1

3.2 Probabilitatea de eroare 0.1 si 1 rulare/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 7/50 0/50 0/50 6/50 0/50

Percentage error [%] 14 0 0 12 0

C1B

Bits with errors 2/132 4/132 24/132 9/132 0/132

Percentage error [%] 1.52 3 18.18 6.82 0

C2

Bits with errors 8/78 7/78 7/78 6/78 3/78

Percentage error [%] 10.26 8.97 8.98 7.69 3.85

Probabilitatea de eroare 0.1 si 2 rulari/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 5/50 4/50 24/50 2/50 1/50

Percentage error [%] 5 4 27 2 1

C1B

Bits with errors 18/132 29/132 23/132 4/132 30/132

Percentage error [%] 6.82 10.98 8.71 1.52 11.36

C2

Bits with errors 15/78 30/78 16/78 18/78 14/78

Percentage error [%] 9.62 19.23 10.26 11.54 8.97

Probabilitatea de eroare 0.1 si 5 rulari/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 15/50 15/50 20/50 2/50 14/50

Percentage error [%] 7.2 6 8 0.8 5.6

C1B

Bits with errors 12/132 41/132 52/132 64/132 67/132

Percentage error [%] 3.18 6.21 7.88 9.7 10.15

C2

Bits with errors 42/78 56/78 33/78 32/78 41/78

Percentage error [%] 10.78 14.36 8.46 8.21 10.51

Probabilitatea de eroare 0.1 si 10 rulari/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 11/50 55/50 36/50 38/50 43/50

Percentage error [%] 2.2 11 7.2 7.6 8.6

C1B

Bits with errors 100/132 116/132 105/132 144/132 134/132

Percentage error [%] 7.58 8.79 7.95 10.91 10.15

C2

Bits with errors 69/78 69/78 85/78 74/78 73/78

Percentage error [%] 8.85 8.85 10.9 9.49 9.36

2

Probabilitatea de eroare 0.1 si 20 rulari/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 80/50 58/50 63/50 36/50 92/50

Percentage error [%] 8 5.8 6.3 3.6 9.2

C1B

Bits with errors 197/132 258/132 210/132 154/132 153/132

Percentage error [%] 7.46 9.77 7.95 5.83 5.8

C2

Bits with errors 164/78 144/78 166/78 157/78 132/78

Percentage error [%] 10.51 9.23 10.64 10.06 8.46

Probabilitatea de eroare 0.1 si 50 rulari/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 234/50 123/50 195/50 199/50 145/50

Percentage error [%] 9.36 4.95 7.8 7.96 5.8

C1B

Bits with errors 464/132 386/132 450/132 527/132 424/132

Percentage error [%] 7.02 5.85 6.82 7.98 6.42

C2

Bits with errors 400/78 405/78 380/78 354/78 387/78

Percentage error [%] 10.26 10.38 9.74 9 9.92

Probabilitatea de eroare 0.1 si 100 rulari/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 339/50 414/50 294/50 235/50 332/50

Percentage error [%] 6.78 8.28 5.88 4.7 6.64

C1B

Bits with errors 921/132 954/132 834/132 879/132 869/132

Percentage error [%] 6.98 7.23 6.32 6.66 6.58

C2

Bits with errors 741/78 760/78 817/78 741/78 764/78

Percentage error [%] 9.5 9.74 10.47 9.5 9.79

Probabilitatea de eroare 0.1 si 200 rulari/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 773/50 756/50 737/50 627/50 714/50

