SherbyNet - /page/wikibook/entry.mu

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</style><div role="note" class="hatnote navigation-not-searchable">This article is about binary codes used in radiocommunications. For the authentication codes used to command a launch of nuclear weapons, see <a href="Gold_Codes" title="Gold Codes">Gold Codes</a>.</div>

<p>A <b>Gold code</b>, also known as <b>Gold sequence</b>, is a type of binary <a href="Sequence" title="Sequence">sequence</a>, used in <a href="Telecommunications" title="Telecommunications">telecommunications</a> (<a href="CDMA" class="mw-redirect" title="CDMA">CDMA</a>)<sup id="cite_ref-George-Hamid-Miller_2008_1-0" class="reference"><a href="#cite_note-George-Hamid-Miller_2008-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and satellite navigation (<a href="GPS" class="mw-redirect" title="GPS">GPS</a>).<sup id="cite_ref-GPS_2009_2-0" class="reference"><a href="#cite_note-GPS_2009-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Gold codes are named after Robert Gold.<sup id="cite_ref-Gold_2011_3-0" class="reference"><a href="#cite_note-Gold_2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Gold_1967_4-0" class="reference"><a href="#cite_note-Gold_1967-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Gold codes have bounded small <a href="Cross-correlation" title="Cross-correlation">cross-correlations</a> within a set, which is useful when multiple devices are broadcasting in the same frequency range. A set of Gold code sequences consists of 2<sup><i>n</i></sup> + 1 sequences each one with a period of 2<sup><i>n</i></sup> − 1.

</p><p>A set of Gold codes can be generated with the following steps. Pick two <a href="Maximum_length_sequence" title="Maximum length sequence">maximum length sequences</a> of the same length 2<sup><i>n</i></sup> − 1 such that their absolute <a href="Cross-correlation" title="Cross-correlation">cross-correlation</a> is less than or equal to 2<sup>(<i>n</i>+2)/2</sup>, where <i>n</i> is the size of the <a href="Linear-feedback_shift_register" title="Linear-feedback shift register">linear-feedback shift register</a> used to generate the maximum length sequence.<sup id="cite_ref-Gold_1967_4-1" class="reference"><a href="#cite_note-Gold_1967-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The set of the 2<sup><i>n</i></sup> − 1 <a href="Exclusive-or" class="mw-redirect" title="Exclusive-or">exclusive-ors</a> of the two sequences in their various phases (i.e. translated into all relative positions) together with the two maximum length sequences form a set of 2<sup><i>n</i></sup> + 1 Gold code sequences. The highest absolute cross-correlation in this set of codes is 2<sup>(<i>n</i>+2)/2</sup> + 1 for even <i>n</i> and 2<sup>(<i>n</i>+1)/2</sup> + 1 for odd <i>n</i>.

</p><p>The <a href="Exclusive_or" title="Exclusive or">exclusive or</a> of two different Gold codes from the same set is another Gold code in some phase.

</p><p>Within a set of Gold codes about half of the codes are balanced – the number of ones and zeros differs by only one.<sup id="cite_ref-Holmes_2007_5-0" class="reference"><a href="#cite_note-Holmes_2007-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p><p>Gold codes are used in <a href="GPS" class="mw-redirect" title="GPS">GPS</a>. The <a href="GPS_signals#Coarse/acquisition_code" title="GPS signals">GPS C/A</a> ranging codes are Gold codes of period 1,023.

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<ul><li><a href="Hadamard_code" title="Hadamard code">Hadamard code</a></li>

<li><a href="Kasami_code" title="Kasami code">Kasami code</a></li>

<li><a href="Zadoff%E2%80%93Chu_sequence" title="Zadoff–Chu sequence">Zadoff–Chu sequence</a></li>

<li><a href="Complementary_sequences" title="Complementary sequences">Complementary sequences</a></li>

<li><a href="Space_Network" title="Space Network">Space Network</a> – a NASA system that uses Gold codes</li></ul>

