h4><p>SOH 00000001 帧开始符 （Start of Header）</p><p>EOT 00000100 帧结束符 （End of Transmission）</p><p>非 ASCII 采用字符填充法实现透明传输</p><p>ESC EOT 填充转义字符 (ESC)</p><p>实现复杂和不兼容性, 不常用.</p><p>eg. PPP 字节填充 <a target="_blank" rel="external nofollow noopener noreferrer" href="/go.html?u=aHR0cHM6Ly93d3cucmZjLWVkaXRvci5vcmcvcmZjL3JmYzE2NjIudHh0">RFC 1662</a></p><h3 id="零比特填充法"><a href="#零比特填充法" class="headerlink" title="零比特填充法"></a>零比特填充法</h3><p>01111110 ......... 01111110</p><p>发送端, 扫描整个信息字段, 只要有连续 5 个连续 1 就立即填入 1 个 0.</p><p>接收端, 收到一个帧时, 先找到标志字段确定边界, 再用硬件对比特流进行扫描, 发现连续 5 个 1 就把后面的 0 删掉.</p><p>保证了透明传输: 在传送的比特流中可以传送任意比特组合, 而不引起对帧边界的判断错误.</p><h3 id="违规编码法"><a href="#违规编码法" class="headerlink" title="违规编码法"></a>违规编码法</h3><p>曼切斯特编码 "高 - 低","低 - 高"</p><p>用 "高 - 高","低 - 低" 来定界帧的起始和终止</p><p>普遍使用的帧同步法是 比特填充法和违规编码法.</p></div><div class="story post-story"><h2 id="差错控制"><a href="#差错控制" class="headerlink" title="差错控制"></a>差错控制</h2><h3 id="差错从何而来"><a href="#差错从何而来" class="headerlink" title="差错从何而来"></a>差错从何而来</h3><ul><li>线路本身电气特性产生的随机噪声, 信道固有, 随机存在 (提高信噪比减少或避免干扰)</li><li>外界特定的短暂原因造成的冲击噪声是产生差错的主要原因 (利用编码技术来解决)</li></ul><p>位错 (bit 位出错 0 变 1 1 变 0)<br>帧错 (丢失, 重复, 失序)</p><h3 id="检错编码-奇偶校验码"><a href="#检错编码-奇偶校验码" class="headerlink" title="检错编码-奇偶校验码"></a>检错编码 - 奇偶校验码</h3><p>奇校验码: "1" 的个数为奇数<br>偶校验码: "1" 的个数为偶数</p><p>只能检查出奇数个比特错误, 检错能力为 50%.</p><h3 id="检错编码-CRC循环冗余码"><a href="#检错编码-CRC循环冗余码" class="headerlink" title="检错编码-CRC循环冗余码"></a>检错编码 - CRC 循环冗余码</h3><p>要传的数据 生成多项式 FCS 帧检验序列 / 冗余码</p><p> 5 / 2 ..... 1</p><p>最终发送数据 5 + 1=6</p><p>接收的数据 生成多项式</p><p> 6 / 2 ..... 0</p><p>余数为 0, 判定无错, 接受</p><ol><li>准备待传有效数据 分组</li></ol><p>d d d d d d</p><ol start="2"><li>每个组都加上冗余码构成帧再发送</li></ol><p>d 位 + r 位 FCS</p><p>双方商定的除数 / 生成多项式 r + 1 位</p><p>1101</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="3.413ex" height="2.452ex" role="img" focusable="false" viewBox="0 -833.9 1508.6 1083.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="1x^3+1x^2+0x^1+1x^0"><g data-mml-node="mn" data-latex="1"><path data-c="31" d="M269 666C228 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559L365 274 80 274C64 274 56 266 56 250 56 234 64 226 80 226L365 226 365-59C365-75 373-83 389-83 405-83 413-75 413-59L413 226 698 226C714 226 722 234 722 250 722 263 711 274 698 274Z"></path></g><g data-mml-node="mn" data-latex="1" transform="translate(1000.2,0)"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g><g data-mml-node="msup" data-latex="x^0" transform="translate(1500.2,0)"><g data-mml-node="mi" data-latex="x"><path data-c="1D465" d="M527 373C527 419 482 442 432 442 389 442 355 419 329 373 308 419 273 442 222 442 173 442 133 419 101 374 74 335 60 306 60 287 60 278 65 273 75 273 84 273 90 278 92 287 111 345 153 413 220 413 253 413 269 392 269 351 269 330 251 252 216 118 199 51 169 18 126 18 112 18 99 21 88 26 114 36 127 54 127 80 127 106 114 119 87 119 54 119 29 91 29 58 29 12 76-11 125-11 167-11 201 12 228 58 247 12 283-11 335-11 383-11 423 12 455 57 482 96 496 125 496 144 496 153 491 158 481 158 472 158 467 153 464 144 447 87 402 18 337 18 304 18 287 38 287 79 287 92 292 120 303 165L337 300C356 375 387 413 431 413 445 413 458 410 469 405 442 396 429 378 429 351 429 325 443 312 470 312 502 312 527 341 527 373Z"></path></g><g data-mml-node="mn" transform="translate(605,363) scale(0.707)" data-latex="0"><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z"></path></g></g></g></g></svg></mjx-container></p><p>FCS 帧检验序列计算方式:</p><p>模二 A.K.A 异或 (同 