S0

S1

S2

S3

00 00 00 00 00 00 00

11 11 11 11 11

10 10 1001 01 01 01

10 10 10 10 10

11 11 11 11 1100 00 00

01 01 01

J 0 1 2 3 4 5 65+1

75+2

Trellis Diagram

Code Tree

S0

S0

S2

S0

S2

S1

S3

S0

S2

S1

S3

S0

S2

S1

S3

00

1

10

01

00

00

00

00 00

11

11

11

11

1001

1100

011000

11

1001

1100

0110

0011

1001

1100

011000

11

1001

1100

0110

10

01

10

10

11

11

00

01

00

11

10

01

01

11

00

10

01

10

01

11

0

S0

S0

S2

S0

S2

S1

S3

S0

S2

S1

S3

S0

S2

S1

S3

00

1

10

01

00

00

00

00 00

11

11

11

11

1001

1100

011000

11

1001

1100

0110

0011

1001

1100

0110

0011

1001

1100

0110

10

01

10

10

11

11

00

01

00

11

10

01

01

11

00

10

01

10

01

11

0

S2

S3

S0

01

11

Code Tree (Encoding )

S0

S1

S2

S3

00 00 00 00 00 00 00

11 11 11 11 11

10 10 1001 01 01 01

10 10 10 10 10

11 11 11 11 1100 00 00

01 01 01

J 0 1 2 3 4 5 65+1

75+2

1 0 1 1 1

01

Trellis Diagram (Encoding)

S0

S1

S2

S3

00 00 00 00 00 00 00

11 11 11 11 11

10 10 1001 01 01 01

10 10 10 10 10

11 11 11 11 1100 00 00

01 01 01

J 0 1 2 3 4 5 65+1

75+2

1011 00 01 10 01 11

(2)

(0)

(3)

(3)

(0)

(2)

(3)(2)

(5)(0)

(4)(2)

(4)(3)

(3)(3)

(3)(3)

(2)(4)

(0)(5)

(4)(3)

(4)(3)

(3)(1)

(5)(0)

1

01

1

1

Viterbi Algorithm

S0

S1

S2

S3

00 00 00 00 00 00 00

11 11 11 11 11

10 10 1001 01 01 01

10 10 10 10 10

11 11 11 11 1100 00 00

01 01 01

J 0 1 2 3 4 5 65+1

75+2

1011 01 01 10 01 11

(2)

(0)

(3)

(3)

(0)

(2)

(4)(3)

(4)(1)

(5)(3)

(3)(4)

(4)(4)

(4)(4)

(3)(4)

(1)(5)

(5)(4)

(5)(4)

(4)(2)

(6)(1)

1

01

1

1

Viterbi Algorithm

Sequential Decoding

• Consider (2,1,1) convolutional encoder

( Eg:)

C(1)

C(2)FFP

S0

S0

S1

S0

S1

S0

S1

S0

S1

S0

S1

S0

S1

S0

S1

11

1

10

01

00

00

00

00

11

11

11

10

01

01

10

00

00

11

10

00

11

10

01

01

00

11

10

01

10

01

11

0

t1t1

bb

0

bb bb

1

1

0 1