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

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</style><cite id="CITEREFGeorgeHamidMiller2001" class="citation web cs1">George, Maria; Hamid, Mujtaba; Miller, Andy (2001-01-10). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080705134550/http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf">"Gold Code Generators in Virtex Devices"</a> <span class="cs1-format">(PDF)</span>. <i>Virtex Series, Virtex-II Series, and Spartan-II family</i> (Application note). 1.1. <a href="Xilinx" title="Xilinx">Xilinx</a>. XAPP217. Archived from <a rel="nofollow" class="external text" href="http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2008-07-05.</cite> (9 pages)</span>

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<li id="cite_note-GPS_2009-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-GPS_2009_2-0">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://archive.today/20120804185510/http://www.kowoma.de/en/gps/signals.htm">"Transmitted GPS Signals"</a>. <i>The GPS System</i>. kowoma GPS. 2009-04-19. Archived from <a rel="nofollow" class="external text" href="http://www.kowoma.de/en/gps/signals.htm">the original</a> on 2012-08-04.</cite></span>

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<li id="cite_note-Gold_2011-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gold_2011_3-0">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170624101852/http://www.rgcsystems.com/ppl1_gold.htm">"Robert Gold, BS, MS, Ph.D."</a> Robert Gold Comm Systems. 2011. Archived from <a rel="nofollow" class="external text" href="http://www.rgcsystems.com/ppl1_gold.htm">the original</a> on 2017-06-24<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-07-18</span></span>.</cite></span>

</li>

<li id="cite_note-Gold_1967-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gold_1967_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gold_1967_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFGold1967" class="citation journal cs1 cs1-prop-long-vol">Gold, Robert (October 1967). "Optimal binary sequences for spread spectrum multiplexing". <i><a href="IEEE_Transactions_on_Information_Theory" title="IEEE Transactions on Information Theory">IEEE Transactions on Information Theory</a></i> (Correspondence). IT-13 (4): <span class="nowrap">619–</span>621. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTIT.1967.1054048">10.1109/TIT.1967.1054048</a>.</cite></span>

</li>

<li id="cite_note-Holmes_2007-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Holmes_2007_5-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFHolmes2007" class="citation book cs1">Holmes, Jack K. (2007-06-30). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-AUfAQAAIAAJ"><i>Spread Spectrum Systems for GNSS and Wireless Communications</i></a>. GNSS Technology and Applications Series. Vol. 45. Artech House. p. 100. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-59693-083-4</bdi>.</cite></span>

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<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFGoiser1998" class="citation book cs1 cs1-prop-foreign-lang-source">Goiser, Alois M. J. (1998). "4.3.2. Gold-Folgen" [Gold sequences]. <i>Handbuch der Spread-Spectrum Technik</i> [<i>Handbook of the spread-spectrum technique</i>] (in German) (1 ed.). Vienna, Austria: <a href="Springer_Verlag" class="mw-redirect" title="Springer Verlag">Springer Verlag</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>3-211-83080-4</bdi>.</cite></li>

<li><cite id="CITEREFSkaugHjelmstad1985" class="citation book cs1">Skaug, Reidar; Hjelmstad, Jens F. (1985). "Coding for bandwidth spreading". In Flood, J. E.; Hughes, C. J. (eds.). <i>Spread Spectrum in Communication</i>. IEE Telecommunications Series. Vol. 12 (1 ed.). London, UK: Peter Peregrinus Ltd. / <a href="The_Institution_of_Electrical_Engineers" class="mw-redirect" title="The Institution of Electrical Engineers">The Institution of Electrical Engineers</a>. pp. 82–. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-86341-034-0</bdi>.</cite> (xii+201+1 pages)</li>