0 异 1)</p><p>d 位 + r 位 0 / 生成多项式 = 商 ..... r 位 FCS</p><h4 id="例子"><a href="#例子" class="headerlink" title="例子"></a>例子</h4><p>要发送的数据 1101 0110 11 CRC 校验 生成多项式 10011</p><ol><li>加 0 生成多项式的阶为 r, 则加 r 个 0 (多项式 r 位阶为 r-1)</li></ol><p>10011 生成多项式<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="2.282ex" height="2.47ex" role="img" focusable="false" viewBox="0 -841.7 1008.6 1091.7"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="x^4+x^1+x^0"><g data-mml-node="msup" data-latex="x^4"><g data-mml-node="mi" data-latex="x"><path data-c="1D465" d="M527 373C527 419 482 442 432 442 389 442 355 419 329 373 308 419 273 442 222 442 173 442 133 419 101 374 74 335 60 306 60 287 60 278 65 273 75 273 84 273 90 278 92 287 111 345 153 413 220 413 253 413 269 392 269 351 269 330 251 252 216 118 199 51 169 18 126 18 112 18 99 21 88 26 114 36 127 54 127 80 127 106 114 119 87 119 54 119 29 91 29 58 29 12 76-11 125-11 167-11 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fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="x^4+x^1+x^0"><g data-mml-node="mo" data-latex="+"><path data-c="2B" d="M698 274 413 274 413 559C413 575 405 583 389 583 373 583 365 575 365 559L365 274 80 274C64 274 56 266 56 250 56 234 64 226 80 226L365 226 365-59C365-75 373-83 389-83 405-83 413-75 413-59L413 226 698 226C714 226 722 234 722 250 722 263 711 274 698 274Z"></path></g><g data-mml-node="msup" data-latex="x^1" transform="translate(1000.2,0)"><g data-mml-node="mi" data-latex="x"><path data-c="1D465" d="M527 373C527 419 482 442 432 442 389 442 355 419 329 373 308 419 273 442 222 442 173 442 133 419 101 374 74 335 60 306 60 287 60 278 65 273 75 273 84 273 90 278 92 287 111 345 153 413 220 413 253 413 269 392 269 351 269 330 251 252 216 118 199 51 169 18 126 18 112 18 99 21 88 26 114 36 127 54 127 80 127 106 114 119 87 119 54 119 29 91 29 58 29 12 76-11 125-11 167-11 201 12 228 58 247 12 283-11 335-11 383-11 423 12 455 57 482 96 496 125 496 144 496 153 491 158 481 158 472 158 467 153 464 144 447 87 402 18 337 18 304 18 287 38 287 79 287 92 292 120 303 165L337 300C356 375 387 413 431 413 445 413 458 410 469 405 442 396 429 378 429 351 429 325 443 312 470 312 502 312 527 341 527 373Z"></path></g><g data-mml-node="mn" transform="translate(605,363) scale(0.707)" data-latex="1"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g></g></g></g></svg><mjx-break size="3"></mjx-break><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="4.545ex" height="2.452ex" role="img" focusable="false" viewBox="0 -833.9 2008.8 1083.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="x^4+x^1+x^0"><g data-mml-node="mo" data-latex="+"><path data-c="2B" d="M698 274 413 274 413 559C413 575 405 583 389 583 373 583 365 575 365 559L365 274 80 274C64 274 56 266 56 250 56 234 64 226 80 226L365 226 365-59C365-75 373-83 389-83 405-83 413-75 413-59L413 226 698 226C714 226 722 234 722 250 722 263 711 274 698 274Z"></path></g><g data-mml-node="msup" data-latex="x^0" transform="translate(1000.2,0)"><g data-mml-node="mi" data-latex="x"><path data-c="1D465" d="M527 373C527 419 482 442 432 442 389 442 355 419 329 373 308 419 273 442 222 442 173 442 133 419 101 374 74 335 60 306 60 287 60 278 65 273 75 273 84 273 90 278 92 287 111 345 153 413 220 413 253 413 269 392 269 351 269 330 251 252 216 118 199 51 169 18 126 18 112 18 99 21 88 26 114 36 127 54 127 80 127 106 114 119 87 119 54 119 29 91 29 58 29 12 76-11 125-11 167-11 201 12 228 58 247 12 