rs.ps

reed-solomon编码的java实现

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(Benjamin Barras)setjob
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initializepage
(Benjamin Barras; page: 1 of 24)setjob
%%EndPageSetup
gS 0 0 576 820 rC
47 46 481 728 rC
47 46 481 714 rC
gR
gS 11 10 553 750 rC
47 75 :M
f66 sf
36 u66 :p
103.001 :m
3.439(Index)A
47 120 :M
f93 sf
-.139(1.)A
103 120 :M
f122 sf
1.568 .157(Codes de Reed-Solomon . . . . . . . . . . . . . . . . . . . .)J
487 120 :M
f93 sf
(2)S
47 139 :M
.555 .056(1.1 )J
117 139 :M
.757(D\216finition)A
f122 sf
.833 .083(  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 139 :M
f93 sf
(2)S
47 158 :M
.383(1.2)A
117 158 :M
.835(Information)A
f122 sf
.842 .084( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )J
487 158 :M
f93 sf
(2)S
47 177 :M
.555 .056(1.3 )J
117 177 :M
.91(Exemple)A
f122 sf
.742 .074(  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )J
487 177 :M
f93 sf
(2)S
47 196 :M
-.139(2.)A
103 196 :M
f122 sf
1.131 .113(Corps de Galois . . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 196 :M
f93 sf
(3)S
47 215 :M
.555 .056(2.1 )J
117 215 :M
3.821 .382(Propri\216t\216s d\325un corps fini)J
f122 sf
.904 .09( . . . . . . . . . . . . . . . . . . . .)J
487 215 :M
f93 sf
(3)S
47 234 :M
.555 .056(2.2 )J
117 234 :M
3.183 .318(Construction  d\325un corps fini)J
f122 sf
.828 .083( . . . . . . . . . . . . . . . . . .)J
487 234 :M
f93 sf
(4)S
47 253 :M
.388 .039(2.2.1 )J
132 253 :M
4.112 .411(Repr\216sentation des \216l\216ments )J
f122 sf
.861 .086(. . . . . . . . . . . . . . .)J
487 253 :M
f93 sf
(4)S
47 272 :M
.388 .039(2.2.2 )J
132 272 :M
.884(Exemple)A
f122 sf
.739 .074( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 272 :M
f93 sf
(5)S
47 291 :M
-.139(3.)A
103 291 :M
f122 sf
1.324 .132(Technique de codage  . . . . . . . . . . . . . . . . . . . . . . .)J
487 291 :M
f93 sf
(8)S
47 310 :M
.555 .056(3.1 )J
117 310 :M
.885(Exemple)A
f122 sf
.739 .074( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 310 :M
f93 sf
1.812(10)A
47 329 :M
-.139(4.)A
103 329 :M
f122 sf
1.482 .148(Technique de d\216codage . . . . . . . . . . . . . . . . . . . . .)J
487 329 :M
f93 sf
1.812(11)A
47 348 :M
.555 .056(4.1 )J
117 348 :M
5.279 .528(Equation fondamentale)J
f122 sf
.726 .073(  . . . . . . . . . . . . . . . . . . . . . .)J
487 348 :M
f93 sf
1.812(12)A
47 367 :M
.555 .056(4.2 )J
117 367 :M
5.569 .557(Algorithme d\325Euclide)J
f122 sf
.852 .085( . . . . . . . . . . . . . . . . . . . . . . . .)J
487 367 :M
f93 sf
1.812(13)A
47 386 :M
.555 .056(4.3 )J
117 386 :M
6.296 .63(Reed-Solomon algorithme)J
f122 sf
.815 .081(  . . . . . . . . . . . . . . . . . . .)J
487 386 :M
f93 sf
1.812(14)A
47 405 :M
.555 .056(4.4 )J
117 405 :M
2.404 .24(Sch\216ma d\325Horner  )J
f122 sf
.64 .064(. . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 405 :M
f93 sf
1.812(15)A
47 424 :M
.555 .056(4.5 )J
117 424 :M
3.824 .382(Exemple de d\216codage)J
f122 sf
