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class="menu navigation"><div class="list-h"><a target="_blank" rel="external nofollow noopener noreferrer" href="https://github.com/MHuiG" active-action="action-https:githubcomMHuiG"><i class="fa-brands fa-github color-github fa-fw"></i><p>Github</p></a><a href="/pages/friends/" active-action="action-pagesfriends"><i class="fa-duotone fa-link color-friends fa-fw"></i><p>友链</p></a><a href="/pages/about/" active-action="action-pagesabout"><i class="fa-duotone fa-user-tie color-about fa-fw"></i><p>关于</p></a><a href="https://www.travellings.cn/go-by-clouds.html" target="_blank" active-action="action-https:wwwtravellingscngo-by-cloudshtml" rel="external nofollow noopener noreferrer"><i class="fa-duotone fa-subway color-travellings fa-fw"></i><p>Travelling</p></a></div></div></div></div><div id="scroll-down" style="display:none"><i class="fa fa-chevron-down scroll-down-effects"></i></div></div></div><div id="safearea"><div 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="MHuiG"></span><span hidden itemprop="post" itemscope itemtype="http://schema.org/Post"><meta itemprop="name" content="MHuiG"><meta itemprop="description" content="MHuiG&#39;s Blog (MHuiG的博客) MHuiG&#39;s Neverland（MHuiG的梦幻岛） —— MHuiG(@MHuiG) 随便写写画画的地方 - 技术博客"></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="https://www.rfc-editor.org/rfc/rfc7042.txt">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="https://www.rfc-editor.org/rfc/rfc1662.txt">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"><svg style="vertical-align:-.186ex" xmlns="http://www.w3.org/2000/svg" width="21.949ex" height="2.072ex" role="img" focusable="false" viewBox="0 -833.9 9701.5 915.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 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386T222 442Q257 442 286 424T329 379Q371 442 430 442 467 442 494 420T522 361Q522 332 508 314T481 292 458 288Q439 288 427 299T415 328Q415 374 465 391 454 404 425 404 412 404 406 402 368 386 350 336 290 115 290 78 290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145 504 144 502 134 486 77 440 33T333-11Q263-11 227 52 186-10 133-10H127Q78-10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101 142 81 130 66T107 46 94 41L91 40Q91 39 97 36T113 29 132 26Q168 26 194 71 203 87 217 139T245 247 261 313Q266 340 266 352 266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"/></g><g data-mml-node="mn" transform="translate(605,363) scale(0.707)"><path data-c="30" d="M96 585Q152 666 249 666 297 666 345 640T423 548Q460 465 460 320 460 165 417 83 397 41 362 16T301-15 250-22Q224-22 198-16T137 16 82 83Q39 165 39 320 39 494 96 585ZM321 597Q291 629 250 629 208 629 178 597 153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16 290 16 318 46 347 76 354 130T362 333Q362 478 354 524T321 597Z"/></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"><svg style="vertical-align:-.186ex" xmlns="http://www.w3.org/2000/svg" width="12.377ex" height="2.09ex" role="img" focusable="false" viewBox="0 -841.7 5470.5 923.7"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msup"><g data-mml-node="mi"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442 467 442 494 420T522 361Q522 332 508 314T481 292 458 288Q439 288 427 299T415 328Q415 374 465 391 454 404 425 404 412 404 406 402 368 386 350 336 290 115 290 78 290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145 504 144 502 134 486 77 440 33T333-11Q263-11 227 52 186-10 133-10H127Q78-10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101 142 81 130 66T107 46 94 41L91 40Q91 39 97 36T113 29 132 26Q168 26 194 71 203 87 217 139T245 247 261 313Q266 340 266 352 266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"/></g><g data-mml-node="mn" transform="translate(605,363) scale(0.707)"><path data-c="34" d="M462 0Q444 3 333 3 217 3 199 0H190V46H221Q241 46 248 46T265 48 279 53 286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675 336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212 183 211H293Z"/></g></g><g data-mml-node="mo" transform="translate(1230.8,0)"><path data-c="2B" d="M56 237T56 250 70 270H369V420L370 570Q380 583 389 583 402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401-82 391-82H389 387Q375-82 