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ofdm technology under the supervision of great scientist sklar
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内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/622b61b215da9b288b39c506/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622b61b215da9b288b39c506/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Fundamentals of Turbo Codes</div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls1 ws1">by</div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 ls2 ws1">Bernard Sklar</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls3 ws1">Introduction</div><div class="t m0 x4 h5 y5 ff2 fs3 fc0 sc0 ls4 ws2">Concatenated coding schemes were first proposed by Forney [1] as a m<span class="_ _0"></span>ethod for</div><div class="t m0 x4 h5 y6 ff2 fs3 fc0 sc0 ls5 ws3">achieving large coding gains by combining tw<span class="ls6">o or more relatively sim<span class="_ _0"></span>ple building-</span></div><div class="t m0 x4 h5 y7 ff2 fs3 fc0 sc0 ls7 ws4">block or</div><div class="t m0 x5 h6 y8 ff3 fs3 fc0 sc0 ls8 ws1"> </div><div class="t m0 x6 h7 y9 ff4 fs3 fc0 sc0 ls9 ws5">component codes</div><div class="t m0 x7 h5 ya ff2 fs3 fc0 sc0 lsa ws5"> (sometimes called </div><div class="t m0 x8 h7 y9 ff4 fs3 fc0 sc0 lsb ws6">constituent codes</div><div class="t m0 x9 h5 ya ff2 fs3 fc0 sc0 lsa ws7">). The resulting</div><div class="t m0 x4 h5 yb ff2 fs3 fc0 sc0 ls4 ws2">codes had the error-correction capability of much longer codes, and they were</div><div class="t m0 x4 h5 yc ff2 fs3 fc0 sc0 ls9 ws5">endowed with a structure that permitted <span class="lsa">relatively easy to moderately complex</span></div><div class="t m0 x4 h5 yd ff2 fs3 fc0 sc0 ls9 ws5">decoding. A serial concatenation of code<span class="ls6 ws8">s is most often used for power-limited</span></div><div class="t m0 x4 h5 ye ff2 fs3 fc0 sc0 ls4 ws2">systems such as transmitters on deep-s<span class="lsa ws7">pace probes. The most popular of these</span></div><div class="t m0 x4 h5 yf ff2 fs3 fc0 sc0 lsa ws9">schemes consists of a Reed-Solomon outer<span class="ls4 ws2"> (applied first, removed last) code</span></div><div class="t m0 x4 h5 y10 ff2 fs3 fc0 sc0 ls5 ws3">followed by a convolutional inner (applied la<span class="lsc wsa">st, removed first) code [2].<span class="_ _0"></span> A turbo</span></div><div class="t m0 x4 h5 y11 ff2 fs3 fc0 sc0 lsa ws7">code can be thought of as a refinement of<span class="ls9"> the concatenated encoding structure plus</span></div><div class="t m0 x4 h5 y12 ff2 fs3 fc0 sc0 lsb ws6">an iterative algorithm for decoding <span class="ls8 wsb">the associated code sequence.</span></div><div class="t m0 x4 h5 y13 ff2 fs3 fc0 sc0 lsb ws6">Turbo codes were first introduced in 1993 by Berrou, Glavieux, and</div><div class="t m0 x4 h5 y14 ff2 fs3 fc0 sc0 lsa ws7">Thitimajshima, and reported in [3, 4]<span class="_ _0"></span>, wher<span class="lsd wsc">e a scheme is described that achieves a</span></div><div class="t m0 x4 h5 y15 ff2 fs3 fc0 sc0 lse wsd">bit-error probability of 10</div><div class="t m0 xa h8 y16 ff2 fs4 fc0 sc0 lsf ws1">-5</div><div class="t m0 xb h5 y17 ff2 fs3 fc0 sc0 ls10 ws9"> using a rate 1/2 code over an additive white Gaussian</div><div class="t m0 x4 h5 y18 ff2 fs3 fc0 sc0 ls11 ws5">noise (AWGN) channel and BPSK modulation at an </div><div class="t m0 xc h7 y19 ff4 fs3 fc0 sc0 ls8 ws1">E</div><div class="t m0 xd h9 y1a ff4 fs4 fc0 sc0 ls8 ws1">b</div><div class="t m0 xe h7 y1b ff4 fs3 fc0 sc0 ls12 ws1">/N</div><div class="t m0 xf h8 y1c ff2 fs4 fc0 sc0 ls8 ws1">0</div><div class="t m0 x10 h5 y1d ff2 fs3 fc0 sc0 ls13 wse"> of 0.7 dB. The codes are</div><div class="t m0 x4 h5 y1e ff2 fs3 fc0 sc0 ls12 wsf">constructed by using two or more component<span class="ls14 ws2"> codes on different interleaved versions</span></div><div class="t m0 x4 h5 y1f ff2 fs3 fc0 sc0 ls10 ws9">of the same information sequence. Whereas, <span class="ls11 ws5">for conventional codes, the final step at</span></div><div class="t m0 x4 h5 y20 ff2 fs3 fc0 sc0 ls14 ws2">the decoder yields hard-decision decoded bits (or, more generally, decoded symbols),</div><div class="t m0 x4 h5 y21 ff2 fs3 fc0 sc0 ls15 ws10">for a concatenated scheme such as a tu<span class="ls14 ws2">rbo code to work properly, the decoding</span></div><div class="t m0 x4 h5 y22 ff2 fs3 fc0 sc0 ls14 ws6">algorithm should not limit itself to passing hard decisions am<span class="_ _0"></span>ong the decoders. To</div><div class="t m0 x4 h5 y23 ff2 fs3 fc0 sc0 ls14 ws2">best exploit the information learned fro<span class="ls15 ws10">m each decoder, the decoding algorithm must</span></div><div class="t m0 x4 h5 y24 ff2 fs3 fc0 sc0 ls13 wse">effect an exchange of soft decisions rather than hard decisions. For a system with two</div><div class="t m0 x4 h5 y25 ff2 fs3 fc0 sc0 ls14 ws2">component codes, the concept behind turbo <span class="ls16 ws8">decoding is to pass soft decisions from</span></div><div class="t m0 x4 h5 y26 ff2 fs3 fc0 sc0 ls17 wsa">the output of one decoder to the input of the <span class="ws5">other decoder, and to iterate this process</span></div><div class="t m0 x4 h5 y27 ff2 fs3 fc0 sc0 ls10 ws9">several times so as to produce more reliable decisions.</div><div class="t m0 x4 h4 y28 ff1 fs2 fc0 sc0 ls18 ws11">Likelihood Functions</div><div class="t m0 x4 h5 y29 ff2 fs3 fc0 sc0 ls4 ws2">The mathematical foundations of hypothesis testing rest on Bayes&#8217; theorem<span class="_ _0"></span>. For</div><div class="t m0 x4 h5 y2a ff2 fs3 fc0 sc0 lsa ws7">communications engineering, where app<span class="lsc wsa">lications involving an AWGN channel are</span></div><div class="t m0 x4 h5 y2b ff2 fs3 fc0 sc0 lsa ws7">of great interest, the most useful <span class="lsd wsc">form of Bayes&#8217; theorem expresses the </span></div><div class="t m0 x11 h7 y2c ff4 fs3 fc0 sc0 ls19 ws12">a posteriori</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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