Percentage error [%] 7.73 7.56 7.37 6.27 7.14

C1B

Bits with errors 1793/132 1869/132 1788/132 1844/132 1840/132

Percentage error [%] 6.79 7.08 6.77 6.98 6.97

C2

Bits with errors 1582/78 1489/78 1546/78 1534/78 1602/78

Percentage error [%] 10.14 9.54 9.91 9.83 10.27

3

Probabilitatea de eroare 0.1 si 500 rulari/simulare

Simulare Grupa

1 2 3 4 5

C1A

Bits with errors 1580/50 1631/50 1573/50 1570/50 1629/50

Percentage error [%] 6.32 6.52 6.29 6.28 6.52

C1B

Bits with errors 4710/132 4782/132 4752/132 4832/132 4559/132

Percentage error [%] 7.14 7.25 7.2 7.32 6.91

C2

Bits with errors 3992/78 3899/78 3904/78 3898/78 3879/98

Percentage error [%] 10.24 10 10.01 9.99 9.95

C1A

Nr. simulare 1 2 3 4 5 media

1 14 0 0 12 0 5.2

2 5 4 27 2 1 7.8

5 7.2 6 8 0.8 5.6 5.52

10 2.2 11 7.2 7.6 8.6 7.32

20 8 5.8 6.3 3.6 9.2 6.58

50 9.36 4.95 7.8 7.96 5.8 7.174

100 6.78 8.28 5.88 4.7 6.64 6.456

200 7.73 7.56 7.37 6.27 7.14 7.214

500 6.32 6.52 6.29 6.28 6.52 6.386

0

1

2

3

4

5

6

7

8

9

0 100 200 300 400 500 600

C1A

4

C1B

Nr. simulare 1 2 3 4 5 media

1 1.52 3 18.18 6.82 0 5.904

2 6.82 10.98 8.71 1.52 11.36 7.878

5 3.18 6.21 7.88 9.7 10.15 7.424

10 7.58 8.79 7.95 10.91 10.15 9.076

20 7.46 9.77 7.95 5.83 5.8 7.362

50 7.02 5.85 6.82 7.98 6.42 6.818

100 6.98 7.23 6.32 6.66 6.58 6.754

200 6.79 7.08 6.77 6.98 6.97 6.918

500 7.14 7.25 7.2 7.32 6.91 7.164

C2

Nr. simulare 1 2 3 4 5 media

1 10.26 8.97 8.98 7.69 3.85 7.95

2 9.62 19.23 10.26 11.54 8.97 11.924

5 10.78 14.36 8.46 8.21 10.51 10.464

10 8.85 8.85 10.9 9.49 9.36 9.49

20 10.51 9.23 10.64 10.06 8.46 9.78

50 10.26 10.38 9.74 9 9.92 9.86

100 9.5 9.74 10.47 9.5 9.79 9.8

200 10.14 9.54 9.91 9.83 10.27 9.938

500 10.24 10 10.01 9.99 9.95 10.038

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300 400 500 600

C1B

5

General

Nr. of runs C1A C1B C2

1 5.2 5.904 7.95

2 7.8 7.878 11.924

5 5.52 7.424 10.464

10 7.32 9.076 9.49

20 6.58 7.362 9.78

50 7.174 6.818 9.86

100 6.456 6.754 9.8

200 7.214 6.918 9.938

500 6.386 7.164 10.038

3.3 500 rulari/simulare

Probabilitate 0.01 0.02 0.03 0.05 0.07 0.09

C1A Bits with errors 0/50 1/50 8/50 106/50 373/50 1160/50

Percentage error [%] 0 0 0.3 0.42 1.49 4.64

C1B Bits with errors 4/132 7/132 48/132 195/132 1179/132 3334/132

Percentage error [%] 0.01 0.01 0.07 0.3 1.79 5.05

C2 Bits with errors 376/78 780/78 1174/78 1923/78 2764/78 3460/78

Percentage error [%] 0.96 2 3.01 4.93 7.09 8.87

Probabilitate 0.1 0.15 0.2 0.3 0.5

C1A Bits with errors 1687/50 5294/50 8205/50 11141/50 12624/50

Percentage error [%] 6.75 21.18 32.82 44.56 50.5

C1B Bits with errors 4579/132 14789/132 22556/132 29805 32914/132

Percentage error [%] 6.94 22.4 34.18 45.16 49.87

C2 Bits with errors 3964/78 5822/78 7699/78 11661/78 19470/78

Percentage error [%] 10.16 14.93 19.74 29.9 49.92

0

2

4

6

8

10

12

14

0 100 200 300 400 500 600

C1A C1B C2

6

Pe 0.01 0.02 0.03 0.05 0.07 0.09 0.1 0.15 0.2 0.3 0.5

C1A 0 0 0.3 0.42 1.49 4.64 6.75 21.18 32.82 44.56 50.5

C1B 0.01 0.01 0.07 0.3 1.79 5.05 6.94 22.4 34.18 45.16 49.87

C2 0.96 2 3.01 4.93 7.09 8.87 10.16 14.93 19.74 29.9 49.92

3.5 500 rulari/simulare, all ones

Probabilitate 0.01 0.0.2 0.05 0.1 0.2 0.5

Erori canal Bits with errors 4/378 7/378 19/378 37/378 75/378 189/378

Percentage error [%] 1.06 1.85 5.03 9.79 19.84 50

Erori decodor Bits with errors 0/189 0/189 0/189 12/189 63/189 92/189

Percentage error [%] 0 0 0 6.25 33.33 48.68

3.5 Eroare la fiecare 2/4/8 biti

Eroare la fiecare 2 4 8

Erori canal Bits with errors 189/378 95/378 48/378

Percentage error [%] 50 25.13 12.7

Erori decodor Bits with errors 132/189 54/189 0/189

Percentage error [%] 69.84 28.57 0

3.5 Erori in rafale

Burst errors

Simulari : P(birth)=0.1 P(death)=0.9

P(birth)=0.1 P(death)=0.1

P(birth)=0.9 P(death)=0.1

Erori canal

Bits with errors 37/278 185/378 340/378

Percentage error [%]

9.79 48.94 89.95

Erori decodor

Bits with errors 12/189 46/189 69/189

Percentage error [%]

