/+
, Shu LinDaniel J.Costello,
turbo codeLDPC codepolar50%50%email: [email protected]
1
State Key Laboratory of Integrated Services Networks
1.1
XYnm
P(y=b|x=a), a=(a1,a2,...an)X, b=(b1,b2,...bm)Y,n(m)
p(y=b|x=a), a=(a1,a2,...an)X, b=(b1,b2,...bm)Y, n(m)
m=nP(y=b|x=a)=P(y1|x1)P(y2|x2)...P(yn|xn) DMCm=np(y=b|x=a)= p(y1|x1)p(y2|x2)...p(yn|xn)
ISIy=Ax+n
AA=UTUA y= UTUx+nx=UTxy=UTyn=UTny=x+nxyUX-YX-Y
DMC
DMCDMC
State Key Laboratory of Integrated Services Networks
ShannonRCe
00001111nn1(n,1),()R=1/n
n=200110110n=3000111001, 010, 100, 011, 101, 110
n=4000011110001, 0010, 0100, 1000, 0011, 0101, 0110, 1100, 1001, 1010, 0111, 1101, 1110, 1011
MBPSKMFSK
()
State Key Laboratory of Integrated Services Networks
ExampleC: (1111011000)R: (0110010110)CRE1001001110R = C + E E(Error Pattern)
C1C2C1C2C1=10101, C2=01111, d(C1,C2)=3
C w(C1)=3, w(C2)=4
(n, k)d0d0
(n, k) 1) ed0>=e+1 2) td0>=2t+1 3) te (e>=t)d0>=e+t+1 4) t d0>=2t++1
R1/REsEbEb=Es/R
=(dB) (dB)
CRRn(n0,k0,m)p
BPSKAWGN
Chart3
0.01
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0.15
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0.25
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0.35
0.4
0.45
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0.55
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0.65
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0.75
0.8
0.855
0.9
0.951
0.97
0.98
0.99
0.995
0.999
(Eb/N0(dB))
R
Sheet1
-1.5480.01
-1.440.05
-1.2850.1
-1.1260.15
-0.9630.2
-0.7930.25
-0.6160.3
-0.4320.35
-0.2360.4
-0.0320.45
0.1880.5
0.4240.55
0.6820.6
0.960.65
1.2750.7
1.6280.75
2.0450.8
2.60.855
3.2050.9
4.2180.951
4.8410.97
5.3070.98
6.0230.99
6.6510.995
7.8640.999
Sheet1
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
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(Eb/N0(dB))
R
Sheet2
Sheet3
MC R RC,M
Shannon(1948)Hamming (1950)Forney(1966), (60)RSBCH(60)TCMUngerboeck(1982),Forney(1984)TurboBerrou(1993) LDPC Gallager(1963),Macky(1996),Tarokh(2000)PolarE.Arikan, 2009