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📄 reed_solomon.ps

📁 rs encoder in matlab 7,3
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b(Co)s(des)224 516y Ft(1)67 b(In)n(tro)r(duction)224 617 y Fs(A)18 b(Reed-Solomon)g(\(RS\))g(co)q(de)g(is)g(an)f(error-correcting)g(co)q(de)h(\014rst)f(describ)q(ed)j(in)e(a)224 674 y(pap)q(er)c(b)o(y)g(Reed)h(and)f(Solomon)g(in)g(1960)f([8)o(].)19 b(Enco)q(ding)c(data)e(using)i(an)e(RS)i(co)q(de)f(is)224 730 y(relativ)o(ely)k(straigh)o(tforw)o(ard,)d(but)i(deco)q(ding)i(is)e(time-consuming.)27 b(Despite)17b(ma)s(jor)224 787 y(e\016ciency)j(impro)o(v)o(emen)o(ts)e(made)h(b)o(y)f(Berlek)m(amp)i(and)e(others)g(during)i(the)e(1960's)224843 y([1,)11 b(4,)g(5,)h(7],)f(only)i(in)g(the)f(past)g(few)f(y)o(ears)h(has)g(it)g(b)q(ecome)h(computationally)g(p)q(ossible)224899 y(to)19 b(send)i(high-bandwidth)h(data)d(using)i(RS)f(co)q(des.)34b(Recen)o(t)21 b(applications)g(of)f(RS)224 956 y(co)q(des)d(include)i(CD-R)o(OMs,)e(wireless)g(comm)o(unications,)g(space)g(comm)o(unications,)224 1012 y(DSL,)e(D)o(VD,)f(and)i(digital)g(TV.)2951069 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b(so)eFr(m)p Fs(\()p Fr(x)p Fs(\))e Fn(2)h Fr(F)6 b Fs([)pFr(x)p Fs(].)295 738 y(Recall)18 b(that)e(there)h(is)g(exactly)h(one)e(p)q(olynomial)j(of)d(degree)h Fr(k)c Fn(\000)e Fs(1)17b(that)f(passes)224 795 y(through)f Fr(k)h Fs(p)q(oin)o(ts)g(\()pFr(x)617 802 y Fq(0)636 795 y Fr(;)8 b(y)679 802 y Fq(0)699795 y Fs(\))p Fr(;)g(:)g(:)g(:)k(;)c Fs(\()p Fr(x)870802 y Fp(k)q Fo(\000)p Fq(1)935 795 y Fr(;)g(y)978 802

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