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<title>6b/8b encoding</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">6b/8b encoding</span></span>

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<p>In telecommunications, <b>6b/8b</b> is a line code that expands 6-<a href="../Bit" title="Bit">bit</a> codes to 8-bit symbols for the purposes of maintaining <a href="../DC_bias" title="DC bias">DC-balance</a> in a communications system.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>The 6b/8b encoding is a <a href="../Balanced_code" class="mw-redirect" title="Balanced code">balanced code</a> --

each 8-bit output symbol contains 4 zero bits and 4 one bits. So the code can, like a <a href="../Parity_bit" title="Parity bit">parity bit</a>, detect all single-bit errors.

</p><p>The number of 8-bit patterns with 4 bits set is the <a href="../Binomial_coefficient" title="Binomial coefficient">binomial coefficient</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tbinom {8}{4}}}">

<mrow>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\tbinom {8}{4}}}</annotation>

</semantics>

</math></span><img src="../9ca85fa5ff237bb719f8d4441b4110746c03860f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.952ex; height:3.343ex;" alt="{\displaystyle {\tbinom {8}{4}}}" loading="lazy"></span> = 70. Further excluding the patterns <code>11110000</code> and <code>00001111</code>, this allows 68 coded patterns: 64 data codes, plus 4 additional control codes.

</p>

<div class="mw-heading mw-heading2"><h2 id="Coding_rules">Coding rules</h2></div>

<p>The 64 possible 6-bit input codes can be classified according to their disparity, the number of 1 bits minus the number of 0 bits:

</p>

<th>Zeros</th>

<th>Disparity</th>

<th>Number

</th></tr>

<tr>

<td>1

</td></tr>

<tr>

<td>6

</td></tr>

<tr>

<td>15

</td></tr>

<tr>

<td>20

</td></tr>

<tr>

<td>15

</td></tr>

<tr>

<td>6

</td></tr>

<tr>

<td>1

</td></tr></tbody></table>

<p>The 6-bit input codes are mapped to 8-bit output symbols as follows:

</p>

<ul><li>The 20 6-bit codes with disparity 0 are prefixed with <code>10</code><br><i>Example: 000111 → <b>10</b>000111</i><br><i>Example: 101010 → <b>10</b>101010</i></li>

<li>The 15 6-bit codes with disparity +2, other than <code>001111</code>, are prefixed with <code>00</code><br><i>Example: 010111 → <b>00</b>010111</i></li>

<li>The 15 6-bit codes with disparity −2, other than <code>110000</code>, are prefixed with <code>11</code><br><i>Example: 101000 → <b>11</b>101000</i></li>

<li>The remaining 20 codes: 12 with disparity ±4, 2 with disparity ±6, <code>001111</code>, <code>110000</code>, and the 4 control codes, are assigned to codes beginning with <code>01</code> as follows:</li></ul>

<th>Input</th>

<th>Output

</th>

</td>

<th>Input</th>

<th>Output

</th>

</td>

<th>Complement

</th></tr>

<tr>

</td>

</td>

<td>01_xx__x

</td></tr>

<tr>

<td rowspan="6">−4

</td>

</td>

<td rowspan="6">+4

</td>

</td>

<td rowspan="2">01xx____

</td></tr>

<tr>

</td>

</td></tr>

<tr>

</td>

</td>

<td rowspan="2">01x____x

</td></tr>

<tr>

</td>

</td></tr>

<tr>

</td>

</td>

<td rowspan="2">01_____xx

</td></tr>

<tr>

</td>

</td></tr>

<tr>

</td>

</td>

<td>01____x__

</td></tr>

<tr>

<td rowspan="2">Control

</td>

</td>

<td rowspan="2">Control

</td>

</td>

</td></tr>

<tr>

</td>

</td></tr></tbody></table>

<p>No data symbol contains more than four consecutive matching bits, and because the patterns <code>11110000</code> and <code>00001111</code> are excluded, no data symbol begins or ends with more than three identical bits.

Thus, the longest run of identical bits that will be produced is 6. (I.e. this is a (0,5) <a href="../Run_length_limited" class="mw-redirect" title="Run length limited">RLL code</a>, with a worst-case <a href="../Running_disparity" class="mw-redirect" title="Running disparity">running disparity</a> of +3 to −3.)

</p><p>Any occurrence of 6 consecutive identical bits constitutes a comma sequence or sync mark or <a href="../Syncword" title="Syncword">syncword</a>; it identifies the symbol boundaries precisely.

Those 6 bits straddle the inter-symbol boundary with exactly 3 of those identical bits at the end of one symbol, and 3 of those identical bits at the start of the following next symbol.

