第9章 差错控制编码
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Transcript of 第9章 差错控制编码
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9 9.1 9.2 9.3 9.4 9.5 9.6
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9.1 ,(),.
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: ,
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12331TI23ACKNAK,,.
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1 2 3 4 5 6 2 3 4 5 6 7 8 91 2 3 4 5 6 2 3 4 5 6 7 8 9NAK2 (,,)
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9.2
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3
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4nkn k n k = r 1 d0
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d0 e d0 e + 1 t d0 2 t + 1 t e d0 e + t +1Bd0BA12BB345d0
- AB1te01PP
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n=7 P=10-3 P(1) 710-3 P(2) 2.110-5 P(3) 3.510-8
,,1 ~ 2,.
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9.3 ,,1().
,
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,,,
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1(0).10,.
,,,1.
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9.4 .,,,. (2). ()
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,S,. S=0,S=1 ., rr,2r-1,,2r-1.(n,k),2r-1n .
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(n,k)k=4,,r3, n=k+r=7
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n=2r 1 k= 2r 1 r r12
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=1=
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HH Pr k Ir r r [ P Ir ]H 2=
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QGAG
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A
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AB=[bn-1 bn-2 b0] B A = E E= [en-1 en-2 e0]
B=A+E
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3
3
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10S0
B1B2B32 S2=H 1 E=[1 0 0 0 0 0] 1
S3=H 3 E=[0 0 1 0 0 0] 3
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,(0)
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9.5 9.5.1 ,,.,,,.n
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F(x) = N(x) Q(x) + R(x) F(x) R(x) ( N(x) )
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, T(x)n,xi T(x)xn +1,. T(x)
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nk2k
gxk-10k0 0k00k-1gx0n-k
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g(x),xg(x),x2g(x), xk-1g(x),,G
mk-1 mk-2 m0
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T(x)g(x),,k-1g(x).g(X) T(x) = h(x) g(x) g(x), xkg(x)xn+1, =1
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g(x) xn+1n k, g(x) .
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9.5.2 n,k)g(x),xn+1n-kg(x). T(x)g(x),m(x). n-k0
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(7,3) m(x)=x2+x, g(x)= x4 +x2+ x+1
r(x)
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a+b+cd+mfeS73m a b c d e f0 0 0 0 0 0 01 1 1 1 0 1 11 1 0 0 1 1 10 1 0 1 0 1 00 0 1 0 1 0 00 0 0 1 0 1 10 0 0 0 1 0 00 0 0 0 0 1 1f=mf=e
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R(x)g(x),, R(x)g(x), .
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9.6 ,.kn,kn,,.n k,N-1,Nn.NnN,(n,k,N)
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6 5 4 3 2 1+bicibicik=1, n=2, N=6
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b6 b5 b4 b3 b2 b1++S6 S5 S4 S3 S2 S1+ (2,1,6)bicici13?
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b1,(1)
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(1)E(b1),12(b1~b6,c1~c6)2,E(b1)=1, (2)331. 3,,1,b1,E(b1).(2)
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Hb10
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1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1
H1
nn-k
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H170
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In-k n-kPi n-kk0 n-k
h=[ PN 0 PN-1 0 PN-2 0 P1 In-k ]
hH1
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G g g=[ IK Q1 0 Q2 0 Q3 0 QN ]Ik k Qi =PiT k n-k 0 k
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313 a m1m200 b m1m201 c m1m210 d m1m211 M3 M2 M1++ mjmjy1jY2j
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313a
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313
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313aabbccda111110101000011100001010abcd111000110101100001011010
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a11010111
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nkNkn2k2k(N-1)2k2k