.697 .07( . . . . . . . . . . . . . . . . . . . . . . .)J
487 424 :M
f93 sf
1.812(16)A
47 443 :M
.555 .056(4.6 )J
117 443 :M
3.691 .369(d\216tection d\325erreurs > t)J
f122 sf
.921 .092(  . . . . . . . . . . . . . . . . . . . . . .)J
487 443 :M
f93 sf
1.812(18)A
47 462 :M
-.139(5.)A
103 462 :M
f122 sf
1.989 .199(Pr\216sentation du programme . . . . . . . . . . . . . . . . .)J
487 462 :M
f93 sf
1.812(19)A
47 481 :M
.555 .056(5.1 )J
117 481 :M
.785(Classes)A
f122 sf
.708 .071(  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 481 :M
f93 sf
1.812(19)A
47 500 :M
.555 .056(5.2 )J
117 500 :M
3.664 .366(Liste de fichiers)J
f122 sf
.893 .089(  . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 500 :M
f93 sf
1.812(20)A
47 519 :M
-.139(6.)A
103 519 :M
f122 sf
.962 .096(Conclusions  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 519 :M
f93 sf
1.812(21)A
47 538 :M
.575(A.1)A
103 538 :M
f122 sf
.93 .093(Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 538 :M
f93 sf
1.812(22)A
47 557 :M
.575(A.2)A
103 557 :M
f122 sf
1.114 .111(R\216f\216rences  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)J
487 557 :M
f93 sf
1.812(24)A
gR
gS 47 761 481 13 rC
gR
gS 11 725 553 49 rC
261 771 :M
f135 sf
.413 .041(Page )J
f148 sf
(1)S
gR
endp
showpage
%%Page: 2 2
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initializepage
(Benjamin Barras; page: 2 of 24)setjob
%%EndPageSetup
gS 0 0 576 820 rC
47 46 481 728 rC
47 46 481 714 rC
gR
gS 11 10 553 750 rC
47 65 :M
f161 sf
3.671 .367(1. )J
f174 sf
24 u174 :p
286.128 :m
11.427 1.143(Codes de Reed-Solomon)J
47 113 :M
f161 sf
5.682 .568(1.1 )J
f174 sf
24 u174 :p
119.709 :m
2.336(D\216finition)A
95 155 :M
f93 sf
6.19 .619(Les codes de Reed-Solomon )J
328 155 :M
6.515 .652(RS\(k,t\) sont form\216s de n )J
47 176 :M
2.989 .299(symboles, avec n = q - 1 au maximum et )J
355 176 :M
1.74 .174(q = 2)J
f187 sf
0 -4 rm
.828(k)A
0 4 rm
f93 sf
3.407 .341(, chaque symbole )J
47 195 :M
3.526 .353(appartenant \210 GF\(q\) qui est le corps de Galois \(Galois Field\) \210 q )J
47 214 :M
4.445 .444(\216l\216ments, k repr\216sente donc le nombre de bits par symbole. Le )J
47 233 :M
5.38 .538(nombre )J
110 233 :M
5.713 .571(t repr\216sente le nombre de symboles d\325erreurs que ce )J
47 252 :M
3.536 .354(code sera capable de corriger.)J
47 271 :M
( )S
47 295 :M
f161 sf
5.288 .529(1.2 )J
f174 sf
24 u174 :p
142.262 :m
2.354(Information)A
95 333 :M
f93 sf
8.037 .804(Le nombre de symboles de contr\231le est de 2t. Par )J
47 352 :M
4.773 .477(cons\216quent, le nombre de symboles d\325information que l\325on peut  )J
47 371 :M
3.204 .32(transmettre est de m = n - 2t.)J
47 414 :M
f161 sf
4.831 .483(1.3 )J
f174 sf
24 u174 :p
98.9 :m
2.528(Exemple)A
95 452 :M
f93 sf
4.617 .462(Soit le code RS\(4,3\) )J
258 452 :M
4.827 .483(form\216 de n = 15 symboles, chaque )J
47 471 :M
3.468 .347(symbole \216tant contenu dans )J
257 471 :M
2.792 .279(GF\(16\), donc 4 bits par symbole. Soit )J