</p>

<ul><li><a href="../8b/10b_encoding" title="8b/10b encoding">8b/10b encoding</a>, another fixed-table system with a higher <a href="../Code_rate" title="Code rate">code rate</a> but less error detection.</li>

<li><a href="../64b/66b_encoding" title="64b/66b encoding">64b/66b encoding</a>, linear feedback register.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFKees_A._Schouhamer_Immink2004" class="citation book cs1"><a href="../Kees_Schouhamer_Immink" title="Kees Schouhamer Immink">Kees A. Schouhamer Immink</a> (November 2004). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/codesformassdata0000scho"><i>Codes for Mass Data Storage Systems</i></a></span> (Second fully revised ed.). Eindhoven, The Netherlands: Shannon Foundation Publishers. <a href="../ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>90-74249-27-2</bdi><span class="reference-accessdate">. Retrieved <span class="nowrap">2015-08-23</span></span>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li>Freepatents online, United States patent 6,876,315: <a rel="nofollow" class="external text" href="http://www.freepatentsonline.com/6876315.html">DC-balanced 6B/8B transmission code with local parity</a>.</li></ul>

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</style><div id="Line_coding_(digital_baseband_transmission)443" style="font-size:114%;margin:0 4em"><a href="../Line_coding" class="mw-redirect" title="Line coding">Line coding</a> (digital baseband transmission)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main articles</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="../Unipolar_encoding" title="Unipolar encoding">Unipolar encoding</a></li>

<li><a href="../Bipolar_encoding" title="Bipolar encoding">Bipolar encoding</a></li>

<li><a href="../On%E2%80%93off_keying" title="On–off keying">On–off keying</a></li>

<li><a href="../Mark_and_space" title="Mark and space">Mark and space</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basic <a href="../Line_code" title="Line code">line codes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="../Return-to-zero" title="Return-to-zero">Return to zero (RZ)</a></li>

<li><a href="../Non-return-to-zero#Non-return-to-zero_level" title="Non-return-to-zero">Non-return-to-zero, level (NRZ/NRZ-L)</a></li>

<li><a href="../Non-return-to-zero#Non-return-to-zero_inverted" title="Non-return-to-zero">Non-return-to-zero, inverted (NRZ-I)</a></li>

<li><a href="../Non-return-to-zero#Non-return-to-zero_space" title="Non-return-to-zero">Non-return-to-zero, space (NRZ-S)</a></li>

<li><a href="../Manchester_code" title="Manchester code">Manchester</a></li>

<li><a href="../Differential_Manchester_encoding" title="Differential Manchester encoding">Differential Manchester/biphase (Bi-φ)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Extended line codes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="../Conditioned_diphase" class="mw-redirect" title="Conditioned diphase">Conditioned diphase</a></li>

<li><a href="../Bipolar_encoding#Alternate_mark_inversion" title="Bipolar encoding">Alternate mark inversion</a></li>

<li><a href="../Modified_AMI_code" title="Modified AMI code">Modified AMI code</a></li>

<li><a href="../Coded_mark_inversion" title="Coded mark inversion">Coded mark inversion</a></li>

<li><a href="../MLT-3_encoding" title="MLT-3 encoding">MLT-3 encoding</a></li>

<li><a href="../Hybrid_ternary_code" title="Hybrid ternary code">Hybrid ternary code</a></li>

<li><a href="../8b/10b_encoding" title="8b/10b encoding">8b/10b encoding</a></li>

<li><a href="../64b/66b_encoding" title="64b/66b encoding">64b/66b encoding</a></li>

<li><a href="../Eight-to-fourteen_modulation" title="Eight-to-fourteen modulation">Eight-to-fourteen modulation</a></li>

<li><a href="../Delay_encoding" class="mw-redirect" title="Delay encoding">Delay/Miller encoding</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Optical line codes</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="../Carrier-suppressed_return-to-zero" class="mw-redirect" title="Carrier-suppressed return-to-zero">Carrier-suppressed return-to-zero</a></li>

<li><a href="../Alternate-phase_return-to-zero" class="mw-redirect" title="Alternate-phase return-to-zero">Alternate-phase return-to-zero</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div>

<ul><li><i>See also:</i> <a href="../Baseband" title="Baseband">Baseband</a></li>

<li><a href="../Digital_signal" title="Digital signal">Digital signal</a></li>

<li><a href="../Digital_transmission" class="mw-redirect" title="Digital transmission">Digital transmission</a></li>

<li><a href="../Ethernet_physical_layer" title="Ethernet physical layer">Ethernet physical layer</a></li>

<li><a href="../Modulation" class="mw-redirect" title="Modulation">Pulse modulation methods</a></li>

<li><a href="../Pulse-amplitude_modulation" title="Pulse-amplitude modulation">Pulse-amplitude modulation</a> (PAM)</li>

<li><a href="../Pulse-code_modulation" title="Pulse-code modulation">Pulse-code modulation</a> (PCM)</li>

<li><a href="../Serial_communication" title="Serial communication">Serial communication</a></li>

<li>Category:Line codes</li></ul>

</div></td></tr></tbody></table></div></div>

<p><br>

</p>

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