00 01 10 11 s[0]s[1] s[2]s[3]s[4] 00 11 10 01 00 11 10 00 01 10 11 00 11 10 01 00 11 10 00 01 10 11 00 11 10 01 00 11 10 00 01 10 11 00 11 10 01 00 11.

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Presentation transcript:

s[0]s[1] s[2]s[3]s[4]

s[0]s[1] s[2]s[3]s[4]

s[0]s[1] s[2]s[3]s[4]

s[0]s[1] z[0], z[1]

s[0]s[1] 00: z[0]+z[1] z[0], z[1]=0.9,0.8

s[0]s[1] 00: z[0]+z[1] z[0], z[1]=0.9,

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9,

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] z[2], z[3]=-0.1,0.5

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] z[2], z[3]=-0.1,0.5

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] z[2], z[3]=-0.1,0.5

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] z[2], z[3]=-0.1,

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1,

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1,

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1,

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1,

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3,0.2 s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, =2.6 s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, = =-1.6 s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, = =-2.2 s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, = =-0.6 s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, = =1.4 s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] : -z[2]+z[3] z[2], z[3]=-0.1, z[4], z[5]=0.3, s[3]

s[0]s[1] 00: z[0]+z[1] 11: -z[0]-z[1] z[0], z[1]=0.9, s[2] 00: z[2]+z[3] 11 z[2], z[3]=-0.1, z[4], z[5]=0.3, s[3]

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, s[3]

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, s[3]s[4] z[6], z[7]=-2, = =-5.2

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, s[3]s[4] z[6], z[7]=-2,-2 5.2

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, s[3]s[4] z[6], z[7]=-2, = =1.4

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, s[3]s[4] z[6], z[7]=-2,

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, s[3]s[4] z[6], z[7]=-2, = =1.2

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, s[3]s[4] z[6], z[7]=-2,

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, s[3]s[4] z[6], z[7]=-2, = =1.6

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, s[3]s[4] z[6], z[7]=-2,

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,

00 Viterbi estimate of info bits:

s[0]s[1] s[2]s[3]s[4]

s[0]s[1] s[2]s[3]s[4] S[5] s[6] Extend by two states

s[0]s[1] s[2]s[3]s[4] S[5] s[6] With termination at 00

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,

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,-1

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,

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,

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 (accounting for termination) of four info bits: 0001

s[0]s[1] s[2]s[3]s[4] s[5]s[6]

Info bit sequence: 100… Codeword: … Input weight=1 Output weight =

Info bit sequence: 1100… Codeword: … Input weight=2 Output weight = 6

s[0]s[1] s[2]s[3]s[4] s[5]s[6]