283-11 335-11 383-11 423 12 455 57 482 96 496 125 496 144 496 153 491 158 481 158 472 158 467 153 464 144 447 87 402 18 337 18 304 18 287 38 287 79 287 92 292 120 303 165L337 300C356 375 387 413 431 413 445 413 458 410 469 405 442 396 429 378 429 351 429 325 443 312 470 312 502 312 527 341 527 373Z"></path></g><g data-mml-node="mn" transform="translate(605,363) scale(0.707)" data-latex="0"><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z"></path></g></g></g></g></svg></mjx-container> 阶为 4</p><ol start="2"><li>模 2 除法 数据加 0 后除以多项式, 余数为冗余码/FCS/CRC 校验码的比特序列</li></ol><p>1101 0110 11 0000 / 10011 余数 1110</p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1701674901233/image-20231204152714825.png" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1701674901233/image-20231204152714825.png" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="模2除法"></p><p>最终发送数据 1101 0110 11 1110</p><p>接收端检错过程</p><p>把收到的每一个帧都除以同样的除数, 然后检查得到余数 R.</p><ul><li>余数为 0, 判定帧没有差错, 接受.</li><li>余数不为 0, 判定帧有差错, 丢弃.</li></ul><p>FCS 的生成以及接收端的 CRC 检验都是由硬件实现, 处理迅速, 因此不会延误数据的传输.</p><p>链路层使用 CRC 检验能够实现无差错比特传输, 不能实现可靠传输</p><h3 id="纠错码-海明码"><a href="#纠错码-海明码" class="headerlink" title="纠错码-海明码"></a>纠错码 - 海明码</h3><ol><li>确定校验码位数 r</li><li>确定校验码和数据的位置</li><li>求出校验码值</li><li>检错并纠错</li></ol><h4 id="海明距离"><a href="#海明距离" class="headerlink" title="海明距离"></a>海明距离</h4><p>两个合法编码 (码字) 的对应比特取值不同的比特数称为这两个码字的海明距离 (码距),一个有效编码集中, 任意两个合法编码 (码字) 的海明距离的最小值称为该编码集的海明距离 (码距).</p><h4 id="1-确定校验码位数r"><a href="#1-确定校验码位数r" class="headerlink" title="1. 确定校验码位数r"></a>1. 确定校验码位数 r</h4><p>数据/信息有 m 位, 冗余码/校验码有 r 位</p><p>校验码一共有<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="2.041ex" height="1.528ex" role="img" focusable="false" viewBox="0 -675.5 901.9 675.5"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2^r"><g data-mml-node="msup" data-latex="2^r"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g><g data-mml-node="mi" transform="translate(533,363) scale(0.707)" data-latex="r"><path data-c="1D45F" d="M436 374C436 416 395 442 351 442 302 442 261 419 227 372 217 411 183 442 136 442 95 442 65 410 44 345 34 312 29 293 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 150 413 159 399 159 371 159 358 154 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 110-11 130-11 143-1 150 19L169 91C180 134 187 162 190 175L221 303C223 311 231 324 244 343 271 381 302 413 351 413 363 413 373 411 382 406 352 397 337 378 337 351 337 325 351 312 378 312 411 312 436 341 436 374Z"></path></g></g></g></g></svg></mjx-container> 种取值</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="2.041ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 901.9 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2^r \ge m+r+1"><g data-mml-node="msup" data-latex="2^r"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g><g data-mml-node="mi" transform="translate(533,363) scale(0.707)" data-latex="r"><path data-c="1D45F" d="M436 374C436 416 395 442 351 442 302 442 261 419 227 372 217 411 183 442 136 442 95 442 65 410 44 345 34 312 29 293 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 150 413 159 399 159 371 159 358 154 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 110-11 130-11 143-1 150 19L169 91C180 134 187 162 190 175L221 303C223 311 231 324 244 343 271 381 302 413 351 413 363 413 373 411 382 406 352 397 337 378 337 351 337 325 351 312 378 312 411 312 436 341 436 374Z"></path></g></g></g></g></svg><mjx-break