Trellis Coded Modulation
Ungerboek Partitioning of 8-PAM
© Tallal Elshabrawy
Four State Trellis with Parallel Paths
S0
4
2 6
4
2
6
2
6
2
6
S1
0
0
4
0
2 6
0
4
0
4
1
S2
3 7
3
S3
© Tallal Elshabrawy
5
3 7
1
7
1
5
5
0
4
1
1
3
7
2 6
5
3 7
3
5
7
1
5
3
Four State Trellis with Parallel Paths
dmin for 3 Consecutive Symbols 0 0 0
2 6
S1
S2
3 7
3
S3
7
2 6
0
4
5
3 7
3
1
7
1
5
5
2 6
0
4
1
Distance between 0 0 0 and 0 0 4
© Tallal Elshabrawy
0
4
2
6
0
4
2
6
0
4
2
6
S0
5
1
3 7
3
7
1
5
0
4
5
1
Four State Trellis with Parallel Paths
dmin for 3 Consecutive Symbols 0 0 0
Distance between 0 0 0 and 0 0 4
d[0,0,0][, 0,0,4] = 0 + 0 + 82 = 8
© Tallal Elshabrawy
Four State Trellis with Parallel Paths
dmin for 3 Consecutive Symbols 0 0 0
2 6
S1
S2
3 7
3
S3
7
2 6
0
4
5
3 7
3
1
7
1
5
5
2 6
0
4
1
Distance between 0 0 0 and 2 1 2
© Tallal Elshabrawy
0
4
2
6
0
4
2
6
0
4
2
6
S0
5
1
3 7
3
7
1
5
0
4
5
1
Four State Trellis with Parallel Paths
dmin for 3 Consecutive Symbols 0 0 0
Distance between 0 0 0 and 2 1 2
d[0,0,0][, 2,1,2] = 42 + 22 + 42 = 6 = dmin
© Tallal Elshabrawy
8PAM-TCM
Trellis Representation of 4 PAM
dmin for 3 Consecutive Symbols 0 0 0
S0
S0
dmin
4PAM
0
0
0
1
1
1
2
3
2
3
2
3
3
2
0
0
0
-3
-1
1
1
1
2
3
2
3
2
3
= 02 + 02 + 22 = 2
© Tallal Elshabrawy
1
0
1
3
d4PAM  2
Coding Gain Four State Trellis TCM
Coding Gain Four State Trellis TCM
G  dB 
ES
ES
8PAM
4PAM
G  dB 
© Tallal Elshabrawy
8PAM TCM
2
 dmin

8PAMTCM

ES 8PAM 

 10  log10 
2
 dmin 4PAM



E
S
4PAM


2  72  2  52  2  32  2  12

 21
8
2  32  2  12

5
4
8PAM TCM
 36 21 
 10  log10 
  3.3 dB
 45 
9
Set Partitioning of 16 QAM
A0
B0
C0
B1
C1
D0
© Tallal Elshabrawy
D1
D2
C2
D3
D4
C3
D5
D6
D7
10
Calculating Min. Distance in Partition A
ES
10
3
dA  2
ES
10
ES
10

3
3
© Tallal Elshabrawy
ES
10

ES
10
ES
10
3
ES
10
ES
10
ES
10
11
Calculating Min. Distance in Partition B
ES
10
3
dB  2
2ES
10
ES
10

3
3
© Tallal Elshabrawy
ES
10

ES
10
ES
10
3
ES
10
ES
10
ES
10
12
Calculating Min. Distance in Partition C
ES
10
3
dC  4
ES
10
ES
10

3
3
© Tallal Elshabrawy
ES
10

ES
10
ES
10
3
ES
10
ES
10
ES
10
13
Calculating Min. Distance in Partition D
ES
10
3
dD  4
ES
10
2ES
10

3
3
© Tallal Elshabrawy
ES
10

ES
10
ES
10
3
ES
10
ES
10
ES
10
14
Set Partitioning of 16 QAM
dA  2
A0
dB  2
B0
dC  4
C0
D0
dD  4
D1
ES
10
2ES
10
B1
C1
D2
ES
10
C2
D3
D4
C3
D5
D6
D7
2ES
10
© Tallal Elshabrawy
15