6.35 24.34 36.51

-10

0

10

20

30

40

50

60

0 0.1 0.2 0.3 0.4 0.5 0.6

C1A C1B C2

7

3.6 5 simulari, 1rulare/simulare, all ones

P=0.01 1 2 3 4 5

Erori canal Bits with errors 7/378 1/378 6/378 3/378 7/378

Percentage error [%] 1.85 0.26 1.59 0.79 1.85

Erori decodor Bits with errors 0/189 0/189 0/189 0/189 0/189

Percentage error [%] 0 0 0 0 0

P=0.02 1 2 3 4 5

Erori canal Bits with errors 4/378 10/378 11/378 6/378 10/378

Percentage error [%] 1.06 2.65 2.91 1.59 2.65

Erori decodor Bits with errors 0/189 0/189 0/189 0/189 0/189

Percentage error [%] 0 0 0 0 0

P=0.05 1 2 3 4 5

Erori canal Bits with errors 14/378 25/378 21/378 10/378 20/378

Percentage error [%] 3.7 6.61 5.56 2.65 5.29

Erori decodor Bits with errors 0/189 7/189 0/189 0/189 0/189

Percentage error [%] 0 3.7 0 0 0

P=0.1 1 2 3 4 5

Erori canal Bits with errors 39/378 32/378 43/378 34/378 32/378

Percentage error [%] 10.32 8.48 11.38 8.99 8.47

Erori decodor Bits with errors 8/189 7/189 12/189 16/189 7/189

Percentage error [%] 4.23 3.7 6.35 8.47 3.7

P=0.2 1 2 3 4 5

Erori canal Bits with errors 78/378 96/378 79/378 59/378 76/378

Percentage error [%] 20.63 25.4 20.9 15.61 20.11

Erori decodor Bits with errors 77/189 89/189 57/189 41/389 64/389

Percentage error [%] 40.74 47.09 30.16 21.69 33.86

P=0.5 1 2 3 4 5

Erori canal Bits with errors 191/378 193/378 181/378 168/378 199/378

Percentage error [%] 50.53 51.06 47.88 44.44 52.65

Erori decodor Bits with errors 82/189 86/189 94/189 97/189 100/189

Percentage error [%] 43.39 45.5 49.74 51.32 52.91

Nr. simulare 1 2 3 4 5

P=0.1 1.85 0.26 1.59 0.79 1.85

P=0.02 1.06 2.65 2.91 1.59 2.65

P=0.05 3.7 6.61 5.56 2.65 5.29

P=0.1 10.32 8.48 11.38 8.99 8.47

P=0.2 20.63 25.4 20.9 15.61 20.11

P=0.5 50.53 51.06 47.88 44.44 52.65

8

Eroare la fiecare 2 4 8

Erori canal Bits with errors 189/378 95/378 48/378

Percentage error [%] 50 25.13 12.7

Erori decodor Bits with errors 132/189 55/189 0/189

Percentage error [%] 69.84 29.63 0

3.7 probabilitate de eroare n x 0.01, numar de rulari 500, biti generati aleator

Probabilitate: 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Erori canal

Bits with errors 3/378 6/378 11/378 14/378 18/378 22/378 26/378

Percentage error [%] 0.79 1.59 2.91 3.7 4.76 5.82 6.88

Erori decodor

Bits with errors 0/189 0/189 0/189 0/189 0/189 1/189 3/189

Percentage error [%] 0 0 0 0 0 0.53 1.59

Probabilitate: 0.08 0.09 0.1 0.11 0.12 0.13

