第9章 差错控制编码

9 9.1 9.2 9.3 9.4 9.5 9.6

9.1 ,(),.

: ,

12331TI23ACKNAK,,.

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 (,,)

9.2

3

4nkn k n k = r 1 d0

d0 e d0 e + 1 t d0 2 t + 1 t e d0 e + t +1Bd0BA12BB345d0

n=7 P=10-3 P(1) 710-3 P(2) 2.110-5 P(3) 3.510-8

,,1 ~ 2,.

9.3 ,,1().

,

,,,

1(0).10,.

,,,1.

9.4 .,,,. (2). ()

,S,. S=0,S=1 ., rr,2r-1,,2r-1.(n,k),2r-1n .

(n,k)k=4,,r3, n=k+r=7

n=2r 1 k= 2r 1 r r12

=1=

HH Pr k Ir r r [ P Ir ]H 2=

QGAG

A

AB=[bn-1 bn-2 b0] B A = E E= [en-1 en-2 e0]

B=A+E

3

3

10S0

B1B2B32 S2=H 1 E=[1 0 0 0 0 0] 1

S3=H 3 E=[0 0 1 0 0 0] 3

,(0)

9.5 9.5.1 ,,.,,,.n

F(x) = N(x) Q(x) + R(x) F(x) R(x) ( N(x) )

, T(x)n,xi T(x)xn +1,. T(x)

nk2k

gxk-10k0 0k00k-1gx0n-k

g(x),xg(x),x2g(x), xk-1g(x),,G

mk-1 mk-2 m0

T(x)g(x),,k-1g(x).g(X) T(x) = h(x) g(x) g(x), xkg(x)xn+1, =1

g(x) xn+1n k, g(x) .

9.5.2 n,k)g(x),xn+1n-kg(x). T(x)g(x),m(x). n-k0

(7,3) m(x)=x2+x, g(x)= x4 +x2+ x+1

r(x)

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

R(x)g(x),, R(x)g(x), .

9.6 ,.kn,kn,,.n k,N-1,Nn.NnN,(n,k,N)

6 5 4 3 2 1+bicibicik=1, n=2, N=6

b6 b5 b4 b3 b2 b1++S6 S5 S4 S3 S2 S1+ (2,1,6)bicici13?

b1,(1)

(1)E(b1),12(b1~b6,c1~c6)2,E(b1)=1, (2)331. 3,,1,b1,E(b1).(2)

Hb10

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

H170

In-k n-kPi n-kk0 n-k

h=[ PN 0 PN-1 0 PN-2 0 P1 In-k ]

hH1

G g g=[ IK Q1 0 Q2 0 Q3 0 QN ]Ik k Qi =PiT k n-k 0 k

313 a m1m200 b m1m201 c m1m210 d m1m211 M3 M2 M1++ mjmjy1jY2j

313a

313

313aabbccda111110101000011100001010abcd111000110101100001011010

a11010111

nkNkn2k2k(N-1)2k2k