A Simple Scheme for Belief Propagation Decoding of BCH and RS Codes in Multimedia Transmissions

<table>Simulated BER (a) and FER (b) for the DVB-S2 BCH code with <svg height="15.1375" id="M177" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 78.8125 15.1375" width="78.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,8.6,14.938)"><path d="M152 404l81 35q23 10 41 10q81 0 139 -61.5t58 -149.5q0 -107 -74.5 -178.5t-176.5 -71.5q-71 0 -147 36v555q0 48 -9.5 59.5t-56.5 15.5v23q79 10 145 35v-308zM152 374v-258q0 -20 6 -35q7 -19 30 -37t58 -18q63 0 99.5 50t36.5 137q0 82 -43.5 131t-108.5 49
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<g transform="matrix(.017,-0,0,-.017,31.412,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,46.099,10.862)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g><g transform="matrix(.017,-0,0,-.017,54.259,10.862)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,62.418,10.862)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,70.578,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg>. The performance of an LDPC code with the same length and rate is also shown for comparison.</table>

International Journal of Digital Multimedia Broadcasting

fig6

Figure 6

Figure 6: A Simple Scheme for Belief Propagation Decoding of BCH and RS Codes in Multimedia Transmissions 