369-68V230H70Q56 237 56 250Z"/></g><g data-mml-node="msup" transform="translate(2231,0)"><g data-mml-node="mi"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442 467 442 494 420T522 361Q522 332 508 314T481 292 458 288Q439 288 427 299T415 328Q415 374 465 391 454 404 425 404 412 404 406 402 368 386 350 336 290 115 290 78 290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145 504 144 502 134 486 77 440 33T333-11Q263-11 227 52 186-10 133-10H127Q78-10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101 142 81 130 66T107 46 94 41L91 40Q91 39 97 36T113 29 132 26Q168 26 194 71 203 87 217 139T245 247 261 313Q266 340 266 352 266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"/></g><g data-mml-node="mn" transform="translate(605,363) scale(0.707)"><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 54 315 52T339 48 401 46H427V0H416Q395 3 257 3 121 3 100 0H88V46H114Q136 46 152 46T177 47 193 50 201 52 207 57 213 61V578Z"/></g></g><g data-mml-node="mo" transform="translate(3461.8,0)"><path data-c="2B" d="M56 237T56 250 70 270H369V420L370 570Q380 583 389 583 402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401-82 391-82H389 387Q375-82 369-68V230H70Q56 237 56 250Z"/></g><g data-mml-node="msup" transform="translate(4462,0)"><g data-mml-node="mi"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442 467 442 494 420T522 361Q522 332 508 314T481 292 458 288Q439 288 427 299T415 328Q415 374 465 391 454 404 425 404 412 404 406 402 368 386 350 336 290 115 290 78 290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145 504 144 502 134 486 77 440 33T333-11Q263-11 227 52 186-10 133-10H127Q78-10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101 142 81 130 66T107 46 94 41L91 40Q91 39 97 36T113 29 132 26Q168 26 194 71 203 87 217 139T245 247 261 313Q266 340 266 352 266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"/></g><g data-mml-node="mn" transform="translate(605,363) scale(0.707)"><path data-c="30" d="M96 585Q152 666 249 666 297 666 345 640T423 548Q460 465 460 320 460 165 417 83 397 41 362 16T301-15 250-22Q224-22 198-16T137 16 82 83Q39 165 39 320 39 494 96 585ZM321 597Q291 629 250 629 208 629 178 597 153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16 290 16 318 46 347 76 354 130T362 333Q362 478 354 524T321 597Z"/></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"><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"><g data-mml-node="msup"><g data-mml-node="mn"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315 301 241Q265 210 201 149L142 93 218 92Q375 92 385 97 392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19 31Q50 38 56 46T86 81Q115 113 136 137 145 147 170 174T204 211 233 244 261 278 284 308 305 340 320 369 333 401 340 431 343 464Q343 527 309 573T212 619Q179 619 154 602T119 569 109 550Q109 549 114 549 132 549 151 535T170 489Q170 464 154 447T109 429Z"/></g><g data-mml-node="mi" transform="translate(533,363) scale(0.707)"><path data-c="1D45F" d="M21 287Q22 290 23 295T28 317 38 348 53 381 73 411 99 433 132 442Q161 442 183 430T214 408 225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400 430 381 430 363 430 333 417 315T391 292 366 288Q346 288 334 299T322 328Q322 376 378 392 356 405 342 405 286 405 239 331 229 315 224 298T190 165Q156 25 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 114 189T154 366Q154 405 128 405 107 405 92 377T68 316 57 280Q55 278 41 278H27Q21 284 21 287Z"/></g></g></g></g></svg></mjx-container> 种取值</p><p><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.312ex" xmlns="http://www.w3.org/2000/svg" width="14.727ex" height="1.841ex" role="img" focusable="false" viewBox="0 -675.5 6509.3 813.5"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msup"><g data-mml-node="mn"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315 301 241Q265 210 201 149L142 93 218 92Q375 92 385 97 392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19 31Q50 38 56 46T86 81Q115 113 136 137 145 147 170 174T204 211 233 244 261 278 284 308 305 340 320 369 333 401 340 431 343 464Q343 527 309 573T212 619Q179 619 154 602T119 569 109 550Q109 549 114 549 132 549 151 535T170 489Q170 464 154 447T109 429Z"/></g><g data-mml-node="mi" transform="translate(533,363) scale(0.707)"><path