size="4"></mjx-break><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="4.375ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1933.8 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2^r \ge m+r+1"><g data-mml-node="mo" data-latex="\ge"><path data-c="2265" d="M684 310C694 315 699 322 699 333 699 344 694 352 684 357L110 629C107 630 103 631 99 631 83 631 75 623 75 606 75 597 80 590 89 586L623 333 89 80C80 76 75 69 75 60 75 43 83 35 99 35 103 35 107 36 110 38M678-72 100-72C84-72 76-80 76-95 76-111 84-119 100-119L678-119C694-119 702-111 702-95 702-83 691-72 678-72Z"></path></g><g data-mml-node="mi" data-latex="m" transform="translate(1055.8,0)"><path data-c="1D45A" d="M657 442C596 442 543 412 498 353 489 412 451 442 383 442 324 442 273 416 231 363 223 407 188 442 137 442 96 442 66 409 45 344 34 312 29 293 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 66 299 84 375 107 413 134 413 152 413 161 399 161 371 161 358 156 331 145 290L88 63C84 51 79 25 79 19 79-1 90-11 111-11 131-11 145-1 152 19 153 24 160 49 171 92L192 181 222 295C233 318 250 341 272 365 301 397 337 413 380 413 413 413 429 391 429 348 429 335 424 308 414 267L387 153C380 124 364 64 356 32 355 25 354 21 354 19 354-1 365-11 387-11 398-11 406-8 413-1 428 14 429 21 435 48L494 285C497 298 511 321 535 353 565 393 605 413 654 413 687 413 703 391 703 348 703 309 683 236 642 129 633 106 629 87 629 74 629 25 666-11 714-11 759-11 793 14 818 64 838 104 848 131 848 144 848 153 843 158 832 158 825 157 818 148 813 137 791 58 759 18 716 18 703 18 696 28 696 47 696 62 702 84 714 115 755 222 775 295 775 333 775 404 728 442 657 442Z"></path></g></g></g></svg><mjx-break size="3"></mjx-break><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="3.283ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1451.2 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2^r \ge m+r+1"><g data-mml-node="mo" data-latex="+"><path data-c="2B" d="M698 274 413 274 413 559C413 575 405 583 389 583 373 583 365 575 365 559L365 274 80 274C64 274 56 266 56 250 56 234 64 226 80 226L365 226 365-59C365-75 373-83 389-83 405-83 413-75 413-59L413 226 698 226C714 226 722 234 722 250 722 263 711 274 698 274Z"></path></g><g data-mml-node="mi" data-latex="r" transform="translate(1000.2,0)"><path data-c="1D45F" d="M436 374C436 416 395 442 351 442 302 442 261 419 227 372 217 411 183 442 136 442 95 442 65 410 44 345 34 312 29 293 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 150 413 159 399 159 371 159 358 154 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 110-11 130-11 143-1 150 19L169 91C180 134 187 162 190 175L221 303C223 311 231 324 244 343 271 381 302 413 351 413 363 413 373 411 382 406 352 397 337 378 337 351 337 325 351 312 378 312 411 312 436 341 436 374Z"></path></g></g></g></svg><mjx-break size="3"></mjx-break><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="3.394ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1500.2 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2^r \ge m+r+1"><g data-mml-node="mo" data-latex="+"><path data-c="2B" d="M698 274 413 274 413 559C413 575 405 583 389 583 373 583 365 575 365 559L365 274 80 274C64 274 56 266 56 250 56 234 64 226 80 226L365 226 365-59C365-75 373-83 389-83 405-83 413-75 413-59L413 226 698 226C714 226 722 234 722 250 722 263 711 274 698 274Z"></path></g><g data-mml-node="mn" data-latex="1" transform="translate(1000.2,0)"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g></g></g></svg></mjx-container> 海明不等式</p><p>要发送的数据: D = 1100</p><p>数据的位数 m = 4<br>满足不等式的最小 r 为 3<br>D = 1100 的海明码应该有 4 + 3=7 位<br>其中原数据 4 位, 校验码 3 位</p><h4 id="2-确定校验码和数据的位置"><a href="#2-确定校验码和数据的位置" class="headerlink" title="2. 