47 490 :M
3.624 .362(sous forme polyn\231miale :)J
76 528 :M
1.534 .153(w\(x\) = w)J
f148 sf
0 2 rm
.455(14)A
0 -2 rm
.207 .021( )J
f93 sf
.93 .093(. x)J
f148 sf
0 -3 rm
.455(14)A
0 3 rm
f93 sf
.7 .07( +  w)J
f148 sf
0 2 rm
.455(13)A
0 -2 rm
.207 .021( )J
f93 sf
.93 .093(. x)J
f148 sf
0 -3 rm
.455(13)A
0 3 rm
f93 sf
.772 .077( +  ... + w)J
f148 sf
0 2 rm
.455(1)A
0 -2 rm
.207 .021( )J
f93 sf
.93 .093(. x)J
f148 sf
0 -3 rm
.455(1)A
0 3 rm
f93 sf
.889 .089( + w)J
f148 sf
0 2 rm
(0)S
0 -2 rm
76 549 :M
f93 sf
2.069 .207(avec w)J
f148 sf
0 2 rm
.169(i)A
0 -2 rm
f93 sf
1.661 .166( contenu dans GF\(16\) pour i = 0,..,14.)J
47 589 :M
7.355 .735(Les coefficients w)J
f148 sf
0 2 rm
1.406(0)A
0 -2 rm
.703(,)A
f93 sf
2.557(w)A
f148 sf
0 2 rm
1.406(1)A
0 -2 rm
.703(,)A
f93 sf
.984(...)A
f148 sf
.703(,)A
f93 sf
2.557(w)A
f148 sf
0 2 rm
1.406(5)A
0 -2 rm
f93 sf
5.198 .52( sont les symboles du contr\231le de )J
47 610 :M
5.727 .573(parit\216 \(parity check\), et les coefficients )J
358 610 :M
1.57(w)A
f148 sf
0 2 rm
.863(6)A
0 -2 rm
.432(,)A
f93 sf
1.57(w)A
f148 sf
0 2 rm
.863(7)A
0 -2 rm
.432(,)A
f93 sf
.604(...)A
f148 sf
.432(,)A
f93 sf
1.57(w)A
f148 sf
0 2 rm
.863(14)A
0 -2 rm
f93 sf
3.742 .374( repr\216sente )J
47 631 :M
5.209 .521(les symboles d\325information \210 transmettre.)J
gR
gS 47 761 481 13 rC
gR
gS 11 725 553 49 rC
261 771 :M
f135 sf
.413 .041(Page )J
f148 sf
(2)S
gR
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showpage
%%Page: 3 3
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initializepage
(Benjamin Barras; page: 3 of 24)setjob
%%EndPageSetup
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47 46 481 728 rC
47 46 481 714 rC
gR
gS 11 10 553 750 rC
47 65 :M
f161 sf
4.052 .405(2. )J
f174 sf
24 u174 :p
189.63 :m
9.674 .967(Corps de Galois)J
76 103 :M
f93 sf
2.623 .262(La notation pour la suite, sera la suivante :)J
76 141 :M
3.203 .32(- F repr\216sente un corps fini \(Field\).)J
76 160 :M
1.887 .189(- F)J
f148 sf
0 2 rm
.797(p)A
0 -2 rm
f93 sf
3.1 .31( repr\216sente le corps fini \210 p \216l\216ments.)J
76 183 :M
2.141 .214(- F)J
f187 sf
0 -4 rm
.76(*)A
0 4 rm
f93 sf
3.93 .393( repr\216sente le groupe multiplicatif du corps F.)J
47 226 :M
f161 sf
5.996 .6(2.1 )J
f174 sf
24 u174 :p
302.268 :m
10.088 1.009(Propri\216t\216s d\325un corps fini)J
95 264 :M
f93 sf
4.39 .439(On rappelle ici, quelques propri\216t\216s utiles des corps finis. )J
47 283 :M
3.155 .315(Soit F un corps fini de caract\216ristique p ayant q \216l\216ments. Alors,)J
47 323 :M
.422 .042(  a\))J
82 323 :M
1.853 .185(F est un F)J
f148 sf
0 2 rm
.654(p)A
0 -2 rm
f93 sf
2.624 .262(-espace vectoriel de dimension k, avec q = p)J
f187 sf
0 -4 rm
.706(k)A
0 4 rm
f93 sf
(.)S
47 346 :M
.857 .086(  b\))J
82 346 :M
2.874 .287(Le groupe additif de F est isomorphe au groupe \(Z/pZ,+\))J
f187 sf
0 -4 rm
.717(k)A
0 4 rm
f93 sf
(.)S
47 370 :M
.776 .078(  c\))J
82 370 :M
1.362(F)A
f148 sf
0 -3 rm
.619(*)A
0 3 rm
f93 sf