data-c="1D45F" d="M21 287Q22 290 23 295T28 317 38 348 53 381 73 411 99 433 132 442Q161 442 183 430T214 408 225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400 430 381 430 363 430 333 417 315T391 292 366 288Q346 288 334 299T322 328Q322 376 378 392 356 405 342 405 286 405 239 331 229 315 224 298T190 165Q156 25 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 114 189T154 366Q154 405 128 405 107 405 92 377T68 316 57 280Q55 278 41 278H27Q21 284 21 287Z"/></g></g><g data-mml-node="mo" transform="translate(1179.7,0)"><path data-c="2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431 687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76 83 77 83 79 82 86 98 95 117 105 248 167 326 204 378 228L626 346 360 472Q291 505 200 548 112 589 98 597T83 616ZM84-118Q84-108 99-98H678Q694-104 694-118 694-130 679-138H98Q84-131 84-118Z"/></g><g data-mml-node="mi" transform="translate(2235.5,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341 56 388 88 425 132 442 175 435 205 417 221 395 229 376L231 369Q231 367 232 367L243 378Q303 442 384 442 401 442 415 440T441 433 460 423 475 411 485 398 493 385 497 373 500 364 502 357L510 367Q573 442 659 442 713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145 857 144 853 130 845 101 831 73T785 17 716-10Q669-10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291 466 157Q433 26 428 16 415-11 385-11 372-11 364-4T353 8 350 18Q350 29 384 161L420 307Q423 322 423 345 423 404 379 404H374Q288 404 229 303L222 291 189 157Q156 26 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 112 181 151 335 151 342 154 357 154 369 154 405 129 405 107 405 92 377T69 316 57 280Q55 278 41 278H27Q21 284 21 287Z"/></g><g data-mml-node="mo" transform="translate(3335.7,0)"><path data-c="2B" d="M56 237T56 250 70 270H369V420L370 570Q380 583 389 583 402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401-82 391-82H389 387Q375-82 369-68V230H70Q56 237 56 250Z"/></g><g data-mml-node="mi" transform="translate(4335.9,0)"><path data-c="1D45F" d="M21 287Q22 290 23 295T28 317 38 348 53 381 73 411 99 433 132 442Q161 442 183 430T214 408 225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400 430 381 430 363 430 333 417 315T391 292 366 288Q346 288 334 299T322 328Q322 376 378 392 356 405 342 405 286 405 239 331 229 315 224 298T190 165Q156 25 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 114 189T154 366Q154 405 128 405 107 405 92 377T68 316 57 280Q55 278 41 278H27Q21 284 21 287Z"/></g><g data-mml-node="mo" transform="translate(5009.1,0)"><path data-c="2B" d="M56 237T56 250 70 270H369V420L370 570Q380 583 389 583 402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401-82 391-82H389 387Q375-82 369-68V230H70Q56 237 56 250Z"/></g><g data-mml-node="mn" transform="translate(6009.3,0)"><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 54 315 52T339 48 401 46H427V0H416Q395 3 257 3 121 3 100 0H88V46H114Q136 46 152 46T177 47 193 50 201 52 207 57 213 61V578Z"/></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"><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"><g data-mml-node="msup"><g data-mml-node="mn"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315 301 241Q265 210 201 149L142 93 218 92Q375 92 385 97 392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19 31Q50 38 56 46T86 81Q115 113 136 137 145 147 170 174T204 211 233 244 261 278 284 308 305 340 320 369 333 401 340 431 343 464Q343 527 309 573T212 619Q179 619 154 602T119 569 109 550Q109 549 114 549 132 549 151 535T170 489Q170 464 154 447T109 429Z"/></g><g data-mml-node="mi" transform="translate(533,363) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341 56 388 89 425 135 442Q171 442 195 424T225 390 231 369Q231 367 232 367L243 378Q304 442 382 442 436 442 469 415T503 336 465 179 427 52Q427 26 444 26 450 26 453 27 482 32 505 65T540 145Q542 153 560 153 580 153 580 145 580 144 576 130 568 101 554 73T508 17 439-10Q392-10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291 189 157Q156 26 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 112 180T152 343Q153 348 153 366 153 405 129 405 91 405 66 305 60 285 60 284 58 278 41 278H27Q21 284 21 287Z"/></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 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