确定校验码和数据的位置"></a>2. 确定校验码和数据的位置</h4><p>校验码放在序号为<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="2.279ex" height="1.528ex" role="img" focusable="false" viewBox="0 -675.5 1007.3 675.5"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2^n"><g data-mml-node="msup" data-latex="2^n"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g><g data-mml-node="mi" transform="translate(533,363) scale(0.707)" data-latex="n"><path data-c="1D45B" d="M537 137C514 58 481 18 440 18 427 18 420 28 420 47 420 61 426 84 438 115 478 224 498 296 498 333 498 403 451 442 381 442 322 442 271 416 230 363 222 407 187 442 136 442 80 442 58 390 44 345 34 313 29 294 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 151 413 160 399 160 371 160 358 155 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 111-11 130-11 144-1 151 19 153 24 159 49 170 92L191 181 221 295C232 318 249 341 270 365 299 397 335 413 378 413 411 413 427 391 427 348 427 310 406 234 363 120 356 102 353 87 353 74 353 25 390-11 438-11 482-11 517 14 542 64 561 104 571 131 571 144 571 153 566 158 555 158 552 158 537 149 537 137Z"></path></g></g></g></g></svg></mjx-container> 的位置</p><figure class="highlight plaintext"><table><tbody><tr><td class="code"><pre><span class="line">序号 7 6 5 4 3 2 1</span><br><span class="line">值 1 1 0 x_4 0 x_2 x_1</span><br></pre></td></tr></tbody></table></figure><h4 id="3-求出校验码值"><a href="#3-求出校验码值" class="headerlink" title="3. 求出校验码值"></a>3. 求出校验码值</h4><figure class="highlight plaintext"><table><tbody><tr><td class="code"><pre><span class="line"> 1** *1* **1</span><br><span class="line">二进制 111 110 101 100 011 010 001</span><br><span class="line">序号 7 6 5 4 3 2 1</span><br><span class="line">值 1 1 0 x_4 0 x_2 x_1</span><br></pre></td></tr></tbody></table></figure><p>4: 负责 4567 的校验</p><p>2: 负责 2367 的校验</p><p>1: 负责 1357 的校验</p><p>采用偶校验 x_4 = 0 x_2 = 0 x_1 = 1</p><figure class="highlight plaintext"><table><tbody><tr><td class="code"><pre><span class="line"> 1** *1* **1</span><br><span class="line">二进制 111 110 101 100 011 010 001</span><br><span class="line">序号 7 6 5 4 3 2 1</span><br><span class="line">值 1 1 0 0 0 0 1</span><br></pre></td></tr></tbody></table></figure><h4 id="4-检错并纠错"><a href="#4-检错并纠错" class="headerlink" title="4. 检错并纠错"></a>4. 检错并纠错</h4><p>若接收数据 1110001 偶校验</p><p>4: 负责 4567 的校验 0111 x</p><p>2: 负责 2367 的校验 0011 v</p><p>1: 负责 1357 的校验 1011 x</p><p>错误位是 5</p><p>偶校验 (异或为 0)</p><p>x_4 异或 0 异或 1 异或 1 异或 1 = 0 x_4 = 1</p><p>x_2: 0011 x_2=0</p><p>x_1: 1011 x_1=1</p><p>x_4 x_2 x_1</p><p>1 0 1</p><p>101 转十进制为 5 ,错误位是 5</p></div><div class="story post-story"><h2 id="流量控制方法"><a href="#流量控制方法" class="headerlink" title="流量控制方法"></a>流量控制方法</h2><h3 id="停止等待协议"><a href="#停止等待协议" class="headerlink" title="停止等待协议"></a>停止等待协议</h3><p>每发送完一个帧就停止发送, 等待对方的确认, 在收到确认后再发送下一个帧</p><p>发送窗口大小 = 1 接收窗口大小 = 1</p><h3 id="滑动窗口协议"><a href="#滑动窗口协议" class="headerlink" title="滑动窗口协议"></a>滑动窗口协议</h3><p>发送窗口 接收窗口</p><p>后退 N 帧协议 (GBN)</p><p>发送窗口大小 > 1 接收窗口大小 = 1</p><p>选择重传协议 (SR)</p><p>发送窗口大小 > 1 接收窗口大小 > 1</p><p>可靠传输: 发送端发啥接收端收啥</p><p>流量控制: 控制发送速率, 使接收方有足够缓冲空间接收每一个帧</p><p>滑动窗口解决 流量控制和可靠传输.</p></div></div><div class="footer"></div><div class="article-meta" id="bottom"><div 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