<li><cite id="CITEREFRudolphRudolph2011" class="citation book cs1 cs1-prop-foreign-lang-source">Rudolph, Dietmar; Rudolph, Matthias (2011-04-12). "46.3.1 Gold-Codes". <a rel="nofollow" class="external text" href="http://www.diru-beze.de/modulationen/skripte/Modulationsverfahren.pdf"><i>Modulationsverfahren</i></a> <span class="cs1-format">(PDF)</span> (in German). Cottbus, Germany: <a href="Brandenburg_University_of_Technology" title="Brandenburg University of Technology">Brandenburg University of Technology</a> (BTU). pp. <span class="nowrap">212–</span>214. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210616042506/http://www.diru-beze.de/modulationen/skripte/Modulationsverfahren.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2021-06-16<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-06-14</span></span>.</cite> (xiv+225 pages)</li></ul>

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</style><div id="Spread_spectrum_in_digital_communications293" style="font-size:114%;margin:0 4em"><a href="Spread_spectrum" title="Spread spectrum">Spread spectrum</a> in digital communications</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" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Spread_spectrum" title="Spread spectrum">Spread spectrum</a></li>

<li><a href="Code-division_multiple_access" title="Code-division multiple access">Code-division multiple access (CDMA)</a></li></ul>

<dl><dt>History</dt>

<dd><a href="Spread_spectrum#Commercial_use" title="Spread spectrum">Commercial use</a></dd>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Spread spectrum <i>methods</i></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Direct-sequence_spread_spectrum" title="Direct-sequence spread spectrum">Direct-sequence spread spectrum</a> (DSSS)</li>

<li><a href="Frequency-hopping_spread_spectrum" title="Frequency-hopping spread spectrum">Frequency-hopping spread spectrum</a> (FHSS)</li>

<li><a href="Chirp_spread_spectrum" title="Chirp spread spectrum">Chirp spread spectrum</a> (CSS)</li>

<li><a href="Time-hopping" title="Time-hopping">Time-hopping spread spectrum</a> (THSS)</li></ul>

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

<li><a href="TD-SCDMA" class="mw-redirect" title="TD-SCDMA">TD-SCDMA</a></li>

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

<ul><li><a href="Space_Network" title="Space Network">Space Network</a> (NASA)</li>

<li><a href="Galileo_(satellite_navigation)" title="Galileo (satellite navigation)">Galileo</a></li>

<li><a href="GLONASS" title="GLONASS">GLONASS</a></li>

<li><a href="Bluetooth" title="Bluetooth">Bluetooth</a></li>

<li><a href="Cordless_telephone" title="Cordless telephone">Cordless phones</a>: <a href="Digital_Enhanced_Cordless_Telecommunications" class="mw-redirect" title="Digital Enhanced Cordless Telecommunications">DECT</a></li></ul>

<dl><dt><a href="Mobile_phone" title="Mobile phone">Cellular</a></dt>

<dd><a href="Evolution-Data_Optimized" title="Evolution-Data Optimized">EV-DO</a> Mobile</dd>

<dd><a href="CdmaOne" title="CdmaOne">IS-95</a> (aka cdmaOne)</dd>

<dd><a href="Qualcomm" title="Qualcomm">Qualcomm</a></dd>

<dd><a href="Verizon_Wireless" class="mw-redirect" title="Verizon Wireless">Verizon</a></dd></dl>

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

<ul><li><a href="Pseudorandom_noise#PN_Code" title="Pseudorandom noise">PN (pseudorandom noise) code</a></li>

<li><a href="Near%E2%80%93far_problem" title="Near–far problem">Near–far problem</a></li>

<li><a href="Spectral_density" title="Spectral density">Power spectral density</a> (PSD)</li>

<li><a href="Process_gain" title="Process gain">Process gain</a></li>

<li><a href="Rake_receiver" title="Rake receiver">Rake receiver</a></li>

<li><a href="Low_probability_of_intercept" class="mw-redirect" title="Low probability of intercept">Low probability of intercept</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<dd><a href="Data_transmission" class="mw-redirect" title="Data transmission">Digital communication</a></dd>

<dd><a href="Modulation" class="mw-redirect" title="Modulation">Modulation</a></dd>

<dd><a href="Statistical_time-division_multiplexing" title="Statistical time-division multiplexing">Statistical multiplexing</a></dd>

<dd><a href="Waveform" title="Waveform">Waveform</a></dd></dl>

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