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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Punctured code</span></span>
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</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="Puncturing_(topology)" class="mw-redirect" title="Puncturing (topology)">Puncturing (topology)</a>.</div>
<p>In <a href="Coding_theory" title="Coding theory">coding theory</a>, <b>puncturing</b> is the process of removing some of the <a href="Parity_bit" title="Parity bit">parity bits</a> after encoding with an <a href="Error_correction_and_detection" class="mw-redirect" title="Error correction and detection">error-correction code</a>. This has the same effect as encoding with an error-correction code with a higher rate, or less redundancy. However, with puncturing the same decoder can be used regardless of how many bits have been punctured, thus puncturing considerably increases the flexibility of the system without significantly increasing its complexity.
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<p>A pre-defined pattern of puncturing is used in an encoder, in some cases. Then, the inverse operation, known as depuncturing, is implemented by the decoder.
</p><p>Puncturing is used in <a href="UMTS" title="UMTS">UMTS</a> during the rate matching process. It is also used in <a href="Wi-Fi" title="Wi-Fi">Wi-Fi</a>, Wi-SUN, <a href="GPRS" title="GPRS">GPRS</a>, <a href="EDGE_(telecommunication)" title="EDGE (telecommunication)">EDGE</a>, <a href="DVB-T" title="DVB-T">DVB-T</a> and <a href="Digital_Audio_Broadcasting" title="Digital Audio Broadcasting">DAB</a>, as well as in the <a href="Digital_Radio_Mondiale" title="Digital Radio Mondiale">DRM</a> Standards.
</p><p>Puncturing is often used with the <a href="Viterbi_algorithm" title="Viterbi algorithm">Viterbi algorithm</a> in coding systems.
</p><p>During <a href="Radio_Resource_Control" title="Radio Resource Control">Radio Resource Control</a> (RRC) Connection set procedure, during sending NBAP radio link setup message the uplink puncturing limit will send to NODE B, along with U/L spreading factor & U/L scrambling code.<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>Puncturing was introduced by <a href="Gustave_Solomon" title="Gustave Solomon">Gustave Solomon</a> and <a href="J._J._Stiffler" title="J. J. Stiffler">J. J. Stiffler</a> in 1964.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>
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<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Singleton_bound" title="Singleton bound">Singleton bound</a>, an upper bound in coding theory</li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">
Chris Johnson.
<a rel="nofollow" class="external text" href="https://books.google.com/books?id=sHGO_I_q0c8C">"Radio Access Networks for UMTS: Principles and Practice"</a>.
2011.</span>
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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFSolomomStiffler1964" class="citation news cs1">Solomom, G.; Stiffler, J. J. (1964). "Punctured Systematic Cyclic Codes". <i>IEEE Convention Record</i>. Vol. 12.</cite> </span>
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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFSolomonStiffler1965" class="citation journal cs1">Solomon, G.; Stiffler, J.J. (April 1965). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0019-9958%2865%2990080-X">"Algebraically punctured cyclic codes"</a>. <i>Information and Control</i>. <b>8</b> (2): <span class="nowrap">170–</span>79. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0019-9958%2865%2990080-X">10.1016/S0019-9958(65)90080-X</a></span>.</cite> </span>
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<ul><li><cite id="CITEREFPless2011" class="citation book cs1"><a href="Vera_Pless" title="Vera Pless">Pless, Vera</a> (2011). <a href="Introduction_to_the_Theory_of_Error-Correcting_Codes" title="Introduction to the Theory of Error-Correcting Codes"><i>Introduction to the Theory of Error-Correcting Codes</i></a>. Wiley Series in Discrete Mathematics and Optimization. Vol. 48 (Third ed.). John Wiley & Sons. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1118030998</bdi>.</cite></li></ul>
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