Erori canal

Bits with errors 29/378 34/378 37/378 41/378 45/378 49/378

Percentage error [%] 7.67 8.99 9.79 10.85 11.9 12.96

Erori decodor

Bits with errors 5/189 8/189 12/189 17/189 23/189 28/189

Percentage error [%] 2.65 4.23 6.38 8.99 12.17 14.81

Pe 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13

Pi% 0.79 1.59 2.91 3.7 4.76 5.82 6.88 7.67 8.99 9.79 10.85 11.9 12.96

Po% 0 0 0 0 0 0.53 1.59 2.65 4.23 6.38 8.99 12.17 14.81

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7

Serie1 Serie2 Serie3 Serie4 Serie5

9

3.8 5 simulari pentru erori in rafale, 1 rulare/simulare, all ones

Burst errors Simulari : 1 2 3 4 5

P(birth)=0.1 P(death)=0.9

Erori canal

Bits with errors 34/378 38/378 46/378 24/378 44/378

Percentage error [%] 8.99 10.05 12.17 6.35 11.64

Erori decodor

Bits with errors 19/189 4/189 11/189 1/189 23/189

Percentage error [%] 10.05 2.12 5.82 0.53 12.17

Burst errors Simulari : 1 2 3 4 5

P(birth)=0.1 P(death)=0.1

Erori canal

Bits with errors 166/378 233/378 165/378 179/378 157/378

Percentage error [%] 43.92 61.64 43.35 47.35 41.53

Erori decodor

Bits with errors 41/189 49/189 48/189 50/189 48/189

Percentage error [%] 21.69 25.93 25.4 26.46 25.4

Burst errors Simulari : 1 2 3 4 5

P(birth)=0.9 P(death)=0.1

Erori canal

Bits with errors 341/378 341/378 332/378 338/378 335/378

Percentage error [%] 20.21 30.21 87.83 89.42 81.62

Erori decodor

Bits with errors 68/189 69/189 71/189 69/189 65/189

Percentage error [%] 35.98 36.81 37.57 36.51 34.39

1.1 Strategia FEC aplicata asupra datelor inainte de transmisie semnalului vocal i se adauga un crc inainte de fec

pentru o mai buna detectie a erorii. turbo codurile sunt utilizate in sistemele celulare din generatia a treia

precum UMTS sub denumirea de WCDMA. Secventa de informatie este codata de doua ori, avand un

interleaver intre cele doua coduri. Rolul acestuia este de a asigura independenta secventelor de biti provenite

de la cele doua codoare. la decodare se utilizeaza doua decodoare rsc.

1.2 Deoarece in cadrul acestor tipuri de erori, bitii nu sunt independenti, erorile sunt corelate intre ele, iar

detectia si corectia lor este mult mai dificila decat in cazul erorilor singulare. astfel, blocul de sondaj si decizie

din cadrul decodorului poate interpreta gresit secventele primite, rata de eroare fiind mai mare

-2

0

2

4

6

8

10

12

14

16

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Pi% Po%