00 01 10 11 s[1] 00 11 u 1 /c 1 (1) c 1 (2) 00 01 10 11 s[2] 00 11 01 10 u 2 /c 2 (1) c 2 (2) 00 01 10 11 s[3] 00 11 10 01 00 11 10 u 3 /c 3 (1) c 3 (2)

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Presentation transcript:

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] /c 5 (1) c 5 (2) s[6] /c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1,-1

s[1] 11 u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] /c 5 (1) c 5 (2) s[6] /c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1,-1 5.5

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] /c 5 (1) c 5 (2) s[6] /c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1,

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] /c 5 (1) c 5 (2) s[6] /c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1,

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] /c 5 (1) c 5 (2) s[6] /c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1,

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1,

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α1

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α α2α

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α α2α α3α

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α α2α α3α α4α

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α α2α α3α α4α α5α α6α

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α α2α α3α α4α α5α α6α β6β

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α α2α α3α α4α α5α α6α β6β β5β

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α α2α α3α α4α α5α α6α β6β β5β β4β

s[1] u 1 /c 1 (1) c 1 (2) s[2] u 2 /c 2 (1) c 2 (2) s[3] u 3 /c 3 (1) c 3 (2) s[4] u 4 /c 4 (1) c 4 (2) s[5] 0/c 5 (1) c 5 (2) s[6] 0/c 6 (1) c 6 (2) s[7] y 1, y 2 =0.9,0.8y 3, y 4 =-0.1,0.5y 5, y 6 =0.3,0.2 y 7, y 8 =-2,-2y 9, y 10 =-2,2y 11, y1 2 =-1, α0α α1α α2α α3α α4α α5α α6α β6β β5β β4β β3β

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 1 α0α0 β0β s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 5.5 α1α1 β1β s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 8.2 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 13.7 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 188 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 197 α5α5 β5β s[7] α6α6 β6β

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 1 α0α0 β0β s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 5.5 α1α1 β1β s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 8.2 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 13.7 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 188 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 197 α5α5 β5β s[7] α6α6 β6β

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 1 α0α0 β0β s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 5.5 α1α1 β1β s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 8.2 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 13.7 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 188 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 197 α5α5 β5β s[7] α6α6 β6β

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 1 α0α0 β0β s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 5.5 α1α1 β1β s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 8.2 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 13.7 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 188 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 197 α5α5 β5β s[7] α6α6 β6β

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 1 α0α0 β0β s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 5.5 α1α1 β1β s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 8.2 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 13.7 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 188 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 197 α5α5 β5β s[7] α6α6 β6β

00 s[0]s[1] 00 z[0], z[1]=0.9, s[2] z[2], z[3]=-0.1, z[4], z[5]=0.3,0.2 s[3]s[4] z[6], z[7]=-2, s[5]s[6] z[8], z[9]=-2,2z[10], z[11]=-1, Viterbi estimate of four info bits: 0001

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 1 α0α0 β0β s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 5.5 α1α1 β1β s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 8.2 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 13.7 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 188 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 197 α5α5 β5β s[7] α6α6 β6β

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 0 α0α0 β0β0 -C s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 1.7 α1α1 β1β C C C s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 2.1 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 2.6 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 5.2 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 5.3 α5α5 β5β C s[7] 12.6 α6α6 β6β6 0 -C

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 0 α0α0 β0β0 -C s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 1.7 α1α1 β1β C C C s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 2.1 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 2.6 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 5.2 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 5.3 α5α5 β5β C s[7] 12.6 α6α6 β6β6 0 -C

s[1] y 1, y 2 =0.9,0.8 u 1 /c 1 (1) c 1 (2) 0 α0α0 β0β0 -C s[2] y 3, y 4 =-0.1,0.5 u 2 /c 2 (1) c 2 (2) 1.7 α1α1 β1β C C C s[3] y 5, y 6 =0.3,0.2 u 3 /c 3 (1) c 3 (2) 2.1 α2α2 β2β s[4] y 7, y 8 =-2,-2 u 4 /c 4 (1) c 4 (2) 2.6 α3α3 β3β s[5] y 9, y 10 =-2,2 0/c 5 (1) c 5 (2) 5.2 α4α4 β4β s[6] y 11, y1 2 =-1,-1 0/c 6 (1) c 6 (2) 5.3 α5α5 β5β C s[7] 12.6 α6α6 β6β6 0 -C